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Permutation
Terms modified by Permutation Selected AbstractsTopoisomerase 2, plays a pivotal role in the tumor biology of stage IV thymic neoplasiaCANCER, Issue 3 2007J. M. Liu MD Abstract BACKGROUND. Microsatellite studies in histologic types B3 and C thymic neoplasia detected gains on chromosome 17q, which contains the Her-2/neu and its juxtaposed topoisomerase 2, (T2,) genes. The study aimed to evaluate their impact on tumor biology and survival of advanced thymic neoplasia patients. METHODS. From 1991 to 2005, 36 consecutive stage IV thymic carcinoma patients were treated, 18 men and 18 women, aged 11 to 84 years. There were 22 thymic carcinoma, 13 type B3, and 1 type B2 thymoma. Patients received treatment consisting of surgical resection, combination chemotherapy with the CAP (cyclophosphamide, Adriamycin, cisplatin) regimen, or radiation therapy potentiated by high-dose weekly 5-fluorouracil infusion. Permutations of these 3 treatment modalities were prescribed as necessary. RESULTS. T2, gene amplification was detected in 4 of 14 thymic carcinoma and 1 of 15 type B3 thymoma. Three thymic carcinoma patients had Her-2/neu coamplification and these 3 patients had rapidly growing tumor and extensive disease at initial diagnosis. CAP was prescribed in 28 patients and 20 patients responded (response rate, 71.4%, 95% confidence interval [CI]: 52.8% to 85%); all responders overexpressed (,10% nuclei positive) the T2, protein, whereas 4 nonresponders had very low expression. T2, overexpression predicts CAP response, and its absence predicts resistance (P = .001). Overall survival was significantly prolonged if the tumor was resectable (P = .001), of type B3 histology (P = .0039), and had no Her-2 gene amplification (P = .0081). CONCLUSION. T2, and Her-2/neu genes play a pivotal role in the tumor biology, CAP response, and survival of advanced thymic neoplasia patients. Cancer 2007;109:502,509. © 2006 American Cancer Society. [source] BROKERAGE QUALIFICATIONS IN RINGING OPERATIONS,CRIMINOLOGY, Issue 1 2008CARLO MORSELLI Brokers are fundamental for maintaining flexibility in the networks that embed criminal activities. Our study aims at offering more precision on this key issue by examining the impact that brokers may have on crime-commission processes. To do so, we analyze two stolen-vehicle exportation (or ringing) operations within a framework that merges crime-script analysis and social-network analysis. We assess how diverse degrees of brokerage are distributed across the ringing operations and how the removal of key brokers would have had a disruptive impact by reducing the scope of alternatives for crime-script permutation and flexibility. [source] White-rot fungi combined with lignite granules and lignitic xylite to decolorize textile industry wastewaterENGINEERING IN LIFE SCIENCES (ELECTRONIC), Issue 1 2010Ulrike Böhmer Abstract The feasibility of using immobilized fungi to decolorize textile industry wastewater containing dyes was examined in experiments with: two species of white-rot fungi (a Marasmius species from Indonesia, which produces copious biomass, and Trametes hirsuta, which produces high levels of laccase); two types of lignite products as adsorbents and solid substrates (lignitic xylite and lignite granules); and four simulated wastewaters, each containing a different kinds of reactive textile azo dye. The growth, extracellular enzyme production, dye degradation and dye absorption parameters afforded by each permutation of fungus, substrate and dye were then measured. Both fungal species grew poorly on xylite, but much better on lignite granules. Marasmius sp. produced up to 67,U/L laccase on lignite granules, but just 10,U/L on xylite, and no other detectable extracellular enzymes. T. hirsuta produced 1343,U/L laccase and up to 12,U/L unspecific peroxidase when immobilized on lignite granules, and 898,U/L laccase with 14,U/L unspecific peroxidase when immobilized on xylite. The amount of color lost from the dye solutions depended on both the type of dye and the enzyme levels in the fermenter. [source] Converting Core Compounds into Building Blocks: The Concept of Regiochemically Exhaustive FunctionalizationEUROPEAN JOURNAL OF ORGANIC CHEMISTRY, Issue 10 2005Elena Marzi Abstract In a model study, 3-fluorophenol and 3-fluoropyridine were converted into the each time four possible carboxylic acids by passing through the corresponding organometallic intermediates. As an attempt to generalize the findings reveals, a restricted set of principles and methods suffices to cope with all standard scenarios. The most valuable and versatile tools for the regiochemically exhaustive functionalization of a great variety of substrate patterns are the optionally site-selective metalation (either by reagent/substrate matching or by peripheral coordination control), the use of activating or congesting protective groups and the basicity gradient-driven heavy halogen migration (followed by halogen/metal permutation). (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005) [source] Buttressing Effects Rerouting the Deprotonation and Functionalization of 1,3-Dichloro- and 1,3-DibromobenzeneEUROPEAN JOURNAL OF ORGANIC CHEMISTRY, Issue 23 2003Christophe Heiss Abstract A systematic comparison between 1,3-difluorobenzene, 1,3-dichlorobenzene, and 1,3-dibromobenzene did not reveal major differences in their behavior towards strong bases such as lithium diisopropylamide or lithium 2,2,6,6-tetramethylpiperidide. Thus, all 2,6-dihalobenzoic acids 1 are directly accessible by consecutive treatment with a suitable base and dry ice. In contrast, (2,6-dichlorophenyl)- and (2,6-bromophenyl)triethylsilane (2a and 2b) were found to undergo deprotonation at the 5-position (affording acids 3 and, after deprotection, 4), whereas the 1,3-difluoro analog is known to react at the 4-position. The 2,4-dihalobenzoic acids 7 were selectively prepared from either the silanes 2 (by bromination at the 4-position, metalation and carboxylation of the neighboring position, followed by desilylation and debromination) or the 1,3-dihalo-2-iodobenzenes 8 (by base-promoted migration of iodine to the 4-position followed by iodine/magnesium permutation and subsequent carboxylation). (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003) [source] Analysis of single-locus tests to detect gene/disease associations,GENETIC EPIDEMIOLOGY, Issue 3 2005Kathryn Roeder Abstract A goal of association analysis is to determine whether variation in a particular candidate region or gene is associated with liability to complex disease. To evaluate such candidates, ubiquitous Single Nucleotide Polymorphisms (SNPs) are useful. It is critical, however, to select a set of SNPs that are in substantial linkage disequilibrium (LD) with all other polymorphisms in the region. Whether there is an ideal statistical framework to test such a set of ,tag SNPs' for association is unknown. Compared to tests for association based on frequencies of haplotypes, recent evidence suggests tests for association based on linear combinations of the tag SNPs (Hotelling T2 test) are more powerful. Following this logical progression, we wondered if single-locus tests would prove generally more powerful than the regression-based tests? We answer this question by investigating four inferential procedures: the maximum of a series of test statistics corrected for multiple testing by the Bonferroni procedure, TB, or by permutation of case-control status, TP; a procedure that tests the maximum of a smoothed curve fitted to the series of of test statistics, TS; and the Hotelling T2 procedure, which we call TR. These procedures are evaluated by simulating data like that from human populations, including realistic levels of LD and realistic effects of alleles conferring liability to disease. We find that power depends on the correlation structure of SNPs within a gene, the density of tag SNPs, and the placement of the liability allele. The clearest pattern emerges between power and the number of SNPs selected. When a large fraction of the SNPs within a gene are tested, and multiple SNPs are highly correlated with the liability allele, TS has better power. Using a SNP selection scheme that optimizes power but also requires a substantial number of SNPs to be genotyped (roughly 10,20 SNPs per gene), power of TP is generally superior to that for the other procedures, including TR. Finally, when a SNP selection procedure that targets a minimal number of SNPs per gene is applied, the average performances of TP and TR are indistinguishable. Genet. Epidemiol. © 2005 Wiley-Liss, Inc. [source] Competitive Hebbian learning and the hippocampal place cell system: Modeling the interaction of visual and path integration cuesHIPPOCAMPUS, Issue 3 2001Alex Guazzelli Abstract The hippocampus has long been thought essential for implementing a cognitive map of the environment. However, almost 30 years since place cells were found in rodent hippocampal field CA1, it is still unclear how such an allocentric representation arises from an egocentrically perceived world. By means of a competitive Hebbian learning rule responsible for coding visual and path integration cues, our model is able to explain the diversity of place cell responses observed in a large set of electrophysiological experiments with a single fixed set of parameters. Experiments included changes observed in place fields due to exploration of a new environment, darkness, retrosplenial cortex inactivation, and removal, rotation, and permutation of landmarks. To code for visual cues for each landmark, we defined two perceptual schemas representing landmark bearing and distance information over a linear array of cells. The information conveyed by the perceptual schemas is further processed through a network of adaptive layers which ultimately modulate the resulting activity of our simulated place cells. In path integration terms, our system is able to dynamically remap a bump of activity coding for the displacement of the animal in relation to an environmental anchor. We hypothesize that path integration information is computed in the rodent posterior parietal cortex and conveyed to the hippocampus where, together with visual information, it modulates place cell activity. The resulting network yields a more direct treatment of partial remapping of place fields than other models. In so doing, it makes new predictions regarding the nature of the interaction between visual and path integration cues during new learning and when the system is challenged with environmental changes. Hippocampus 2001;11:216,239. © 2001 Wiley-Liss, Inc. [source] Permutation tests for factorially designed neuroimaging experimentsHUMAN BRAIN MAPPING, Issue 3 2004John Suckling Abstract Permutation methods for analysis of functional neuroimaging data acquired as factorially designed experiments are described and validated. The F ratio was estimated for main effects and interactions at each voxel in standard space. Critical values corresponding to probability thresholds were derived from a null distribution sampled by appropriate permutation of observations. Spatially informed, cluster-level test statistics were generated by applying a preliminary probability threshold to the voxel F maps and then computing the sum of voxel statistics in each of the resulting three-dimensional clusters, i.e., cluster "mass." Using simulations comprising two between- or within-subject factors each with two or three levels, contaminated by Gaussian and non-normal noise, the voxel-wise permutation test was compared to the standard parametric F test and to the performance of the spatially informed statistic using receiver operating characteristic (ROC) curves. Validity of the permutation-testing algorithm and software is endorsed by almost identical performance of parametric and permutation tests of the voxel-level F statistic. Permutation testing of suprathreshold voxel cluster mass, however, was found to provide consistently superior sensitivity to detect simulated signals than either of the voxel-level tests. The methods are also illustrated by application to an experimental dataset designed to investigate effects of antidepressant drug treatment on brain activation by implicit sad facial affect perception in patients with major depression. Antidepressant drug effects in left amygdala and ventral striatum were detected by this software for an interaction between time (within-subject factor) and group (between-subject factor) in a representative two-way factorial design. Hum. Brain Mapping 22:193,205, 2004. © 2004 Wiley-Liss, Inc. [source] IL23R haplotypes provide a large population attributable risk for Crohn's diseaseINFLAMMATORY BOWEL DISEASES, Issue 9 2008Kent D. Taylor PhD Abstract Background: The IL-23 pathway plays a pivotal role in the development of chronic mucosal inflammation seen in the inflammatory bowel diseases. Multiple studies have now established the contribution of the interleukin 23 receptor gene (IL23R) to Crohn's disease (CD) risk in general and of the IL23R R381Q variant in particular. The aim of this work was to estimate the total contribution of this gene to CD risk test using a haplotype approach. Methods: In all, 763 CD subjects and 254 controls were genotyped for single nucleotide polymorphisms in the IL23R gene using Illumina and ABI methods. Haplotypes were assigned using PHASEv2 and tested for association with CD by chi-square and permutation. Results: Haplotypes with both increased and decreased risk for CD were observed in 2 of the 4 observed blocks (Block 2 H1: 55.4% control, 64% CD, P = 0.019; H2: 64.5% control, 54.4% CD, P = 0.006; Block 3 H1: 55.8% control, 64.4% CD, P = 0.013; H2: 47.0% control, 36.6% CD, P = 0.001). The population attributable risk for these haplotypes was substantially larger than that estimated for the IL23R R381Q variant (Block 2 H1 and block 3 H1 ,20%, compared with ,4% for Block 3 H6, containing the variant). Conclusions: These observations suggest that IL23R makes a substantial contribution to CD susceptibility, larger than that estimated from the population frequency of the R381Q variant. These observations also support the expectation that finding "hits" from genomewide association studies will be but an important chapter in the story of unraveling the genetic contribution to CD, rather than the final chapter that brings clarity to all the plot twists of a complicated story. (Inflamm Bowel Dis 2008) [source] Surgical correction of scoliosis: Numerical analysis and optimization of the procedureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2010J. F. Aguilar Madeira Abstract A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ,, n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed. Copyright © 2010 John Wiley & Sons, Ltd. [source] Not everything is everywhere: the distance decay of similarity in a marine host,parasite systemJOURNAL OF BIOGEOGRAPHY, Issue 2 2009Ana Pérez-del-Olmo Abstract Aim, We test the similarity,distance decay hypothesis on a marine host,parasite system, inferring the relationships from abundance data gathered at the lowest scale of parasite community organization (i.e. that of the individual host). Location, Twenty-two seasonal samples of the bogue Boops boops (Teleostei: Sparidae) were collected at seven localities along a coastal positional gradient from the northern North-East Atlantic to the northern Mediterranean coast of Spain. Methods, We used our own, taxonomically consistent, data on parasite communities. The variations in parasite composition and structure with geographical and regional distance were examined at two spatial scales, namely local parasite faunas and component communities, using both presence,absence (neighbour joining distance) and abundance (Mahalanobis distance) data. The influence of geographical and regional distance on faunal/community divergence was assessed through the permutation of distance matrices. Results, Our results revealed that: (1) geographical and regional distances do not affect the species composition in the system under study at the higher scales; (2) geographical distance between localities contributes significantly to the decay of similarity estimated from parasite abundance at the lowest scale (i.e. the individual host); (3) the structured spatial patterns are consistent in time but not across seasons; and (4) a restricted clade of species (the ,core' species of the bogue parasite fauna) contributes substantially to the observed patterns of both community homogenization and differentiation owing to the strong relationship between local abundance and regional distribution of species. Main conclusions, The main factors that tend to homogenize the composition of parasite communities of bogue at higher regional scales are related to the dispersal of parasite colonizers across host populations, which we denote as horizontal neighbourhood colonization. In contrast, the spatial structure detectable in quantitative comparisons only, is related to a vertical neighbourhood colonization associated with larval dispersal on a local level. The stronger decline with distance in the spatial synchrony of the assemblages of the ,core' species indicates a close-echoing environmental synchrony that declines with distance. Our results emphasize the importance of the parasite supracommunity (i.e. parasites that exploit all hosts in the ecosystem) to the decay of similarity with distance. [source] Non-parametric permutation test for the discrimination of float glass samples based on LIBS spectraJOURNAL OF CHEMOMETRICS, Issue 6 2010Erin McIntee Abstract Laser-induced breakdown spectroscopy (LIBS) coupled with non-parametric permutation based hypothesis testing is demonstrated to have good performance in discriminating float glass samples. This type of pairwise sample comparison is important in manufacturing process quality control, forensic science and other applications where determination of a match probability between two samples is required. Analysis of the pairwise comparisons between multiple LIBS spectra from a single glass sample shows that some assumptions required by parametric methods may not hold in practice, motivating the adoption of a non-parametric permutation test. Without rigid distributional assumptions, the permutation test exhibits excellent discriminating power while holding the actual size of Type I error at the nominal level. Copyright © 2010 John Wiley & Sons, Ltd. [source] A diagonal measure and a local distance matrix to display relations between objects and variables,JOURNAL OF CHEMOMETRICS, Issue 1 2010Gergely Tóth Abstract Proper permutation of data matrix rows and columns may result in plots showing striking information on the objects and variables under investigation. To control the permutation first, a diagonal matrix measureD was defined expressing the size relations of the matrix elements. D is essentially the absolute norm of a matrix where the matrix elements are weighted by their distance to the matrix diagonal. Changing the order of rows and columns increases or decreases D. Monte Carlo technique was used to achieve maximum D in the case of the object distance matrix or even minimal D in the case of the variable correlation matrix to get similar objects or variables close together. Secondly, a local distance matrix was defined, where an element reflects the distances of neighboring objects in a limited subspace of the variables. Due to the maximization of D in the local distance matrix by row and column changes of the original data matrix, the similar objects were arranged close to each other and simultaneously the variables responsible for their similarity were collected close to the diagonal part defined by these objects. This combination of the diagonal measure and the local distance matrix seems to be an efficient tool in the exploration of hidden similarities of a data matrix. Copyright © 2009 John Wiley & Sons, Ltd. [source] Design of granule structure: Computational methods and experimental realizationAICHE JOURNAL, Issue 11 2006Mansoor A. Ansari Abstract The spatial distribution of solid components and porosity within a composite granule,its microstructure,is an important attribute as it carries information about the processing history of the granule and determines its end-use application properties, particularly the dissolution rate. In this work, the problem of rational design of granule structure is formulated, and two methods for its solution are proposed,stochastic design, which is based on random permutation of points within the structure using the simulated annealing algorithm, and variational design, which is based on direct simulation of granule formation from its constituent primary particles, followed by direct simulation of granule dissolution. The variational design method is demonstrated in a case study of the effect of primary particle size, radial distribution of components, and composition of a two-component granule (active, excipient) on the dissolution profile. Selected granule structures designed computationally were also physically made by fluid-bed granulation, their structure analyzed by X-ray micro-tomography, and dissolution curves measured. It was confirmed that the designed structures are feasible to manufacture and that they meet the required dissolution profiles. © 2006 American Institute of Chemical Engineers AIChE J, 2006 [source] The effect of genetic and environmental variation on metabolic gene expressionMOLECULAR ECOLOGY, Issue 13 2009CINDA P. SCOTT Abstract What is the relationship between genetic or environmental variation and the variation in messenger RNA (mRNA) expression? To address this, microarrays were used to examine the effect of genetic and environmental variation on cardiac mRNA expression for metabolic genes in three groups of Fundulus heteroclitus: (i) individuals sampled in the field (field), (ii) field individuals acclimated for 6 months to laboratory conditions (acclimated), or (iii) individuals bred for 10 successive generations in a laboratory environment (G10). The G10 individuals have significantly less genetic variation than individuals obtained in the field and had a significantly lower variation in mRNA expression across all genes in comparison to the other two groups (P = 0.001). When examining the gene specific variation, 22 genes had variation in expression that was significantly different among groups with lower variation in G10 individuals than in acclimated individuals. Additionally, there were fewer genes with significant differences in expression among G10 individuals vs. either acclimated or field individuals: 66 genes have statistically different levels of expression vs. 107 or 97 for acclimated or field groups. Based on the permutation of the data, these differences in the number of genes with significant differences among individuals within a group are unlikely to occur by chance (P < 0.01). Surprisingly, variation in mRNA expression in field individuals is lower than in acclimated individuals. Relative to the variation among individual within a group, few genes have significant differences in expression among groups (seven, 2.3%) and none of these are different between acclimated and field individuals. The results support the concept that genetic variation affects variation in mRNA expression and also suggests that temporal environmental variation associated with estuarine environments does not increase the variation among individuals or add to the differences among groups. [source] Distinguished vertices in probabilistic rooted graphsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2010Gary Gordon Abstract The expected number of vertices that remain joined to the root vertex s of a rooted graph Gs when edges are prone to fail is a polynomial EV(Gs; p) in the edge probability p that depends on the location of s. We show that optimal locations for the root can vary arbitrarily as p varies from 0 to 1 by constructing a graph in which every permutation of k -specified vertices is the "optimal" ordering for some p, 0 < p < 1. We also investigate zeroes of EV(Gs; p), proving that the number of vertices of G is bounded by the size of the largest rational zero. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010 [source] Minimizing the cost of placing and sizing wavelength division multiplexing and optical crossconnect equipment in a telecommunications networkNETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2005Belén Melián Abstract Cost reduction is a major concern when designing optical fiber networks. Multiwavelength optical devices are new technology for increasing the capacity of fiber networks while reducing costs, when compared to installing traditional (e.g., SONET) equipment and new fiber. In this article we discuss the development of a metaheuristic method that seeks to optimize the location of Wavelength Division Multiplexing (WDM) and Optical Crossconnect (OXC) equipment in fiber networks. The procedure combines ideas from the scatter search, tabu search, and multistart methodologies. Computational experiments with both real-world and artificial data show the effectiveness of the proposed procedure. The experiments include a comparison with a permutation-based approach and with lower bounds generated with CPLEX. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(4), 199,209 2005 [source] Isomorphisms of the De Bruijn digraph and free-space optical networksNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2002D. Coudert Abstract The de Bruijn digraph B(d, D) has degree d, diameter D, dD vertices, and dD+1 arcs. It is usually defined by words of size D on an alphabet of cardinality d, through a cyclic left-shift permutation on the words, after which the rightmost symbol is changed. In this paper, we show that any digraph defined on words of a given size, through an arbitrary permutation on the alphabet and an arbitrary permutation on the word indices, is isomorphic to the de Bruijn digraph, provided that this latter permutation is cyclic. We use this result to improve from O(dD+1) to the number of lenses required for the implementation of B(d, D) by the Optical Transpose Interconnection System proposed by Marsden et al. [Opt Lett 18 (1993), 1083,1085]. © 2002 Wiley Periodicals, Inc. [source] Fast permutation routing in a class of interconnection networksNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2002Ehab S. Elmallah Abstract This paper considers the following permutation routing problem: Given an N × N augmented data manipulator (ADM) network and a permutation , between its N inputs and outputs, can all the traffic connections of , be routed through the network in one pass? A number of backtrack search algorithms have been devised for recognizing ADM admissible permutations. None of the published results, however, appears to settle the time complexity of the problem. The goal of this paper was to answer the question positively by showing the first polynomial time bound for solving the problem. The devised algorithm requires O(N1.695) time to decide whether a given permutation , is admissible and compute a setting of the switches whenever , is admissible. For many practical applications, the obtained bound compares favorably with the O(N lg N) size of an N -input ADM network. © 2002 Wiley Periodicals, Inc. [source] A multilevel Crout ILU preconditioner with pivoting and row permutationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2007Jan MayerArticle first published online: 4 SEP 200 Abstract In this paper, we present a new incomplete LU factorization using pivoting by columns and row permutation. Pivoting by columns helps to avoid small pivots and row permutation is used to promote sparsity. This factorization is used in a multilevel framework as a preconditioner for iterative methods for solving sparse linear systems. In most multilevel incomplete ILU factorization preconditioners, preprocessing (scaling and permutation of rows and columns of the coefficient matrix) results in further improvements. Numerical results illustrate that these preconditioners are suitable for a wide variety of applications. Copyright © 2007 John Wiley & Sons, Ltd. [source] Multiplicative congruential generators, their lattice structure, its relation to lattice,sublattice transformations and applications in crystallographyACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009Wolfgang Hornfeck An analysis of certain types of multiplicative congruential generators , otherwise known for their application to the sequential generation of pseudo-random numbers , reveals their relation to the coordinate description of lattice points in two-dimensional primitive sublattices. Taking the index of the lattice,sublattice transformation as the modulus of the multiplicative congruential generator, there are special choices for its multiplier which induce a symmetry-preserving permutation of lattice-point coordinates. From an analysis of similar sublattices with hexagonal and square symmetry it is conjectured that the cycle structure of the permutation has its crystallographic counterpart in the description of crystallographic orbits. Some applications of multiplicative congruential generators in structural chemistry and biology are discussed. [source] The S2 subsites of cathepsins K and L and their contribution to collagen degradationPROTEIN SCIENCE, Issue 4 2007Fabien Lecaille Abstract The exchange of residues 67 and 205 of the S2 pocket of human cysteine cathepsins K and L induces a permutation of their substrate specificity toward fluorogenic peptide substrates. While the cathepsin L-like cathepsin K (Tyr67Leu/Leu205Ala) mutant has a marked preference for Phe, the Leu67Tyr/Ala205Leu cathepsin L variant shows an effective cathepsin K-like preference for Leu and Pro. A similar turnaround of inhibition was observed by using specific inhibitors of cathepsin K [1-(N -Benzyloxycarbonyl-leucyl)-5-(N -Boc-phenylalanyl-leucyl)carbohydrazide] and cathepsin L [N -(4-biphenylacetyl)- S -methylcysteine-(D)-Arg-Phe-,-phenethylamide]. Molecular modeling studies indicated that mutations alter the character of both S2 and S3 subsites, while docking calculations were consistent with kinetics data. The cathepsin K-like cathepsin L was unable to mimic the collagen-degrading activity of cathepsin K against collagens I and II, DQ-collagens I and IV, and elastin-Congo Red. In summary, double mutations of the S2 pocket of cathepsins K (Y67L/L205A) and L (L67Y/A205L) induce a switch of their enzymatic specificity toward small selective inhibitors and peptidyl substrates, confirming the key role of residues 67 and 205. However, mutations in the S2 subsite pocket of cathepsin L alone without engineering of binding sites to chondroitin sulfate are not sufficient to generate a cathepsin K-like collagenase, emphasizing the pivotal role of the complex formation between glycosaminoglycans and cathepsin K for its unique collagenolytic activity. [source] Alteration of the disulfide-coupled folding pathway of BPTI by circular permutationPROTEIN SCIENCE, Issue 5 2004Grzegorz Bulaj BPTI, bovine pancreatic trypsin inhibitor; cBPTI, a circular form of BPTI generated by forming a peptide bond between the natural termini; cpBPTI, circularly permuted BPTI. Abstract The kinetics of disulfide-coupled folding and unfolding of four circularly permuted forms of bovine pancreatic trypsin inhibitor (BPTI) were studied and compared with previously published results for both wild-type BPTI and a cyclized form. Each of the permuted proteins was found to be less stable than either the wild-type or circular proteins, by 3,8 kcal/mole. These stability differences were used to estimate effective concentrations of the chain termini in the native proteins, which were 1 mM for the wild-type protein and 2.5 to 4000 M for the permuted forms. The circular permutations increased the rates of unfolding and caused a variety of effects on the kinetics of refolding. For two of the proteins, the rates of a direct disulfide-formation pathway were dramatically increased, making this process as fast or faster than the competing disulfide rearrangement mechanism that predominates in the folding of the wild-type protein. These two permutations break the covalent connectivity among the ,-strands of the native protein, and removal of these constraints appears to facilitate direct formation and reduction of nearby disulfides that are buried in the folded structure. The effects on folding kinetics and mechanism do not appear to be correlated with relative contact order, a measure of overall topological complexity. These observations are consistent with the results of other recent experimental and computational studies suggesting that circular permutation may generally influence folding mechanisms by favoring or disfavoring specific interactions that promote alternative pathways, rather than through effects on the overall topology of the native protein. [source] ReSASC: A resampling-based algorithm to determine differential protein expression from spectral count dataPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 6 2010Kristina M. Little Abstract Label-free methods for MS/MS quantification of protein expression are becoming more prevalent as instrument sensitivity increases. Spectral counts (SCs) are commonly used, readily obtained, and increase linearly with protein abundance; however, a statistical framework has been lacking. To accommodate the highly non-normal distribution of SCs, we developed ReSASC (resampling-based significance analysis for spectral counts), which evaluates differential expression between two conditions by pooling similarly expressed proteins and sampling from this pool to create permutation-based synthetic sets of SCs for each protein. At a set confidence level and corresponding p -value cutoff, ReSASC defines a new p -value, p,, as the number of synthetic SC sets with p>pcutoff divided by the total number of sets. We have applied ReSASC to two published SC data sets and found that ReSASC compares favorably with existing methods while being easy to operate and requiring only standard computing resources. [source] Inferring Haplotype/Disease Association by Joint Use of Case-Parents Trios and Case-Parent PairsANNALS OF HUMAN GENETICS, Issue 3 2010Yue-Qing Hu Summary Recently interest has been increasing in genetic association studies using several closely linked loci. The HAP-TDT method, which uses case-parents trios is powerful for such a task. However, it is not uncommon in practice that one parent is missing for some reason, such as late onset. The case-parents trios are thus reduced to case-parent pairs. Discarding such data could lead to a severe loss of power. In this paper, we propose the HAP-1-TDT method based on case-parent pairs to detect haplotype/disease association. A permutation-based randomisation technique is devised to assess the significance of the test statistic. Furthermore, the combined statistic HAP-C-TDT is developed to use jointly case-parents trios and case-parent pairs. These test statistics can be applied to either phase-known or phase-unknown data. A number of simulation studies are conducted to investigate the validity of the proposed tests; these studies show that the statistics are robust to population structure. Using several disease genes from the literature, we illustrate that incorporating case-parent pairs into an association study leads to noticeable power gain. Moreover, our simulation results suggest that our method has better size and power than UNPHASED. Finally, in simulated scenarios where there are only a few SNPs and risk is determined by two haplotypes that are complementary or near-complementary, our method has better power than TRIMM. [source] European Mathematical Genetics Meeting, Heidelberg, Germany, 12th,13th April 2007ANNALS OF HUMAN GENETICS, Issue 4 2007Article first published online: 28 MAY 200 Saurabh Ghosh 11 Indian Statistical Institute, Kolkata, India High correlations between two quantitative traits may be either due to common genetic factors or common environmental factors or a combination of both. In this study, we develop statistical methods to extract the contribution of a common QTL to the total correlation between the components of a bivariate phenotype. Using data on bivariate phenotypes and marker genotypes for sib-pairs, we propose a test for linkage between a common QTL and a marker locus based on the conditional cross-sib trait correlations (trait 1 of sib 1 , trait 2 of sib 2 and conversely) given the identity-by-descent sharing at the marker locus. The null hypothesis cannot be rejected unless there exists a common QTL. We use Monte-Carlo simulations to evaluate the performance of the proposed test under different trait parameters and quantitative trait distributions. An application of the method is illustrated using data on two alcohol-related phenotypes from the Collaborative Study On The Genetics Of Alcoholism project. Rémi Kazma 1 , Catherine Bonaďti-Pellié 1 , Emmanuelle Génin 12 INSERM UMR-S535 and Université Paris Sud, Villejuif, 94817, France Keywords: Gene-environment interaction, sibling recurrence risk, exposure correlation Gene-environment interactions may play important roles in complex disease susceptibility but their detection is often difficult. Here we show how gene-environment interactions can be detected by investigating the degree of familial aggregation according to the exposure of the probands. In case of gene-environment interaction, the distribution of genotypes of affected individuals, and consequently the risk in relatives, depends on their exposure. We developed a test comparing the risks in sibs according to the proband exposure. To evaluate the properties of this new test, we derived the formulas for calculating the expected risks in sibs according to the exposure of probands for various values of exposure frequency, relative risk due to exposure alone, frequencies of latent susceptibility genotypes, genetic relative risks and interaction coefficients. We find that the ratio of risks when the proband is exposed and not exposed is a good indicator of the interaction effect. We evaluate the power of the test for various sample sizes of affected individuals. We conclude that this test is valuable for diseases with moderate familial aggregation, only when the role of the exposure has been clearly evidenced. Since a correlation for exposure among sibs might lead to a difference in risks among sibs in the different proband exposure strata, we also add an exposure correlation coefficient in the model. Interestingly, we find that when this correlation is correctly accounted for, the power of the test is not decreased and might even be significantly increased. Andrea Callegaro 1 , Hans J.C. Van Houwelingen 1 , Jeanine Houwing-Duistermaat 13 Dept. of Medical Statistics and Bioinformatics, Leiden University Medical Center, The Netherlands Keywords: Survival analysis, age at onset, score test, linkage analysis Non parametric linkage (NPL) analysis compares the identical by descent (IBD) sharing in sibling pairs to the expected IBD sharing under the hypothesis of no linkage. Often information is available on the marginal cumulative hazards (for example breast cancer incidence curves). Our aim is to extend the NPL methods by taking into account the age at onset of selected sibling pairs using these known marginal hazards. Li and Zhong (2002) proposed a (retrospective) likelihood ratio test based on an additive frailty model for genetic linkage analysis. From their model we derive a score statistic for selected samples which turns out to be a weighed NPL method. The weights depend on the marginal cumulative hazards and on the frailty parameter. A second approach is based on a simple gamma shared frailty model. Here, we simply test whether the score function of the frailty parameter depends on the excess IBD. We compare the performance of these methods using simulated data. Céline Bellenguez 1 , Carole Ober 2 , Catherine Bourgain 14 INSERM U535 and University Paris Sud, Villejuif, France 5 Department of Human Genetics, The University of Chicago, USA Keywords: Linkage analysis, linkage disequilibrium, high density SNP data Compared with microsatellite markers, high density SNP maps should be more informative for linkage analyses. However, because they are much closer, SNPs present important linkage disequilibrium (LD), which biases classical nonparametric multipoint analyses. This problem is even stronger in population isolates where LD extends over larger regions with a more stochastic pattern. We investigate the issue of linkage analysis with a 500K SNP map in a large and inbred 1840-member Hutterite pedigree, phenotyped for asthma. Using an efficient pedigree breaking strategy, we first identified linked regions with a 5cM microsatellite map, on which we focused to evaluate the SNP map. The only method that models LD in the NPL analysis is limited in both the pedigree size and the number of markers (Abecasis and Wigginton, 2005) and therefore could not be used. Instead, we studied methods that identify sets of SNPs with maximum linkage information content in our pedigree and no LD-driven bias. Both algorithms that directly remove pairs of SNPs in high LD and clustering methods were evaluated. Null simulations were performed to control that Zlr calculated with the SNP sets were not falsely inflated. Preliminary results suggest that although LD is strong in such populations, linkage information content slightly better than that of microsatellite maps can be extracted from dense SNP maps, provided that a careful marker selection is conducted. In particular, we show that the specific LD pattern requires considering LD between a wide range of marker pairs rather than only in predefined blocks. Peter Van Loo 1,2,3 , Stein Aerts 1,2 , Diether Lambrechts 4,5 , Bernard Thienpont 2 , Sunit Maity 4,5 , Bert Coessens 3 , Frederik De Smet 4,5 , Leon-Charles Tranchevent 3 , Bart De Moor 2 , Koen Devriendt 3 , Peter Marynen 1,2 , Bassem Hassan 1,2 , Peter Carmeliet 4,5 , Yves Moreau 36 Department of Molecular and Developmental Genetics, VIB, Belgium 7 Department of Human Genetics, University of Leuven, Belgium 8 Bioinformatics group, Department of Electrical Engineering, University of Leuven, Belgium 9 Department of Transgene Technology and Gene Therapy, VIB, Belgium 10 Center for Transgene Technology and Gene Therapy, University of Leuven, Belgium Keywords: Bioinformatics, gene prioritization, data fusion The identification of genes involved in health and disease remains a formidable challenge. Here, we describe a novel bioinformatics method to prioritize candidate genes underlying pathways or diseases, based on their similarity to genes known to be involved in these processes. It is freely accessible as an interactive software tool, ENDEAVOUR, at http://www.esat.kuleuven.be/endeavour. Unlike previous methods, ENDEAVOUR generates distinct prioritizations from multiple heterogeneous data sources, which are then integrated, or fused, into one global ranking using order statistics. ENDEAVOUR prioritizes candidate genes in a three-step process. First, information about a disease or pathway is gathered from a set of known "training" genes by consulting multiple data sources. Next, the candidate genes are ranked based on similarity with the training properties obtained in the first step, resulting in one prioritized list for each data source. Finally, ENDEAVOUR fuses each of these rankings into a single global ranking, providing an overall prioritization of the candidate genes. Validation of ENDEAVOUR revealed it was able to efficiently prioritize 627 genes in disease data sets and 76 genes in biological pathway sets, identify candidates of 16 mono- or polygenic diseases, and discover regulatory genes of myeloid differentiation. Furthermore, the approach identified YPEL1 as a novel gene involved in craniofacial development from a 2-Mb chromosomal region, deleted in some patients with DiGeorge-like birth defects. Finally, we are currently evaluating a pipeline combining array-CGH, ENDEAVOUR and in vivo validation in zebrafish to identify novel genes involved in congenital heart defects. Mark Broom 1 , Graeme Ruxton 2 , Rebecca Kilner 311 Mathematics Dept., University of Sussex, UK 12 Division of Environmental and Evolutionary Biology, University of Glasgow, UK 13 Department of Zoology, University of Cambridge, UK Keywords: Evolutionarily stable strategy, parasitism, asymmetric game Brood parasites chicks vary in the harm that they do to their companions in the nest. In this presentation we use game-theoretic methods to model this variation. Our model considers hosts which potentially abandon single nestlings and instead choose to re-allocate their reproductive effort to future breeding, irrespective of whether the abandoned chick is the host's young or a brood parasite's. The parasite chick must decide whether or not to kill host young by balancing the benefits from reduced competition in the nest against the risk of desertion by host parents. The model predicts that three different types of evolutionarily stable strategies can exist. (1) Hosts routinely rear depleted broods, the brood parasite always kills host young and the host never then abandons the nest. (2) When adult survival after deserting single offspring is very high, hosts always abandon broods of a single nestling and the parasite never kills host offspring, effectively holding them as hostages to prevent nest desertion. (3) Intermediate strategies, in which parasites sometimes kill their nest-mates and host parents sometimes desert nests that contain only a single chick, can also be evolutionarily stable. We provide quantitative descriptions of how the values given to ecological and behavioral parameters of the host-parasite system influence the likelihood of each strategy and compare our results with real host-brood parasite associations in nature. Martin Harrison 114 Mathematics Dept, University of Sussex, UK Keywords: Brood parasitism, games, host, parasite The interaction between hosts and parasites in bird populations has been studied extensively. Game theoretical methods have been used to model this interaction previously, but this has not been studied extensively taking into account the sequential nature of this game. We consider a model allowing the host and parasite to make a number of decisions, which depend on a number of natural factors. The host lays an egg, a parasite bird will arrive at the nest with a certain probability and then chooses to destroy a number of the host eggs and lay one of it's own. With some destruction occurring, either natural or through the actions of the parasite, the host chooses to continue, eject an egg (hoping to eject the parasite) or abandon the nest. Once the eggs have hatched the game then falls to the parasite chick versus the host. The chick chooses to destroy or eject a number of eggs. The final decision is made by the host, choosing whether to raise or abandon the chicks that are in the nest. We consider various natural parameters and probabilities which influence these decisions. We then use this model to look at real-world situations of the interactions of the Reed Warbler and two different parasites, the Common Cuckoo and the Brown-Headed Cowbird. These two parasites have different methods in the way that they parasitize the nests of their hosts. The hosts in turn have a different reaction to these parasites. Arne Jochens 1 , Amke Caliebe 2 , Uwe Roesler 1 , Michael Krawczak 215 Mathematical Seminar, University of Kiel, Germany 16 Institute of Medical Informatics and Statistics, University of Kiel, Germany Keywords: Stepwise mutation model, microsatellite, recursion equation, temporal behaviour We consider the stepwise mutation model which occurs, e.g., in microsatellite loci. Let X(t,i) denote the allelic state of individual i at time t. We compute expectation, variance and covariance of X(t,i), i=1,,,N, and provide a recursion equation for P(X(t,i)=z). Because the variance of X(t,i) goes to infinity as t grows, for the description of the temporal behaviour, we regard the scaled process X(t,i)-X(t,1). The results furnish a better understanding of the behaviour of the stepwise mutation model and may in future be used to derive tests for neutrality under this model. Paul O'Reilly 1 , Ewan Birney 2 , David Balding 117 Statistical Genetics, Department of Epidemiology and Public Health, Imperial, College London, UK 18 European Bioinformatics Institute, EMBL, Cambridge, UK Keywords: Positive selection, Recombination rate, LD, Genome-wide, Natural Selection In recent years efforts to develop population genetics methods that estimate rates of recombination and levels of natural selection in the human genome have intensified. However, since the two processes have an intimately related impact on genetic variation their inference is vulnerable to confounding. Genomic regions subject to recent selection are likely to have a relatively recent common ancestor and consequently less opportunity for historical recombinations that are detectable in contemporary populations. Here we show that selection can reduce the population-based recombination rate estimate substantially. In genome-wide studies for detecting selection we observe a tendency to highlight loci that are subject to low levels of recombination. We find that the outlier approach commonly adopted in such studies may have low power unless variable recombination is accounted for. We introduce a new genome-wide method for detecting selection that exploits the sensitivity to recent selection of methods for estimating recombination rates, while accounting for variable recombination using pedigree data. Through simulations we demonstrate the high power of the Ped/Pop approach to discriminate between neutral and adaptive evolution, particularly in the context of choosing outliers from a genome-wide distribution. Although methods have been developed showing good power to detect selection ,in action', the corresponding window of opportunity is small. In contrast, the power of the Ped/Pop method is maintained for many generations after the fixation of an advantageous variant Sarah Griffiths 1 , Frank Dudbridge 120 MRC Biostatistics Unit, Cambridge, UK Keywords: Genetic association, multimarker tag, haplotype, likelihood analysis In association studies it is generally too expensive to genotype all variants in all subjects. We can exploit linkage disequilibrium between SNPs to select a subset that captures the variation in a training data set obtained either through direct resequencing or a public resource such as the HapMap. These ,tag SNPs' are then genotyped in the whole sample. Multimarker tagging is a more aggressive adaptation of pairwise tagging that allows for combinations of two or more tag SNPs to predict an untyped SNP. Here we describe a new method for directly testing the association of an untyped SNP using a multimarker tag. Previously, other investigators have suggested testing a specific tag haplotype, or performing a weighted analysis using weights derived from the training data. However these approaches do not properly account for the imperfect correlation between the tag haplotype and the untyped SNP. Here we describe a straightforward approach to testing untyped SNPs using a missing-data likelihood analysis, including the tag markers as nuisance parameters. The training data is stacked on top of the main body of genotype data so there is information on how the tag markers predict the genotype of the untyped SNP. The uncertainty in this prediction is automatically taken into account in the likelihood analysis. This approach yields more power and also a more accurate prediction of the odds ratio of the untyped SNP. Anke Schulz 1 , Christine Fischer 2 , Jenny Chang-Claude 1 , Lars Beckmann 121 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany 22 Institute of Human Genetics, University of Heidelberg, Germany Keywords: Haplotype, haplotype sharing, entropy, Mantel statistics, marker selection We previously introduced a new method to map genes involved in complex diseases, using haplotype sharing-based Mantel statistics to correlate genetic and phenotypic similarity. Although the Mantel statistic is powerful in narrowing down candidate regions, the precise localization of a gene is hampered in genomic regions where linkage disequilibrium is so high that neighboring markers are found to be significant at similar magnitude and we are not able to discriminate between them. Here, we present a new approach to localize susceptibility genes by combining haplotype sharing-based Mantel statistics with an iterative entropy-based marker selection algorithm. For each marker at which the Mantel statistic is evaluated, the algorithm selects a subset of surrounding markers. The subset is chosen to maximize multilocus linkage disequilibrium, which is measured by the normalized entropy difference introduced by Nothnagel et al. (2002). We evaluated the algorithm with respect to type I error and power. Its ability to localize the disease variant was compared to the localization (i) without marker selection and (ii) considering haplotype block structure. Case-control samples were simulated from a set of 18 haplotypes, consisting of 15 SNPs in two haplotype blocks. The new algorithm gave correct type I error and yielded similar power to detect the disease locus compared to the alternative approaches. The neighboring markers were clearly less often significant than the causal locus, and also less often significant compared to the alternative approaches. Thus the new algorithm improved the precision of the localization of susceptibility genes. Mark M. Iles 123 Section of Epidemiology and Biostatistics, LIMM, University of Leeds, UK Keywords: tSNP, tagging, association, HapMap Tagging SNPs (tSNPs) are commonly used to capture genetic diversity cost-effectively. However, it is important that the efficacy of tSNPs is correctly estimated, otherwise coverage may be insufficient. If the pilot sample from which tSNPs are chosen is too small or the initial marker map too sparse, tSNP efficacy may be overestimated. An existing estimation method based on bootstrapping goes some way to correct for insufficient sample size and overfitting, but does not completely solve the problem. We describe a novel method, based on exclusion of haplotypes, that improves on the bootstrap approach. Using simulated data, the extent of the sample size problem is investigated and the performance of the bootstrap and the novel method are compared. We incorporate an existing method adjusting for marker density by ,SNP-dropping'. We find that insufficient sample size can cause large overestimates in tSNP efficacy, even with as many as 100 individuals, and the problem worsens as the region studied increases in size. Both the bootstrap and novel method correct much of this overestimate, with our novel method consistently outperforming the bootstrap method. We conclude that a combination of insufficient sample size and overfitting may lead to overestimation of tSNP efficacy and underpowering of studies based on tSNPs. Our novel approach corrects for much of this bias and is superior to the previous method. Sample sizes larger than previously suggested may still be required for accurate estimation of tSNP efficacy. This has obvious ramifications for the selection of tSNPs from HapMap data. Claudio Verzilli 1 , Juliet Chapman 1 , Aroon Hingorani 2 , Juan Pablo-Casas 1 , Tina Shah 2 , Liam Smeeth 1 , John Whittaker 124 Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, UK 25 Division of Medicine, University College London, UK Keywords: Meta-analysis, Genetic association studies We present a Bayesian hierarchical model for the meta-analysis of candidate gene studies with a continuous outcome. Such studies often report results from association tests for different, possibly study-specific and non-overlapping markers (typically SNPs) in the same genetic region. Meta analyses of the results at each marker in isolation are seldom appropriate as they ignore the correlation that may exist between markers due to linkage disequlibrium (LD) and cannot assess the relative importance of variants at each marker. Also such marker-wise meta analyses are restricted to only those studies that have typed the marker in question, with a potential loss of power. A better strategy is one which incorporates information about the LD between markers so that any combined estimate of the effect of each variant is corrected for the effect of other variants, as in multiple regression. Here we develop a Bayesian hierarchical linear regression that models the observed genotype group means and uses pairwise LD measurements between markers as prior information to make posterior inference on adjusted effects. The approach is applied to the meta analysis of 24 studies assessing the effect of 7 variants in the C-reactive protein (CRP) gene region on plasma CRP levels, an inflammatory biomarker shown in observational studies to be positively associated with cardiovascular disease. Cathryn M. Lewis 1 , Christopher G. Mathew 1 , Theresa M. Marteau 226 Dept. of Medical and Molecular Genetics, King's College London, UK 27 Department of Psychology, King's College London, UK Keywords: Risk, genetics, CARD15, smoking, model Recently progress has been made in identifying mutations that confer susceptibility to complex diseases, with the potential to use these mutations in determining disease risk. We developed methods to estimate disease risk based on genotype relative risks (for a gene G), exposure to an environmental factor (E), and family history (with recurrence risk ,R for a relative of type R). ,R must be partitioned into the risk due to G (which is modelled independently) and the residual risk. The risk model was then applied to Crohn's disease (CD), a severe gastrointestinal disease for which smoking increases disease risk approximately 2-fold, and mutations in CARD15 confer increased risks of 2.25 (for carriers of a single mutation) and 9.3 (for carriers of two mutations). CARD15 accounts for only a small proportion of the genetic component of CD, with a gene-specific ,S, CARD15 of 1.16, from a total sibling relative risk of ,S= 27. CD risks were estimated for high-risk individuals who are siblings of a CD case, and who also smoke. The CD risk to such individuals who carry two CARD15 mutations is approximately 0.34, and for those carrying a single CARD15 mutation the risk is 0.08, compared to a population prevalence of approximately 0.001. These results imply that complex disease genes may be valuable in estimating with greater precision than has hitherto been possible disease risks in specific, easily identified subgroups of the population with a view to prevention. Yurii Aulchenko 128 Department of Epidemiology & Biostatistics, Erasmus Medical Centre Rotterdam, The Netherlands Keywords: Compression, information, bzip2, genome-wide SNP data, statistical genetics With advances in molecular technology, studies accessing millions of genetic polymorphisms in thousands of study subjects will soon become common. Such studies generate large amounts of data, whose effective storage and management is a challenge to the modern statistical genetics. Standard file compression utilities, such as Zip, Gzip and Bzip2, may be helpful to minimise the storage requirements. Less obvious is the fact that the data compression techniques may be also used in the analysis of genetic data. It is known that the efficiency of a particular compression algorithm depends on the probability structure of the data. In this work, we compared different standard and customised tools using the data from human HapMap project. Secondly, we investigate the potential uses of data compression techniques for the analysis of linkage, association and linkage disequilibrium Suzanne Leal 1 , Bingshan Li 129 Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, USA Keywords: Consanguineous pedigrees, missing genotype data Missing genotype data can increase false-positive evidence for linkage when either parametric or nonparametric analysis is carried out ignoring intermarker linkage disequilibrium (LD). Previously it was demonstrated by Huang et al (2005) that no bias occurs in this situation for affected sib-pairs with unrelated parents when either both parents are genotyped or genotype data is available for two additional unaffected siblings when parental genotypes are missing. However, this is not the case for consanguineous pedigrees, where missing genotype data for any pedigree member within a consanguinity loop can increase false-positive evidence of linkage. The false-positive evidence for linkage is further increased when cryptic consanguinity is present. The amount of false-positive evidence for linkage is highly dependent on which family members are genotyped. When parental genotype data is available, the false-positive evidence for linkage is usually not as strong as when parental genotype data is unavailable. Which family members will aid in the reduction of false-positive evidence of linkage is highly dependent on which other family members are genotyped. For a pedigree with an affected proband whose first-cousin parents have been genotyped, further reduction in the false-positive evidence of linkage can be obtained by including genotype data from additional affected siblings of the proband or genotype data from the proband's sibling-grandparents. When parental genotypes are not available, false-positive evidence for linkage can be reduced by including in the analysis genotype data from either unaffected siblings of the proband or the proband's married-in-grandparents. Najaf Amin 1 , Yurii Aulchenko 130 Department of Epidemiology & Biostatistics, Erasmus Medical Centre Rotterdam, The Netherlands Keywords: Genomic Control, pedigree structure, quantitative traits The Genomic Control (GC) method was originally developed to control for population stratification and cryptic relatedness in association studies. This method assumes that the effect of population substructure on the test statistics is essentially constant across the genome, and therefore unassociated markers can be used to estimate the effect of confounding onto the test statistic. The properties of GC method were extensively investigated for different stratification scenarios, and compared to alternative methods, such as the transmission-disequilibrium test. The potential of this method to correct not for occasional cryptic relations, but for regular pedigree structure, however, was not investigated before. In this work we investigate the potential of the GC method for pedigree-based association analysis of quantitative traits. The power and type one error of the method was compared to standard methods, such as the measured genotype (MG) approach and quantitative trait transmission-disequilibrium test. In human pedigrees, with trait heritability varying from 30 to 80%, the power of MG and GC approach was always higher than that of TDT. GC had correct type 1 error and its power was close to that of MG under moderate heritability (30%), but decreased with higher heritability. William Astle 1 , Chris Holmes 2 , David Balding 131 Department of Epidemiology and Public Health, Imperial College London, UK 32 Department of Statistics, University of Oxford, UK Keywords: Population structure, association studies, genetic epidemiology, statistical genetics In the analysis of population association studies, Genomic Control (Devlin & Roeder, 1999) (GC) adjusts the Armitage test statistic to correct the type I error for the effects of population substructure, but its power is often sub-optimal. Turbo Genomic Control (TGC) generalises GC to incorporate co-variation of relatedness and phenotype, retaining control over type I error while improving power. TGC is similar to the method of Yu et al. (2006), but we extend it to binary (case-control) in addition to quantitative phenotypes, we implement improved estimation of relatedness coefficients, and we derive an explicit statistic that generalizes the Armitage test statistic and is fast to compute. TGC also has similarities to EIGENSTRAT (Price et al., 2006) which is a new method based on principle components analysis. The problems of population structure(Clayton et al., 2005) and cryptic relatedness (Voight & Pritchard, 2005) are essentially the same: if patterns of shared ancestry differ between cases and controls, whether distant (coancestry) or recent (cryptic relatedness), false positives can arise and power can be diminished. With large numbers of widely-spaced genetic markers, coancestry can now be measured accurately for each pair of individuals via patterns of allele-sharing. Instead of modelling subpopulations, we work instead with a coancestry coefficient for each pair of individuals in the study. We explain the relationships between TGC, GC and EIGENSTRAT. We present simulation studies and real data analyses to illustrate the power advantage of TGC in a range of scenarios incorporating both substructure and cryptic relatedness. References Clayton, D. G.et al. (2005) Population structure, differential bias and genomic control in a large-scale case-control association study. Nature Genetics37(11) November 2005. Devlin, B. & Roeder, K. (1999) Genomic control for association studies. Biometics55(4) December 1999. Price, A. L.et al. (2006) Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics38(8) (August 2006). Voight, B. J. & Pritchard, J. K. (2005) Confounding from cryptic relatedness in case-control association studies. Public Library of Science Genetics1(3) September 2005. Yu, J.et al. (2006) A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nature Genetics38(2) February 2006. Hervé Perdry 1 , Marie-Claude Babron 1 , Françoise Clerget-Darpoux 133 INSERM U535 and Univ. Paris Sud, UMR-S 535, Villejuif, France Keywords: Modifier genes, case-parents trios, ordered transmission disequilibrium test A modifying locus is a polymorphic locus, distinct from the disease locus, which leads to differences in the disease phenotype, either by modifying the penetrance of the disease allele, or by modifying the expression of the disease. The effect of such a locus is a clinical heterogeneity that can be reflected by the values of an appropriate covariate, such as the age of onset, or the severity of the disease. We designed the Ordered Transmission Disequilibrium Test (OTDT) to test for a relation between the clinical heterogeneity, expressed by the covariate, and marker genotypes of a candidate gene. The method applies to trio families with one affected child and his parents. Each family member is genotyped at a bi-allelic marker M of a candidate gene. To each of the families is associated a covariate value; the families are ordered on the values of this covariate. As the TDT (Spielman et al. 1993), the OTDT is based on the observation of the transmission rate T of a given allele at M. The OTDT aims to find a critical value of the covariate which separates the sample of families in two subsamples in which the transmission rates are significantly different. We investigate the power of the method by simulations under various genetic models and covariate distributions. Acknowledgments H Perdry is funded by ARSEP. Pascal Croiseau 1 , Heather Cordell 2 , Emmanuelle Génin 134 INSERM U535 and University Paris Sud, UMR-S535, Villejuif, France 35 Institute of Human Genetics, Newcastle University, UK Keywords: Association, missing data, conditionnal logistic regression Missing data is an important problem in association studies. Several methods used to test for association need that individuals be genotyped at the full set of markers. Individuals with missing data need to be excluded from the analysis. This could involve an important decrease in sample size and a loss of information. If the disease susceptibility locus (DSL) is poorly typed, it is also possible that a marker in linkage disequilibrium gives a stronger association signal than the DSL. One may then falsely conclude that the marker is more likely to be the DSL. We recently developed a Multiple Imputation method to infer missing data on case-parent trios Starting from the observed data, a few number of complete data sets are generated by Markov-Chain Monte Carlo approach. These complete datasets are analysed using standard statistical package and the results are combined as described in Little & Rubin (2002). Here we report the results of simulations performed to examine, for different patterns of missing data, how often the true DSL gives the highest association score among different loci in LD. We found that multiple imputation usually correctly detect the DSL site even if the percentage of missing data is high. This is not the case for the naďve approach that consists in discarding trios with missing data. In conclusion, Multiple imputation presents the advantage of being easy to use and flexible and is therefore a promising tool in the search for DSL involved in complex diseases. Salma Kotti 1 , Heike Bickeböller 2 , Françoise Clerget-Darpoux 136 University Paris Sud, UMR-S535, Villejuif, France 37 Department of Genetic Epidemiology, Medical School, University of Göttingen, Germany Keywords: Genotype relative risk, internal controls, Family based analyses Family based analyses using internal controls are very popular both for detecting the effect of a genetic factor and for estimating the relative disease risk on the corresponding genotypes. Two different procedures are often applied to reconstitute internal controls. The first one considers one pseudocontrol genotype formed by the parental non-transmitted alleles called also 1:1 matching of alleles, while the second corresponds to three pseudocontrols corresponding to all genotypes formed by the parental alleles except the one of the case (1:3 matching). Many studies have compared between the two procedures in terms of the power and have concluded that the difference depends on the underlying genetic model and the allele frequencies. However, the estimation of the Genotype Relative Risk (GRR) under the two procedures has not been studied. Based on the fact that on the 1:1 matching, the control group is composed of the alleles untransmitted to the affected child and on the 1:3 matching, the control group is composed amongst alleles already transmitted to the affected child, we expect a difference on the GRR estimation. In fact, we suspect that the second procedure leads to biased estimation of the GRRs. We will analytically derive the GRR estimators for the 1:1 and 1:3 matching and will present the results at the meeting. Family based analyses using internal controls are very popular both for detecting the effect of a genetic factor and for estimating the relative disease risk on the corresponding genotypes. Two different procedures are often applied to reconstitute internal controls. The first one considers one pseudocontrol genotype formed by the parental non-transmitted alleles called also 1:1 matching of alleles, while the second corresponds to three pseudocontrols corresponding to all genotypes formed by the parental alleles except the one of the case (1:3 matching). Many studies have compared between the two procedures in terms of the power and have concluded that the difference depends on the underlying genetic model and the allele frequencies. However, the estimation of the Genotype Relative Risk (GRR) under the two procedures has not been studied. Based on the fact that on the 1:1 matching, the control group is composed of the alleles untransmitted to the affected child and on the 1:3 matching, the control group is composed amongst alleles already transmitted to the affected child, we expect a difference on the GRR estimation. In fact, we suspect that the second procedure leads to biased estimation of the GRR. We will analytically derive the GRR estimator for the 1:1 and 1:3 matching and will present the results at the meeting. Luigi Palla 1 , David Siegmund 239 Department of Mathematics,Free University Amsterdam, The Netherlands 40 Department of Statistics, Stanford University, California, USA Keywords: TDT, assortative mating, inbreeding, statistical power A substantial amount of Assortative Mating (AM) is often recorded on physical and psychological, dichotomous as well as quantitative traits that are supposed to have a multifactorial genetic component. In particular AM has the effect of increasing the genetic variance, even more than inbreeding because it acts across loci beside within loci, when the trait has a multifactorial origin. Under the assumption of a polygenic model for AM dating back to Wright (1921) and refined by Crow and Felsenstein (1968,1982), the effect of assortative mating on the power to detect genetic association in the Transmission Disequilibrium Test (TDT) is explored as parameters, such as the effective number of genes and the allelic frequency vary. The power is reflected by the non centrality parameter of the TDT and is expressed as a function of the number of trios, the relative risk of the heterozygous genotype and the allele frequency (Siegmund and Yakir, 2007). The noncentrality parameter of the relevant score statistic is updated considering the effect of AM which is expressed in terms of an ,effective' inbreeding coefficient. In particular, for dichotomous traits it is apparent that the higher the number of genes involved in the trait, the lower the loss in power due to AM. Finally an attempt is made to extend this relation to the Q-TDT (Rabinowitz, 1997), which involves considering the effect of AM also on the phenotypic variance of the trait of interest, under the assumption that AM affects only its additive genetic component. References Crow, & Felsenstein, (1968). The effect of assortative mating on the genetic composition of a population. Eugen.Quart.15, 87,97. Rabinowitz,, 1997. A Transmission Disequilibrium Test for Quantitative Trait Loci. Human Heredity47, 342,350. Siegmund, & Yakir, (2007) Statistics of gene mapping, Springer. Wright, (1921). System of mating.III. Assortative mating based on somatic resemblance. Genetics6, 144,161. Jérémie Nsengimana 1 , Ben D Brown 2 , Alistair S Hall 2 , Jenny H Barrett 141 Leeds Institute of Molecular Medicine, University of Leeds, UK 42 Leeds Institute for Genetics, Health and Therapeutics, University of Leeds, UK Keywords: Inflammatory genes, haplotype, coronary artery disease Genetic Risk of Acute Coronary Events (GRACE) is an initiative to collect cases of coronary artery disease (CAD) and their unaffected siblings in the UK and to use them to map genetic variants increasing disease risk. The aim of the present study was to test the association between CAD and 51 single nucleotide polymorphisms (SNPs) and their haplotypes from 35 inflammatory genes. Genotype data were available for 1154 persons affected before age 66 (including 48% before age 50) and their 1545 unaffected siblings (891 discordant families). Each SNP was tested for association to CAD, and haplotypes within genes or gene clusters were tested using FBAT (Rabinowitz & Laird, 2000). For the most significant results, genetic effect size was estimated using conditional logistic regression (CLR) within STATA adjusting for other risk factors. Haplotypes were assigned using HAPLORE (Zhang et al., 2005), which considers all parental mating types consistent with offspring genotypes and assigns them a probability of occurence. This probability was used in CLR to weight the haplotypes. In the single SNP analysis, several SNPs showed some evidence for association, including one SNP in the interleukin-1A gene. Analysing haplotypes in the interleukin-1 gene cluster, a common 3-SNP haplotype was found to increase the risk of CAD (P = 0.009). In an additive genetic model adjusting for covariates the odds ratio (OR) for this haplotype is 1.56 (95% CI: 1.16-2.10, p = 0.004) for early-onset CAD (before age 50). This study illustrates the utility of haplotype analysis in family-based association studies to investigate candidate genes. References Rabinowitz, D. & Laird, N. M. (2000) Hum Hered50, 211,223. Zhang, K., Sun, F. & Zhao, H. (2005) Bioinformatics21, 90,103. Andrea Foulkes 1 , Recai Yucel 1 , Xiaohong Li 143 Division of Biostatistics, University of Massachusetts, USA Keywords: Haploytpe, high-dimensional, mixed modeling The explosion of molecular level information coupled with large epidemiological studies presents an exciting opportunity to uncover the genetic underpinnings of complex diseases; however, several analytical challenges remain to be addressed. Characterizing the components to complex diseases inevitably requires consideration of synergies across multiple genetic loci and environmental and demographic factors. In addition, it is critical to capture information on allelic phase, that is whether alleles within a gene are in cis (on the same chromosome) or in trans (on different chromosomes.) In associations studies of unrelated individuals, this alignment of alleles within a chromosomal copy is generally not observed. We address the potential ambiguity in allelic phase in this high dimensional data setting using mixed effects models. Both a semi-parametric and fully likelihood-based approach to estimation are considered to account for missingness in cluster identifiers. In the first case, we apply a multiple imputation procedure coupled with a first stage expectation maximization algorithm for parameter estimation. A bootstrap approach is employed to assess sensitivity to variability induced by parameter estimation. Secondly, a fully likelihood-based approach using an expectation conditional maximization algorithm is described. Notably, these models allow for characterizing high-order gene-gene interactions while providing a flexible statistical framework to account for the confounding or mediating role of person specific covariates. The proposed method is applied to data arising from a cohort of human immunodeficiency virus type-1 (HIV-1) infected individuals at risk for therapy associated dyslipidemia. Simulation studies demonstrate reasonable power and control of family-wise type 1 error rates. Vivien Marquard 1 , Lars Beckmann 1 , Jenny Chang-Claude 144 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany Keywords: Genotyping errors, type I error, haplotype-based association methods It has been shown in several simulation studies that genotyping errors may have a great impact on the type I error of statistical methods used in genetic association analysis of complex diseases. Our aim was to investigate type I error rates in a case-control study, when differential and non-differential genotyping errors were introduced in realistic scenarios. We simulated case-control data sets, where individual genotypes were drawn from a haplotype distribution of 18 haplotypes with 15 markers in the APM1 gene. Genotyping errors were introduced following the unrestricted and symmetric with 0 edges error models described by Heid et al. (2006). In six scenarios, errors resulted from changes of one allele to another with predefined probabilities of 1%, 2.5% or 10%, respectively. A multiple number of errors per haplotype was possible and could vary between 0 and 15, the number of markers investigated. We examined three association methods: Mantel statistics using haplotype-sharing; a haplotype-specific score test; and Armitage trend test for single markers. The type I error rates were not influenced for any of all the three methods for a genotyping error rate of less than 1%. For higher error rates and differential errors, the type I error of the Mantel statistic was only slightly and of the Armitage trend test moderately increased. The type I error rates of the score test were highly increased. The type I error rates were correct for all three methods for non-differential errors. Further investigations will be carried out with different frequencies of differential error rates and focus on power. Arne Neumann 1 , Dörthe Malzahn 1 , Martina Müller 2 , Heike Bickeböller 145 Department of Genetic Epidemiology, Medical School, University of Göttingen, Germany 46 GSF-National Research Center for Environment and Health, Neuherberg & IBE-Institute of Epidemiology, Ludwig-Maximilians University München, Germany Keywords: Interaction, longitudinal, nonparametric Longitudinal data show the time dependent course of phenotypic traits. In this contribution, we consider longitudinal cohort studies and investigate the association between two candidate genes and a dependent quantitative longitudinal phenotype. The set-up defines a factorial design which allows us to test simultaneously for the overall gene effect of the loci as well as for possible gene-gene and gene time interaction. The latter would induce genetically based time-profile differences in the longitudinal phenotype. We adopt a non-parametric statistical test to genetic epidemiological cohort studies and investigate its performance by simulation studies. The statistical test was originally developed for longitudinal clinical studies (Brunner, Munzel, Puri, 1999 J Multivariate Anal 70:286-317). It is non-parametric in the sense that no assumptions are made about the underlying distribution of the quantitative phenotype. Longitudinal observations belonging to the same individual can be arbitrarily dependent on one another for the different time points whereas trait observations of different individuals are independent. The two loci are assumed to be statistically independent. Our simulations show that the nonparametric test is comparable with ANOVA in terms of power of detecting gene-gene and gene-time interaction in an ANOVA favourable setting. Rebecca Hein 1 , Lars Beckmann 1 , Jenny Chang-Claude 147 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany Keywords: Indirect association studies, interaction effects, linkage disequilibrium, marker allele frequency Association studies accounting for gene-environment interactions (GxE) may be useful for detecting genetic effects and identifying important environmental effect modifiers. Current technology facilitates very dense marker spacing in genetic association studies; however, the true disease variant(s) may not be genotyped. In this situation, an association between a gene and a phenotype may still be detectable, using genetic markers associated with the true disease variant(s) (indirect association). Zondervan and Cardon [2004] showed that the odds ratios (OR) of markers which are associated with the disease variant depend highly on the linkage disequilibrium (LD) between the variant and the markers, and whether the allele frequencies match and thereby influence the sample size needed to detect genetic association. We examined the influence of LD and allele frequencies on the sample size needed to detect GxE in indirect association studies, and provide tables for sample size estimation. For discordant allele frequencies and incomplete LD, sample sizes can be unfeasibly large. The influence of both factors is stronger for disease loci with small rather than moderate to high disease allele frequencies. A decline in D' of e.g. 5% has less impact on sample size than increasing the difference in allele frequencies by the same percentage. Assuming 80% power, large interaction effects can be detected using smaller sample sizes than those needed for the detection of main effects. The detection of interaction effects involving rare alleles may not be possible. Focussing only on marker density can be a limited strategy in indirect association studies for GxE. Cyril Dalmasso 1 , Emmanuelle Génin 2 , Catherine Bourgain 2 , Philippe Broët 148 JE 2492 , Univ. Paris-Sud, France 49 INSERM UMR-S 535 and University Paris Sud, Villejuif, France Keywords: Linkage analysis, Multiple testing, False Discovery Rate, Mixture model In the context of genome-wide linkage analyses, where a large number of statistical tests are simultaneously performed, the False Discovery Rate (FDR) that is defined as the expected proportion of false discoveries among all discoveries is nowadays widely used for taking into account the multiple testing problem. Other related criteria have been considered such as the local False Discovery Rate (lFDR) that is a variant of the FDR giving to each test its own measure of significance. The lFDR is defined as the posterior probability that a null hypothesis is true. Most of the proposed methods for estimating the lFDR or the FDR rely on distributional assumption under the null hypothesis. However, in observational studies, the empirical null distribution may be very different from the theoretical one. In this work, we propose a mixture model based approach that provides estimates of the lFDR and the FDR in the context of large-scale variance component linkage analyses. In particular, this approach allows estimating the empirical null distribution, this latter being a key quantity for any simultaneous inference procedure. The proposed method is applied on a real dataset. Arief Gusnanto 1 , Frank Dudbridge 150 MRC Biostatistics Unit, Cambridge UK Keywords: Significance, genome-wide, association, permutation, multiplicity Genome-wide association scans have introduced statistical challenges, mainly in the multiplicity of thousands of tests. The question of what constitutes a significant finding remains somewhat unresolved. Permutation testing is very time-consuming, whereas Bayesian arguments struggle to distinguish direct from indirect association. It seems attractive to summarise the multiplicity in a simple form that allows users to avoid time-consuming permutations. A standard significance level would facilitate reporting of results and reduce the need for permutation tests. This is potentially important because current scans do not have full coverage of the whole genome, and yet, the implicit multiplicity is genome-wide. We discuss some proposed summaries, with reference to the empirical null distribution of the multiple tests, approximated through a large number of random permutations. Using genome-wide data from the Wellcome Trust Case-Control Consortium, we use a sub-sampling approach with increasing density to estimate the nominal p-value to obtain family-wise significance of 5%. The results indicate that the significance level is converging to about 1e-7 as the marker spacing becomes infinitely dense. We considered the concept of an effective number of independent tests, and showed that when used in a Bonferroni correction, the number varies with the overall significance level, but is roughly constant in the region of interest. We compared several estimators of the effective number of tests, and showed that in the region of significance of interest, Patterson's eigenvalue based estimator gives approximately the right family-wise error rate. Michael Nothnagel 1 , Amke Caliebe 1 , Michael Krawczak 151 Institute of Medical Informatics and Statistics, University Clinic Schleswig-Holstein, University of Kiel, Germany Keywords: Association scans, Bayesian framework, posterior odds, genetic risk, multiplicative model Whole-genome association scans have been suggested to be a cost-efficient way to survey genetic variation and to map genetic disease factors. We used a Bayesian framework to investigate the posterior odds of a genuine association under multiplicative disease models. We demonstrate that the p value alone is not a sufficient means to evaluate the findings in association studies. We suggest that likelihood ratios should accompany p values in association reports. We argue, that, given the reported results of whole-genome scans, more associations should have been successfully replicated if the consistently made assumptions about considerable genetic risks were correct. We conclude that it is very likely that the vast majority of relative genetic risks are only of the order of 1.2 or lower. Clive Hoggart 1 , Maria De Iorio 1 , John Whittakker 2 , David Balding 152 Department of Epidemiology and Public Health, Imperial College London, UK 53 Department of Epidemiology and Public Health, London School of Hygiene and Tropical Medicine, UK Keywords: Genome-wide association analyses, shrinkage priors, Lasso Testing one SNP at a time does not fully realise the potential of genome-wide association studies to identify multiple causal variants of small effect, which is a plausible scenario for many complex diseases. Moreover, many simulation studies assume a single causal variant and so more complex realities are ignored. Analysing large numbers of variants simultaneously is now becoming feasible, thanks to developments in Bayesian stochastic search methods. We pose the problem of SNP selection as variable selection in a regression model. In contrast to single SNP tests this approach simultaneously models the effect of all SNPs. SNPs are selected by a Bayesian interpretation of the lasso (Tibshirani, 1996); the maximum a posterior (MAP) estimate of the regression coefficients, which have been given independent, double exponential prior distributions. The double exponential distribution is an example of a shrinkage prior, MAP estimates with shrinkage priors can be zero, thus all SNPs with non zero regression coefficients are selected. In addition to the commonly-used double exponential (Laplace) prior, we also implement the normal exponential gamma prior distribution. We show that use of the Laplace prior improves SNP selection in comparison with single -SNP tests, and that the normal exponential gamma prior leads to a further improvement. Our method is fast and can handle very large numbers of SNPs: we demonstrate its performance using both simulated and real genome-wide data sets with 500 K SNPs, which can be analysed in 2 hours on a desktop workstation. Mickael Guedj 1,2 , Jerome Wojcik 2 , Gregory Nuel 154 Laboratoire Statistique et Génome, Université d'Evry, Evry France 55 Serono Pharmaceutical Research Institute, Plan-les-Ouates, Switzerland Keywords: Local Replication, Local Score, Association In gene-mapping, replication of initial findings has been put forwards as the approach of choice for filtering false-positives from true signals for underlying loci. In practice, such replications are however too poorly observed. Besides the statistical and technical-related factors (lack of power, multiple-testing, stratification, quality control,) inconsistent conclusions obtained from independent populations might result from real biological differences. In particular, the high degree of variation in the strength of LD among populations of different origins is a major challenge to the discovery of genes. Seeking for Local Replications (defined as the presence of a signal of association in a same genomic region among populations) instead of strict replications (same locus, same risk allele) may lead to more reliable results. Recently, a multi-markers approach based on the Local Score statistic has been proposed as a simple and efficient way to select candidate genomic regions at the first stage of genome-wide association studies. Here we propose an extension of this approach adapted to replicated association studies. Based on simulations, this method appears promising. In particular it outperforms classical simple-marker strategies to detect modest-effect genes. Additionally it constitutes, to our knowledge, a first framework dedicated to the detection of such Local Replications. Juliet Chapman 1 , Claudio Verzilli 1 , John Whittaker 156 Department of Epidemiology and Public Health, London School of Hygiene and Tropical Medicine, UK Keywords: FDR, Association studies, Bayesian model selection As genomewide association studies become commonplace there is debate as to how such studies might be analysed and what we might hope to gain from the data. It is clear that standard single locus approaches are limited in that they do not adjust for the effects of other loci and problematic since it is not obvious how to adjust for multiple comparisons. False discovery rates have been suggested, but it is unclear how well these will cope with highly correlated genetic data. We consider the validity of standard false discovery rates in large scale association studies. We also show that a Bayesian procedure has advantages in detecting causal loci amongst a large number of dependant SNPs and investigate properties of a Bayesian FDR. Peter Kraft 157 Harvard School of Public Health, Boston USA Keywords: Gene-environment interaction, genome-wide association scans Appropriately analyzed two-stage designs,where a subset of available subjects are genotyped on a genome-wide panel of markers at the first stage and then a much smaller subset of the most promising markers are genotyped on the remaining subjects,can have nearly as much power as a single-stage study where all subjects are genotyped on the genome-wide panel yet can be much less expensive. Typically, the "most promising" markers are selected based on evidence for a marginal association between genotypes and disease. Subsequently, the few markers found to be associated with disease at the end of the second stage are interrogated for evidence of gene-environment interaction, mainly to understand their impact on disease etiology and public health impact. However, this approach may miss variants which have a sizeable effect restricted to one exposure stratum and therefore only a modest marginal effect. We have proposed to use information on the joint effects of genes and a discrete list of environmental exposures at the initial screening stage to select promising markers for the second stage [Kraft et al Hum Hered 2007]. This approach optimizes power to detect variants that have a sizeable marginal effect and variants that have a small marginal effect but a sizeable effect in a stratum defined by an environmental exposure. As an example, I discuss a proposed genome-wide association scan for Type II diabetes susceptibility variants based in several large nested case-control studies. Beate Glaser 1 , Peter Holmans 158 Biostatistics and Bioinformatics Unit, Cardiff University, School of Medicine, Heath Park, Cardiff, UK Keywords: Combined case-control and trios analysis, Power, False-positive rate, Simulation, Association studies The statistical power of genetic association studies can be enhanced by combining the analysis of case-control with parent-offspring trio samples. Various combined analysis techniques have been recently developed; as yet, there have been no comparisons of their power. This work was performed with the aim of identifying the most powerful method among available combined techniques including test statistics developed by Kazeem and Farrall (2005), Nagelkerke and colleagues (2004) and Dudbridge (2006), as well as a simple combination of ,2-statistics from single samples. Simulation studies were performed to investigate their power under different additive, multiplicative, dominant and recessive disease models. False-positive rates were determined by studying the type I error rates under null models including models with unequal allele frequencies between the single case-control and trios samples. We identified three techniques with equivalent power and false-positive rates, which included modifications of the three main approaches: 1) the unmodified combined Odds ratio estimate by Kazeem & Farrall (2005), 2) a modified approach of the combined risk ratio estimate by Nagelkerke & colleagues (2004) and 3) a modified technique for a combined risk ratio estimate by Dudbridge (2006). Our work highlights the importance of studies investigating test performance criteria of novel methods, as they will help users to select the optimal approach within a range of available analysis techniques. David Almorza 1 , M.V. Kandus 2 , Juan Carlos Salerno 2 , Rafael Boggio 359 Facultad de Ciencias del Trabajo, University of Cádiz, Spain 60 Instituto de Genética IGEAF, Buenos Aires, Argentina 61 Universidad Nacional de La Plata, Buenos Aires, Argentina Keywords: Principal component analysis, maize, ear weight, inbred lines The objective of this work was to evaluate the relationship among different traits of the ear of maize inbred lines and to group genotypes according to its performance. Ten inbred lines developed at IGEAF (INTA Castelar) and five public inbred lines as checks were used. A field trial was carried out in Castelar, Buenos Aires (34° 36' S , 58° 39' W) using a complete randomize design with three replications. At harvest, individual weight (P.E.), diameter (D.E.), row number (N.H.) and length (L.E.) of the ear were assessed. A principal component analysis, PCA, (Infostat 2005) was used, and the variability of the data was depicted with a biplot. Principal components 1 and 2 (CP1 and CP2) explained 90% of the data variability. CP1 was correlated with P.E., L.E. and D.E., meanwhile CP2 was correlated with N.H. We found that individual weight (P.E.) was more correlated with diameter of the ear (D.E.) than with length (L.E). Five groups of inbred lines were distinguished: with high P.E. and mean N.H. (04-70, 04-73, 04-101 and MO17), with high P.E. but less N.H. (04-61 and B14), with mean P.E. and N.H. (B73, 04-123 and 04-96), with high N.H. but less P.E. (LP109, 04-8, 04-91 and 04-76) and with low P.E. and low N.H. (LP521 and 04-104). The use of PCA showed which variables had more incidence in ear weight and how is the correlation among them. Moreover, the different groups found with this analysis allow the evaluation of inbred lines by several traits simultaneously. Sven Knüppel 1 , Anja Bauerfeind 1 , Klaus Rohde 162 Department of Bioinformatics, MDC Berlin, Germany Keywords: Haplotypes, association studies, case-control, nuclear families The area of gene chip technology provides a plethora of phase-unknown SNP genotypes in order to find significant association to some genetic trait. To circumvent possibly low information content of a single SNP one groups successive SNPs and estimates haplotypes. Haplotype estimation, however, may reveal ambiguous haplotype pairs and bias the application of statistical methods. Zaykin et al. (Hum Hered, 53:79-91, 2002) proposed the construction of a design matrix to take this ambiguity into account. Here we present a set of functions written for the Statistical package R, which carries out haplotype estimation on the basis of the EM-algorithm for individuals (case-control) or nuclear families. The construction of a design matrix on basis of estimated haplotypes or haplotype pairs allows application of standard methods for association studies (linear, logistic regression), as well as statistical methods as haplotype sharing statistics and TDT-Test. Applications of these methods to genome-wide association screens will be demonstrated. Manuela Zucknick 1 , Chris Holmes 2 , Sylvia Richardson 163 Department of Epidemiology and Public Health, Imperial College London, UK 64 Department of Statistics, Oxford Center for Gene Function, University of Oxford, UK Keywords: Bayesian, variable selection, MCMC, large p, small n, structured dependence In large-scale genomic applications vast numbers of markers or genes are scanned to find a few candidates which are linked to a particular phenotype. Statistically, this is a variable selection problem in the "large p, small n" situation where many more variables than samples are available. An additional feature is the complex dependence structure which is often observed among the markers/genes due to linkage disequilibrium or their joint involvement in biological processes. Bayesian variable selection methods using indicator variables are well suited to the problem. Binary phenotypes like disease status are common and both Bayesian probit and logistic regression can be applied in this context. We argue that logistic regression models are both easier to tune and to interpret than probit models and implement the approach by Holmes & Held (2006). Because the model space is vast, MCMC methods are used as stochastic search algorithms with the aim to quickly find regions of high posterior probability. In a trade-off between fast-updating but slow-moving single-gene Metropolis-Hastings samplers and computationally expensive full Gibbs sampling, we propose to employ the dependence structure among the genes/markers to help decide which variables to update together. Also, parallel tempering methods are used to aid bold moves and help avoid getting trapped in local optima. Mixing and convergence of the resulting Markov chains are evaluated and compared to standard samplers in both a simulation study and in an application to a gene expression data set. Reference Holmes, C. C. & Held, L. (2006) Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis1, 145,168. Dawn Teare 165 MMGE, University of Sheffield, UK Keywords: CNP, family-based analysis, MCMC Evidence is accumulating that segmental copy number polymorphisms (CNPs) may represent a significant portion of human genetic variation. These highly polymorphic systems require handling as phenotypes rather than co-dominant markers, placing new demands on family-based analyses. We present an integrated approach to meet these challenges in the form of a graphical model, where the underlying discrete CNP phenotype is inferred from the (single or replicate) quantitative measure within the analysis, whilst assuming an allele based system segregating through the pedigree. [source] Duplication, divergence and formation of novel protein topologiesBIOESSAYS, Issue 10 2006Christine Vogel The rearrangement or permutation of protein substructures is an important mode of divergence. Recent work1 explored one possible underlying mechanism called permutation-by-duplication, which produces special forms of motif rearrangements called circular permutations. Permutation-by-duplication, involving gene duplication, fusion and truncation, can produce fully functional intermediate proteins1 and thus represents a feasible mechanism of protein evolution. In spite of this, circular permutations are relatively rare and we discuss possible reasons for their existence. BioEssays 28: 973,978, 2006. © 2006 Wiley Periodicals, Inc. [source] Exact Log-Rank Tests for Unequal Follow-UpBIOMETRICS, Issue 4 2003Georg Heinze Summary. The asymptotic log-rank and generalized Wilcoxon tests are the standard procedures for comparing samples of possibly censored survival times. For comparison of samples of very different sizes, an exact test is available that is based on a complete permutation of log-rank or Wilcoxon scores. While the asymptotic tests do not keep their nominal sizes if sample sizes differ substantially, the exact complete permutation test requires equal follow-up of the samples. Therefore, we have developed and present two new exact tests also suitable for unequal follow-up. The first of these is an exact analogue of the asymptotic log-rank test and conditions on observed risk sets, whereas the second approach permutes survival times while conditioning on the realized follow-up in each group. In an empirical study, we compare the new procedures with the asymptotic log-rank test, the exact complete permutation test, and an earlier proposed approach that equalizes the follow-up distributions using artificial censoring. Results confirm highly satisfactory performance of the exact procedure conditioning on realized follow-up, particularly in case of unequal follow-up. The advantage of this test over other options of analysis is finally exemplified in the analysis of a breast cancer study. [source] OUTLYING OBSERVATIONS AND MISSING VALUES: HOW SHOULD THEY BE HANDLED?CLINICAL AND EXPERIMENTAL PHARMACOLOGY AND PHYSIOLOGY, Issue 5-6 2008John Ludbrook SUMMARY 1The problems of, and best solutions for, outlying observations and missing values are very dependent on the sizes of the experimental groups. For original articles published in Clinical and Experimental Pharmacology and Physiology during 2006,2007, the range of group sizes ranged from three to 44 (,small groups'). In surveys, epidemiological studies and clinical trials, the group sizes range from 100s to 1000s (,large groups'). 2How can one detect outlying (extreme) observations? The best methods are graphical, for instance: (i) a scatterplot, often with mean±2 s; and (ii) a box-and-whisker plot. Even with these, it is a matter of judgement whether observations are truly outlying. 3It is permissable to delete or replace outlying observations if an independent explanation for them can be found. This may be, for instance, failure of a piece of measuring equipment or human error in operating it. If the observation is deleted, it can then be treated as a missing value. Rarely, the appropriate portion of the study can be repeated. 4It is decidedly not permissable to delete unexplained extreme values. Some of the acceptable strategies for handling them are: (i) transform the data and proceed with conventional statistical analyses; (ii) use the mean for location, but use permutation (randomization) tests for comparing means; and (iii) use robust methods for describing location (e.g. median, geometric mean, trimmed mean), for indicating dispersion (range, percentiles), for comparing locations and for regression analysis. 5What can be done about missing values? Some strategies are: (i) ignore them; (ii) replace them by hand if the data set is small; and (iii) use computerized imputation techniques to replace them if the data set is large (e.g. regression or EM (conditional Expectation, Maximum likelihood estimation) methods). 6If the missing values are ignored, or even if they are replaced, it is essential to test whether the individuals with missing values are otherwise indistinguishable from the remainder of the group. If the missing values have not occurred at random, but are associated with some property of the individuals being studied, the subsequent analysis may be biased. [source] Moderate deviations for longest increasing subsequences: The upper tailCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2001Matthias Löwe We derive the upper-tail moderate deviations for the length of a longest increasing subsequence in a random permutation. This concerns the regime between the upper-tail large-deviation regime and the central limit regime. Our proof uses a formula to describe the relevant probabilities in terms of the solution of the rank 2 Riemann-Hilbert problem (RHP); this formula was invented by Baik, Deift, and Johansson [3] to find the central limit asymptotics of the same quantities. In contrast to the work of these authors, who apply a third-order (nonstandard) steepest-descent approximation at an inflection point of the transition matrix elements of the RHP, our approach is based on a (more classical) second-order (Gaussian) saddle point approximation at the stationary points of the transition function matrix elements. © 2001 John Wiley & Sons, Inc. [source] | ||||||||||||||||||||||||||||||||||||||||