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Inference Procedures (inference + procedure)
Selected AbstractsA two-step procedure for constructing confidence intervals of trait loci with application to a rheumatoid arthritis datasetGENETIC EPIDEMIOLOGY, Issue 1 2006Charalampos Papachristou Abstract Preliminary genome screens are usually succeeded by fine mapping analyses focusing on the regions that signal linkage. It is advantageous to reduce the size of the regions where follow-up studies are performed, since this will help better tackle, among other things, the multiplicity adjustment issue associated with them. We describe a two-step approach that uses a confidence set inference procedure as a tool for intermediate mapping (between preliminary genome screening and fine mapping) to further localize disease loci. Apart from the usual Hardy-Weiberg and linkage equilibrium assumptions, the only other assumption of the proposed approach is that each region of interest houses at most one of the disease-contributing loci. Through a simulation study with several two-locus disease models, we demonstrate that our method can isolate the position of trait loci with high accuracy. Application of this two-step procedure to the data from the Arthritis Research Campaign National Repository also led to highly encouraging results. The method not only successfully localized a well-characterized trait contributing locus on chromosome 6, but also placed its position to narrower regions when compared to their LOD support interval counterparts based on the same data. Genet. Epidemiol. 30:18,29, 2006. © 2005 Wiley-Liss, Inc. [source] Modularizing inference in large causal probabilistic networksINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2003Kristian G. Olesen This article describes a number of implementation aspects of modular inference in large medical expert systems based on causal probabilistic networks. Examples are provided from the neuromuscular diagnosting system the muscle and nerve inference network (MUNIN). The inference procedure is outlined and the principal data structure underlying the inference procedure are described. A condensed summary of selected technical details of the inference procedure in causal probabilistic networks (CPNs) is provided. This is required for understanding the implemented modularization of the inference. The modularization of the inference implies a need for transfer of information between modules, which is realized by establishing communication channels between modules. Modules are also used to perform inference by conditioning, a method that reduces storage requirements to a manageable size and thereby prepares the way for MUNINs migration to common PCs. © 2003 Wiley Periodicals, Inc. [source] Failure time regression with continuous covariates measured with errorJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2000Halbo Zhou We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on-going epidemiologic study. [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 Bonaïti-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 naïve 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] Semiparametric Analysis for Recurrent Event Data with Time-Dependent Covariates and Informative CensoringBIOMETRICS, Issue 1 2010C.-Y. Huang Summary Recurrent event data analyses are usually conducted under the assumption that the censoring time is independent of the recurrent event process. In many applications the censoring time can be informative about the underlying recurrent event process, especially in situations where a correlated failure event could potentially terminate the observation of recurrent events. In this article, we consider a semiparametric model of recurrent event data that allows correlations between censoring times and recurrent event process via frailty. This flexible framework incorporates both time-dependent and time-independent covariates in the formulation, while leaving the distributions of frailty and censoring times unspecified. We propose a novel semiparametric inference procedure that depends on neither the frailty nor the censoring time distribution. Large sample properties of the regression parameter estimates and the estimated baseline cumulative intensity functions are studied. Numerical studies demonstrate that the proposed methodology performs well for realistic sample sizes. An analysis of hospitalization data for patients in an AIDS cohort study is presented to illustrate the proposed method. [source] Estimation of population size for additive,multiplicative models based on continuous-time recapture experimentsENVIRONMETRICS, Issue 8 2002Yan Wang Abstract An additive,multiplicative model and a Horvitz,Thompson-type estimator are proposed to estimate the unknown population size in a continuous-time recapture experiment. The proposed inference about the model parameters of the capture intensity is similar to that of Lin and Ying (1995). However, the population size in a recapture experiment is not known and a modification is needed. Simulation results are given to assess the properties of the proposed estimators and the associated inference procedures. A set of recapture data for deer mice is presented to demonstrate the performance of the estimating procedure. Copyright © 2002 John Wiley & Sons, Ltd. [source] Connectionist symbolic rule encoding using a generalized phase-locking mechanismEXPERT SYSTEMS, Issue 1 2000Nam Seog Park This paper describes a connectionist inference architecture which performs standard symbolic inference on a subclass of first-order predicate calculus. This work first involves constructing efficient connectionist mechanisms to represent basic symbol components, dynamic bindings and basic symbolic inference procedures, and devising a set of algorithms which automatically translates input descriptions to localist neural networks. These connectionist mechanisms are built by taking an existing phase-locking mechanism and extending it further to obtain desirable features to represent and manipulate basic symbol structures. The existing phase-locking mechanism represents dynamic bindings very efficiently using temporal synchronous activity between neuron elements but has fundamental limitations in supporting standard symbolic inference. The extension addresses these limitations. The extended system encodes a significant subset of a Horn clause language in a connectionist style. [source] Semiparametric variance-component models for linkage and association analyses of censored trait dataGENETIC EPIDEMIOLOGY, Issue 7 2006G. Diao Abstract Variance-component (VC) models are widely used for linkage and association mapping of quantitative trait loci in general human pedigrees. Traditional VC methods assume that the trait values within a family follow a multivariate normal distribution and are fully observed. These assumptions are violated if the trait data contain censored observations. When the trait pertains to age at onset of disease, censoring is inevitable because of loss to follow-up and limited study duration. Censoring also arises when the trait assay cannot detect values below (or above) certain thresholds. The latent trait values tend to have a complex distribution. Applying traditional VC methods to censored trait data would inflate type I error and reduce power. We present valid and powerful methods for the linkage and association analyses of censored trait data. Our methods are based on a novel class of semiparametric VC models, which allows an arbitrary distribution for the latent trait values. We construct appropriate likelihood for the observed data, which may contain left or right censored observations. The maximum likelihood estimators are approximately unbiased, normally distributed, and statistically efficient. We develop stable and efficient numerical algorithms to implement the corresponding inference procedures. Extensive simulation studies demonstrate that the proposed methods outperform the existing ones in practical situations. We provide an application to the age at onset of alcohol dependence data from the Collaborative Study on the Genetics of Alcoholism. A computer program is freely available. Genet. Epidemiol. 2006. © 2006 Wiley-Liss, Inc. [source] Maximum likelihood estimation in semiparametric regression models with censored dataJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2007D. Zeng Summary., Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the existing models in important directions. We construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters. The maximum likelihood estimators are consistent and asymptotically normal with efficient variances. We develop simple and stable numerical techniques to implement the corresponding inference procedures. Extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings. Applications to three medical studies yield important new insights. We conclude that there is no reason, theoretical or numerical, not to use maximum likelihood estimation for semiparametric regression models. We discuss several areas that need further research. [source] Penalized spline models for functional principal component analysisJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2006Fang Yao Summary., We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients. For the handling of the within-subject correlation, we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject. The resulting data after iteration are theoretically shown to be asymptotically equivalent (in probability) to a set of independent data. This suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data. The effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data. [source] Bayesian change-point analysis for atomic force microscopy and soft material indentationJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 4 2010Daniel Rudoy Summary., Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently, the advent of atomic force microscopy, which operates on the same fundamental principle, has in turn revolutionized the nanoscale analysis of soft biomaterials such as cells and tissues. The paper addresses the inferential problems that are associated with material indentation and atomic force microscopy, through a framework for the change-point analysis of pre-contact and post-contact data that is applicable to experiments across a variety of physical scales. A hierarchical Bayesian model is proposed to account for experimentally observed change-point smoothness constraints and measurement error variability, with efficient Monte Carlo methods developed and employed to realize inference via posterior sampling for parameters such as Young's modulus, which is a key quantifier of material stiffness. These results are the first to provide the materials science community with rigorous inference procedures and quantification of uncertainty, via optimized and fully automated high throughput algorithms, implemented as the publicly available software package BayesCP. To demonstrate the consistent accuracy and wide applicability of this approach, results are shown for a variety of data sets from both macromaterials and micromaterials experiments,including silicone, neurons and red blood cells,conducted by the authors and others. [source] Sen measures of poverty in the United States: Cash versus comprehensive incomes in the 1990sPACIFIC ECONOMIC REVIEW, Issue 2 2001John Formby Recently developed statistical inference procedures for the Sen index and its components , the headcount, income gap and Gini index among the poor , are used to test explicit hypotheses concerning aggregate poverty in the United States for the period 1989 to 1997. Changes in Sen measures of poverty are investigated for cash and comprehensive income using the official poverty line and six additional poverty lines drawn using thresholds set at 50, 75, 125, 150, 175 and 200 percent of the official level. The paper also reports on the effects of using comprehensive income on subgroup poverty rates and on the demographic composition of the poor. [source] Modeling repair events under intermittent failures and failures subject to unsuccessful repairQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2002C. K. Hansen Abstract Intermittent failures are sometimes observed for a repairable system, such as an automobile. Such failures often lead to a series of unsuccessful repair attempts before the source of the failure has been identified and removed. Unsuccessful repair is also observed in cases where the failures are not intermittent. In order to model data involving repeated repair attempts related to the same failure, repair times cannot usually be assumed negligible and the model must be designed or modified to account for these. In this paper, we propose a modified version of the branching Poisson process model introduced by Lewis (1964). We discuss statistical inference procedures for this model and demonstrate these procedures using the service history of a new automobile. Copyright © 2002 John Wiley & Sons, Ltd. [source] Estimation methods for time-dependent AUC models with survival dataTHE CANADIAN JOURNAL OF STATISTICS, Issue 1 2010Hung Hung Abstract The performance of clinical tests for disease screening is often evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Recent developments have extended the traditional setting to the AUC with binary time-varying failure status. Without considering covariates, our first theme is to propose a simple and easily computed nonparametric estimator for the time-dependent AUC. Moreover, we use generalized linear models with time-varying coefficients to characterize the time-dependent AUC as a function of covariate values. The corresponding estimation procedures are proposed to estimate the parameter functions of interest. The derived limiting Gaussian processes and the estimated asymptotic variances enable us to construct the approximated confidence regions for the AUCs. The finite sample properties of our proposed estimators and inference procedures are examined through extensive simulations. An analysis of the AIDS Clinical Trials Group (ACTG) 175 data is further presented to show the applicability of the proposed methods. The Canadian Journal of Statistics 38:8,26; 2010 © 2009 Statistical Society of Canada La performance des tests cliniques pour le dépistage de maladie est souvent évaluée en utilisant l'aire sous la courbe caractéristique de fonctionnements du récepteur (, ROC , ), notée , AUC , . Des développements récents ont généralisé le cadre traditionnel à l'AUC avec un statut de panne binaire variant dans le temps. Sans considérer les covariables, nous commençons par proposer un estimateur non paramétrique pour l'AUC simple et facile à calculer. De plus, nous utilisons des modèles linéaires généralisés avec des coefficients dépendant du temps pour caractériser les AUC, dépendant du temps, comme fonction des covariables. Les procédures d'estimation asociées correspondantes sont proposées afin d'estimer les fonctions paramètres d'intérêt. Les processus gaussiens limites sont obtenus ainsi que les variances asymptotiques estimées afin de construire des régions de confiance approximatives pour les AUC. À l'aide de nombreuses simulations, les propriétés pour de petits échantillons des estimateurs proposés et des procédures d'inférence sont étudiées. Une analyse du groupe d'essais cliniques sur le sida 175 (ACTG 175) est aussi présentée afin de montrer l'applicabilité des méthodes proposées. La revue canadienne de statistique 38: 8,26; 2010 © 2009 Société statistique du Canada [source] Robust sequential designs for nonlinear regressionTHE CANADIAN JOURNAL OF STATISTICS, Issue 4 2002Sanjoy Sinha Abstract The authors introduce the formal notion of an approximately specified nonlinear regression model and investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. They present small-sample simulation studies which indicate that their new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecifi-cation and to heteroscedastic variation. Their simulations also suggest that standard normal-theory inference procedures remain approximately valid under the sequential sampling schemes. The methods are illustrated both by simulation and in an example using data from an experiment described in the chemical engineering literature. Les auteurs définissent formellement le concept de modéle de régression non linéaire approxima-tif et proposentdes plans d'expérience séquentiels pour les situations o4uG la forme paramétrique du modéle ajusté est inexacte. Ils présentent une étude de simulation qui montre que, pour de petits échantillons, leurs nouveaux plans sont largement préférables aux plans usuels en terme de réduction de I'erreur quadratique moyenne associée à rinadéquation du modéle et à l'hétéroscédasticité. Leurs simulations montrent aussi que les procédures d'inférence classiques associées au paradigme normal restent valables, à peu de choses prés, pour ces plans expéimentaux se'quentiels. La methodologie proposde est illustrée par voie de simulation et au moyen d'une application concréte tirée de la pratique du génie chimique. [source] Bootstrapping Autoregression under Non-stationary VolatilityTHE ECONOMETRICS JOURNAL, Issue 1 2008Ke-Li Xu Summary This paper studies robust inference in autoregression around a polynomial trend with stable autoregressive roots under non-stationary volatility. The formulation of the volatility process is quite general including many existing deterministic and stochastic non-stationary volatility specifications. The aim of the paper is two-fold. First, it develops a limit theory for least squares estimators and shows how non-stationary volatility affects the consistency, convergence rates and asymptotic distributions of the slope and trend coefficients estimators in different ways. This complements the results recently obtained by Chung and Park (2007, Journal of Econometrics 137, 230,59. Second, it studies the recursive wild bootstrap procedure of Gonçalves and Kilian (2004, Journal of Econometrics 123, 89,120) in the presence of non-stationary volatility, and shows its validity when the estimates are asymptotically mixed Gaussian. Simulations are performed to compare favourably the recursive wild bootstrap with other inference procedures under non-stationary volatility. [source] Least squares estimation and tests of breaks in mean and variance under misspecificationTHE ECONOMETRICS JOURNAL, Issue 1 2004Jean-Yves Pitarakis Summary In this paper we investigate the consequences of misspecification on the large sample properties of change-point estimators and the validity of tests of the null hypothesis of linearity versus the alternative of a structural break. Specifically this paper concentrates on the interaction of structural breaks in the mean and variance of a time series when either of the two is omitted from the estimation and inference procedures. Our analysis considers the case of a break in mean under omitted-regime-dependent heteroscedasticity and that of a break in variance under an omitted mean shift. The large and finite sample properties of the resulting least-squares-based estimators are investigated and the impact of the two types of misspecification on inferences about the presence or absence of a structural break subsequently analysed. [source] Semiparametric Transformation Models with Random Effects for Joint Analysis of Recurrent and Terminal EventsBIOMETRICS, Issue 3 2009Donglin Zeng Summary We propose a broad class of semiparametric transformation models with random effects for the joint analysis of recurrent events and a terminal event. The transformation models include proportional hazards/intensity and proportional odds models. We estimate the model parameters by the nonparametric maximum likelihood approach. The estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Simple and stable numerical algorithms are provided to calculate the parameter estimators and to estimate their variances. Extensive simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two HIV/AIDS studies are presented. [source] Identifying Subjects Who Benefit from Additional Information for Better Prediction of the Outcome VariablesBIOMETRICS, Issue 3 2009L. Tian Summary Suppose that we are interested in using new bio- or clinical markers, in addition to the conventional markers, to improve prediction or diagnosis of the patient's clinical outcome. The incremental value from the new markers is typically assessed by averaging across patients in the entire study population. However, when measuring the new markers is costly or invasive, an overall improvement does not justify measuring the new markers in all patients. A more practical strategy is to utilize the patient's conventional markers to decide whether the new markers are needed for improving prediction of his/her health outcomes. In this article, we propose inference procedures for the incremental values of new markers across various subgroups of patients classified by the conventional markers. The resulting point and interval estimates can be quite useful for medical decision makers seeking to balance the predictive or diagnostic value of new markers against their associated cost and risk. Our proposals are theoretically justified and illustrated empirically with two real examples. [source] A Semiparametric Odds Ratio Model for Measuring AssociationBIOMETRICS, Issue 2 2007Hua Yun Chen Summary We propose a semiparametric odds ratio model to measure the association between two variables taking discrete values, continuous values, or a mixture of both. Methods for estimation and inference with varying degrees of robustness to model assumptions are studied. Semiparametric efficient estimation and inference procedures are also considered. The estimation methods are compared in a simulation study and applied to the study of associations among genital tract bacterial counts in HIV infected women. [source] Nonparametric Inference for Local Extrema with Application to Oligonucleotide Microarray Data in Yeast GenomeBIOMETRICS, Issue 2 2006Peter X.-K. Summary Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing. [source] Capture,Recapture When Time and Behavioral Response Affect Capture ProbabilitiesBIOMETRICS, Issue 2 2000Anne Chao Summary. We consider a capture,recapture model in which capture probabilities vary with time and with behavioral response. Two inference procedures are developed under the assumption that recapture probabilities bear a constant relationship to initial capture probabilities. These two procedures are the maximum likelihood method (both unconditional and conditional types are discussed) and an approach based on optimal estimating functions. The population size estimators derived from the two procedures are shown to be asymptotically equivalent when population size is large enough. The performance and relative merits of various population size estimators for finite cases are discussed. The bootstrap method is suggested for constructing a variance estimator and confidence interval. An example of the deer mouse analyzed in Otis et al. (1978, Wildlife Monographs62, 93) is given for illustration. [source] Statistical models of syntax learning and useCOGNITIVE SCIENCE - A MULTIDISCIPLINARY JOURNAL, Issue 3 2002Mark Johnson Abstract This paper shows how to define probability distributions over linguistically realistic syntactic structures in a way that permits us to define language learning and language comprehension as statistical problems. We demonstrate our approach using lexical-functional grammar (LFG), but our approach generalizes to virtually any linguistic theory. Our probabilistic models are maximum entropy models. In this paper we concentrate on statistical inference procedures for learning the parameters that define these probability distributions. We point out some of the practical problems that make straightforward ways of estimating these distributions infeasible, and develop a "pseudo-likelihood" estimation procedure that overcomes some of these problems. This method raises interesting questions concerning the nature of the data available to a language learner and the modularity of language learning and processing. [source] | ||||||||||||||||||||||