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## Ratio Test (ratio + test)
Kinds of Ratio Test
## Selected Abstracts## A Conditional Likelihood Ratio Test for Structural Models ECONOMETRICA, Issue 4 2003Marcelo J. MoreiraThis paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak. [source] ## Decision Theory Applied to an Instrumental Variables Model ECONOMETRICA, Issue 3 2007Gary ChamberlainThis paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced-form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear regression functions and a known covariance matrix. A canonical form of the model has parameter vector (,, ,, ,), where ,is the parameter of interest and is normalized to be a point on the unit circle. The reduced-form coefficients on the instrumental variables are split into a scalar parameter ,and a parameter vector ,, which is normalized to be a point on the (k,1)-dimensional unit sphere; ,measures the strength of the association between the endogenous variables and the instrumental variables, and ,is a measure of direction. A prior distribution is introduced for the IV model. The parameters ,, ,, and ,are treated as independent random variables. The distribution for ,is uniform on the unit circle; the distribution for ,is uniform on the unit sphere with dimension k-1. These choices arise from the solution of a minimax problem. The prior for ,is left general. It turns out that given any positive value for ,, the Bayes estimator of ,does not depend on ,; it equals the maximum-likelihood estimator. This Bayes estimator has constant risk; because it minimizes average risk with respect to a proper prior, it is minimax. The same general concepts are applied to obtain confidence intervals. The prior distribution is used in two ways. The first way is to integrate out the nuisance parameter ,in the IV model. This gives an integrated likelihood function with two scalar parameters, ,and ,. Inverting a likelihood ratio test, based on the integrated likelihood function, provides a confidence interval for ,. This lacks finite sample optimality, but invariance arguments show that the risk function depends only on ,and not on ,or ,. The second approach to confidence sets aims for finite sample optimality by setting up a loss function that trades off coverage against the length of the interval. The automatic uniform priors are used for ,and ,, but a prior is also needed for the scalar ,, and no guidance is offered on this choice. The Bayes rule is a highest posterior density set. Invariance arguments show that the risk function depends only on ,and not on ,or ,. The optimality result combines average risk and maximum risk. The confidence set minimizes the average,with respect to the prior distribution for ,,of the maximum risk, where the maximization is with respect to ,and ,. [source] ## Testing for separability of space,time covariances ENVIRONMETRICS, Issue 8 2005Matthew W. MitchellAbstract Separable space,time covariance models are often used for modeling in environmental sciences because of their computational benefits. Unfortunately, there are few formal statistical tests for separability. We adapt a likelihood ratio test based on multivariate repeated measures to the spatio,temporal context. We apply this test to an environmental monitoring data set. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Design of change detection algorithms based on the generalized likelihood ratio test ENVIRONMETRICS, Issue 8 2001Giovanna CapizziAbstract A design procedure for detecting additive changes in a state-space model is proposed. Since the mean of the observations after the change is unknown, detection algorithms based on the generalized likelihood ratio test, GLR, and on window-limited type GLR, are considered. As Lai (1995) pointed out, it is very difficult to find a satisfactory choice of both window size and threshold for these change detection algorithms. The basic idea of this article is to estimate, through the stochastic approximation of Robbins and Monro, the threshold value which satisfies a constraint on the mean between false alarms, for a specified window size. A convenient stopping rule, based on the first passage time of an F -statistic below a fixed boundary, is used to terminate the iterative approximation. Then, the window size which produces the most desirable out-of-control ARL, for a fixed value of the in-control ARL, can be selected. These change detection algorithms are applied to detect biases on the measurements of ozone, recorded from one monitoring site of Bologna (Italy). Comparisons of the ARL profiles reveal that the full-GLR scheme provides much more protection than the window-limited GLR schemes against small shifts in the process, but the modified window-limited GLR provides more protection against large shifts. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Sequential methods and group sequential designs for comparative clinical trials FUNDAMENTAL & CLINICAL PHARMACOLOGY, Issue 5 2003Véronique SébilleAbstract Comparative clinical trials are performed to assess whether a new treatment has superior efficacy than a placebo or a standard treatment (one-sided formulation) or whether two active treatments have different efficacies (two-sided formulation) in a given population. The reference approach is the single-stage design and the statistical test is performed after inclusion and evaluation of a predetermined sample size. In practice, the single-stage design is sometimes difficult to implement because of ethical concerns and/or economic reasons. Thus, specific early termination procedures have been developed to allow repeated statistical analyses to be performed on accumulating data and stop the trial as soon as the information is sufficient to conclude. Two main different approaches can be used. The first one is derived from strictly sequential methods and includes the sequential probability ratio test and the triangular test. The second one is derived from group sequential designs and includes Peto, Pocock, and O'Brien and Fleming methods, , and , spending functions, and one-parameter boundaries. We review all these methods and describe the bases on which they rely as well as their statistical properties. We also compare these methods and comment on their advantages and drawbacks. We present software packages which are available for the planning, monitoring and analysis of comparative clinical trials with these methods and discuss the practical problems encountered when using them. The latest versions of all these methods can offer substantial sample size reductions when compared with the single-stage design not only in the case of clear efficacy but also in the case of complete lack of efficacy of the new treatment. The software packages make their use quite simple. However, it has to be stressed that using these methods requires efficient logistics with real-time data monitoring and, apart from survival studies or long-term clinical trials with censored endpoints, is most appropriate when the endpoint is obtained quickly when compared with the recruitment rate. [source] ## Differential parental transmission of markers in RUNX2 among cleft case-parent trios from four populations GENETIC EPIDEMIOLOGY, Issue 6 2008Jae Woong SullAbstract Isolated cleft lip with or without cleft palate (CL/P) is among the most common human birth defects, with a prevalence around 1 in 700 live births. The Runt-related transcription factor 2 (RUNX2) gene has been suggested as a candidate gene for CL/P based largely on mouse models; however, no human studies have focused on RUNX2 as a risk factor for CL/P. This study examines the association between markers in RUNX2 and isolated, nonsyndromic CL/P using a case-parent trio design, while considering parent-of-origin effects. Case-parent trios from four populations (77 from Maryland, 146 from Taiwan, 35 from Singapore, and 40 from Korea) were genotyped for 24 single nucleotide polymorphisms (SNPs) in the RUNX2 gene. We performed the transmission disequilibrium test on individual SNPs. Parent-of-origin effects were assessed using the transmission asymmetry test and the parent-of-origin likelihood ratio test (PO-LRT). When all trios were combined, the transmission asymmetry test revealed a block of 11 SNPs showing excess maternal transmission significant at the P<0.01 level, plus one SNP (rs1934328) showing excess paternal transmission (P=0.002). For the 11 SNPs showing excess maternal transmission, odds ratios of being transmitted to the case from the mother ranged between 3.00 and 4.00. The parent-of-origin likelihood ratio tests for equality of maternal and paternal transmission were significant for three individual SNPs (rs910586, rs2819861, and rs1934328). Thus, RUNX2 appears to influence risk of CL/P through a parent-of-origin effect with excess maternal transmission. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source] ## An efficient adaptive algorithm for edge detection based on the likelihood ratio test INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2002A. De SantisAbstract The edge detection problem in blurred and noisy 2-D signals is dealt with. An adaptive signal processing algorithm is proposed which marks edge points according to an hypothesis test which compares the likelihoods of two models describing the local signal behaviour in the two cases of absence/presence of an edge. The two models are identified by a regularized least squares estimation algorithm, obtaining a numerically efficient procedure, quite robust with respect to additive noise and blurr perturbation. No global thresholding or data prefiltering is required. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Modelling of small-angle X-ray scattering data using Hermite polynomials JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2001A. K. SwainA new algorithm, called the term-selection algorithm (TSA), is derived to treat small-angle X-ray scattering (SAXS) data by fitting models to the scattering intensity using weighted Hermite polynomials. This algorithm exploits the orthogonal property of the Hermite polynomials and introduces an error-reduction ratio test to select the correct model terms or to determine which polynomials are to be included in the model and to estimate the associated unknown coefficients. With no a priori information about particle sizes, it is possible to evaluate the real-space distribution function as well as three- and one-dimensional correlation functions directly from the models fitted to raw experimental data. The success of this algorithm depends on the choice of a scale factor and the accuracy of orthogonality of the Hermite polynomials over a finite range of SAXS data. An algorithm to select a weighted orthogonal term is therefore derived to overcome the disadvantages of the TSA. This algorithm combines the properties and advantages of both weighted and orthogonal least-squares algorithms and is numerically more robust for the estimation of the parameters of the Hermite polynomial models. The weighting feature of the algorithm provides an additional degree of freedom to control the effects of noise and the orthogonal feature enables the reorthogonalization of the Hermite polynomials with respect to the weighting matrix. This considerably reduces the error in orthogonality of the Hermite polynomials. The performance of the algorithm has been demonstrated considering both simulated data and experimental data from SAXS measurements of dewaxed cotton fibre at different temperatures. [source] ## Cryptic differentiation and geographic variation in genetic diversity of Hall's Babbler Pomatostomus halli JOURNAL OF AVIAN BIOLOGY, Issue 2 2001Grant I. MiuraSequence variation was examined in domain I of the mitochondrial control region in three Queensland populations of Hall's Babbler Pomatostomus halli, a geographically restricted, monotypic songbird in eastern Australia. Surprisingly, we found that domain I sequences were strongly differentiated into two major clades differing by 3.29%. These two clades exhibited nearly complete geographic concordance with northern and southern populations, except for two haplotypes which were sampled in the north of the range but were phylogenetically allied to the southern clade. We also found a seven-fold higher level of genetic diversity in the northern than in the southern populations. Neutrality and molecular clock tests suggested that selection or differences in substitution rates were not responsible for this difference in diversity. However, a maximum likelihood analysis of gene flow between the north and south suggested that the difference in diversity could be due to both greater population size in the north and asymmetric gene flow dominated by south to north dispersal events. A likelihood ratio test rejected a model in which population sizes were equal and rates of gene flow symmetric, and came close to rejecting a model in which only population sizes were constrained to be equal. These results suggest that different population sizes and asymmetric gene flow could be a major source of differences in genetic variation between populations of Hall's Babbler, although ecological and biogeographic causes for these differences are obscure. [source] ## Single-season heteroscedasticity in time series JOURNAL OF FORECASTING, Issue 3 2007Yorghos TripodisAbstract We consider seasonal time series in which one season has variance that is different from all the others. This behaviour is evident in indices of production where variability is highest for the month with the lowest level of production. We show that when one season has different variability from others there are constraints on the seasonal models that can be used; neither dummy and trigonometric models are effective in modelling this type of behaviour. We define a general model that provides an appropriate representation of single-season heteroscedasticity and suggest a likelihood ratio test for the presence of periodic variance in one season.,,Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Sample Size Determination for Categorical Responses JOURNAL OF FORENSIC SCIENCES, Issue 1 2009Dimitris Mavridis Ph.D.Abstract:, Procedures are reviewed and recommendations made for the choice of the size of a sample to estimate the characteristics (sometimes known as parameters) of a population consisting of discrete items which may belong to one and only one of a number of categories with examples drawn from forensic science. Four sampling procedures are described for binary responses, where the number of possible categories is only two, e.g., licit or illicit pills. One is based on priors informed from historical data. The other three are sequential. The first of these is a sequential probability ratio test with a stopping rule derived by controlling the probabilities of type 1 and type 2 errors. The second is a sequential variation of a procedure based on the predictive distribution of the data yet to be inspected and the distribution of the data that have been inspected, with a stopping rule determined by a prespecified threshold on the probability of a wrong decision. The third is a two-sided sequential criterion which stops sampling when one of two competitive hypotheses has a probability of being accepted which is larger than another prespecified threshold. The fifth procedure extends the ideas developed for binary responses to multinomial responses where the number of possible categories (e.g., types of drug or types of glass) may be more than two. The procedure is sequential and recommends stopping when the joint probability interval or ellipsoid for the estimates of the proportions is less than a given threshold in size. For trinomial data this last procedure is illustrated with a ternary diagram with an ellipse formed around the sample proportions. There is a straightforward generalization of this approach to multinomial populations with more than three categories. A conclusion provides recommendations for sampling procedures in various contexts. [source] ## Design for model parameter uncertainty using nonlinear confidence regions AICHE JOURNAL, Issue 8 2001William C. RooneyAn accurate method presented accounts for uncertain model parameters in nonlinear process optimization problems. The model representation is considered in terms of algebraic equations. Uncertain quantity parameters are often discretized into a number of finite values that are then used in multiperiod optimization problems. These discrete values usually range between some lower and upper bound that can be derived from individual confidence intervals. Frequently, more than one uncertain parameter is estimated at a time from a single set of experiments. Thus, using simple lower and upper bounds to describe these parameters may not be accurate, since it assumes the parameters are uncorrelated. In 1999 Rooney and Biegler showed the importance of including parameter correlation in design problems by using elliptical joint confidence regions to describe the correlation among the uncertain model parameters. In chemical engineering systems, however, the parameter estimation problem is often highly nonlinear, and the elliptical confidence regions derived from these problems may not be accurate enough to capture the actual model parameter uncertainty. In this work, the description of model parameter uncertainty is improved by using confidence regions derived from the likelihood ratio test. It captures the nonlinearities efficiently and accurately in the parameter estimation problem. Several examples solved show the importance of accurately capturing the actual model parameter uncertainty at the design stage. [source] ## Sequential case series analysis for pharmacovigilance JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2009Mounia N. HocineSummary., The self-controlled case series method is used to evaluate drug safety, particularly the safety of paediatric vaccines with respect to rare adverse reactions. We propose a group sequential version of the method for prospective surveillance of drug safety. We focus on the surveillance of new vaccines. We develop methods that are based on the sequential probability ratio test applied at predetermined surveillance intervals, using both simple and composite alternative hypotheses. We investigate the properties of the methods analytically in a simple setting and by simulations in more realistic scenarios. The methods are applied to data on influenza vaccine and Bell's palsy, and to data on measles, mumps and rubella vaccine and bleeding disorders. [source] ## Correlating two continuous variables subject to detection limits in the context of mixture distributions JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 5 2005Haitao ChuSummary., In individuals who are infected with human immunodeficiency virus (HIV), distributions of quantitative HIV ribonucleic acid measurements may be highly left censored with an extra spike below the limit of detection LD of the assay. A two-component mixture model with the lower component entirely supported on [0, LD] is recommended to model the extra spike in univariate analysis better. Let LD1 and LD2 be the limits of detection for the two HIV viral load measurements. When estimating the correlation coefficient between two different measures of viral load obtained from each of a sample of patients, a bivariate Gaussian mixture model is recommended to model the extra spike on [0, LD1] and [0, LD2] better when the proportion below LD is incompatible with the left-hand tail of a bivariate Gaussian distribution. When the proportion of both variables falling below LD is very large, the parameters of the lower component may not be estimable since almost all observations from the lower component are falling below LD. A partial solution is to assume that the lower component's entire support is on [0, LD1]×[0, LD2]. Maximum likelihood is used to estimate the parameters of the lower and higher components. To evaluate whether there is a lower component, we apply a Monte Carlo approach to assess the p -value of the likelihood ratio test and two information criteria: a bootstrap-based information criterion and a cross-validation-based information criterion. We provide simulation results to evaluate the performance and compare it with two ad hoc estimators and a single-component bivariate Gaussian likelihood estimator. These methods are applied to the data from a cohort study of HIV-infected men in Rio de Janeiro, Brazil, and the data from the Women's Interagency HIV oral study. These results emphasize the need for caution when estimating correlation coefficients from data with a large proportion of non-detectable values when the proportion below LD is incompatible with the left-hand tail of a bivariate Gaussian distribution. [source] ## A feasibility study of daytime fog and low stratus detection with TERRA/AQUA-MODIS over land METEOROLOGICAL APPLICATIONS, Issue 2 2006Jörg BendixAbstract A scheme for the detection of fog and low stratus over land during daytime based on data of the MODIS (Moderate Resolution Imaging Spectroradiometer) instrument is presented. The method is based on an initial threshold test procedure in the MODIS solar bands 1,7 (0.62,2.155µm). Fog and low stratus detection generally relies on the definition of minimum and maximum fog and low stratus properties, which are converted to spectral thresholds by means of radiative transfer calculations (RTC). Extended sensitivity studies reveal that thresholds mainly depend on the solar zenith angle and, hence, illumination-dependent threshold functions are developed. Areas covered by snow, ice and mid-/high-level clouds as well as bright/hazy land surfaces are omitted from the initial classification result by means of a subsequent cloud-top height test based on MODIS IR band 31 (at 12 µm) and a NIR/VIS ratio test. The validation of the final fog and low stratus mask generally shows a satisfactory performance of the scheme. Validation problems occur due to the late overpass time of the TERRA platform and the time lag between SYNOP and satellite observations. Apparent misclassifications are mainly found at the edge of the fog layers, probably due to over- or underestimation of fog and low stratus cover in the transition zone from fog to haze. Copyright © 2006 Royal Meteorological Society. [source] ## The Likelihood Ratio Test for the Rank of a Cointegration Submatrix, OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2006Paolo ParuoloAbstract This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent,transitory decompositions and of subhypotheses related to neutrality and long-run Granger noncausality. The proposed test has a chi-squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable. [source] ## Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ,Fan' Charts of Inflation, OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2005James MitchellAbstract This paper proposes and analyses the Kullback,Leibler information criterion (KLIC) as a unified statistical tool to evaluate, compare and combine density forecasts. Use of the KLIC is particularly attractive, as well as operationally convenient, given its equivalence with the widely used Berkowitz likelihood ratio test for the evaluation of individual density forecasts that exploits the probability integral transforms. Parallels with the comparison and combination of point forecasts are made. This and related Monte Carlo experiments help draw out properties of combined density forecasts. We illustrate the uses of the KLIC in an application to two widely used published density forecasts for UK inflation, namely the Bank of England and NIESR ,fan' charts. [source] ## Is x-height a better indicator of legibility than type size for drug labels? PACKAGING TECHNOLOGY AND SCIENCE, Issue 5 2003Laura BixAbstract In 1999 the US Food and Drug Administration published a regulation in an attempt to ensure the legibility of OTC drugs, specifying, among other things, a minimum type size of 6 points. This is problematic because different typefaces of the same size vary widely in type heights and, presumably, legibility. We hypothesized that specifying a minimum x-height, the height of the lowercase x, would produce more consistent legibility than the minimum type size specified within the regulation. Twenty-six subjects viewed two groups of typefaces using the Lockhart Legibility Instrument to quantify legibility. The first group contained typefaces that were all 6 points, but, by nature of their design, varied greatly in their x-heights. The second group was made from the same set of typefaces, but these were manipulated so that their x-heights were equal to the average x-height of group 1. A likelihood ratio test indicated that the group that varied in x-height, group 1, produced significantly more variable results than the group with equal x-heights, group 2. This indicates that specifying a minimum type size may not be the best approach for producing consistent legibility. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Adaptive charting schemes based on double sequential probability ratio tests QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 1 2009Yan LiAbstract Sequential probability ratio test (SPRT) control charts are shown to be able to detect most shifts in the mean or proportion substantially faster than conventional charts such as CUSUM charts. However, they are limited in applications because of the absence of the upper bound on the sample size and possibly large sample numbers during implementation. The double SPRT (2-SPRT) control chart, which applies a 2-SPRT at each sampling point, is proposed in this paper to solve some of the limitations of SPRT charts. Approximate performance measures of the 2-SPRT control chart are obtained by the backward method with the Gaussian quadrature in a computer program. On the basis of two industrial examples and simulation comparisons, we conclude that the 2-SPRT chart is competitive in that it is more sensitive and economical for small shifts and has advantages in administration because of fixed sampling points and a proper upper bound on the sample size. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Binomial Mixture Model-based Association Tests under Genetic Heterogeneity ANNALS OF HUMAN GENETICS, Issue 6 2009Hui ZhouSummary Most of the existing association tests for population-based case-control studies are based on comparing the mean genotype scores between the case and control groups, which may not be efficient under genetic heterogeneity. Given that most common diseases are genetically heterogeneous, caused by mutations in multiple loci, it may be beneficial to fully account for genetic heterogeneity in an association test. Here we first propose a binomial mixture model for such a purpose and develop a corresponding mixture likelihood ratio test (MLRT) for a single locus. We also consider two methods to combine single-locus-based MLRTs across multiple loci in linkage disequilibrium to boost power when causal SNPs are not genotyped. We show with a wide spectrum of numerical examples that under genetic heterogeneity the proposed tests are more powerful than some commonly used association tests. [source] ## European Mathematical Genetics Meeting, Heidelberg, Germany, 12th,13th April 2007 ANNALS OF HUMAN GENETICS, Issue 4 2007Article first published online: 28 MAY 200Saurabh Ghosh 11 Indian Statistical Institute, Kolkata, India High correlations between two quantitative traits may be either due to common genetic factors or common environmental factors or a combination of both. In this study, we develop statistical methods to extract the contribution of a common QTL to the total correlation between the components of a bivariate phenotype. Using data on bivariate phenotypes and marker genotypes for sib-pairs, we propose a test for linkage between a common QTL and a marker locus based on the conditional cross-sib trait correlations (trait 1 of sib 1 , trait 2 of sib 2 and conversely) given the identity-by-descent sharing at the marker locus. The null hypothesis cannot be rejected unless there exists a common QTL. We use Monte-Carlo simulations to evaluate the performance of the proposed test under different trait parameters and quantitative trait distributions. An application of the method is illustrated using data on two alcohol-related phenotypes from the Collaborative Study On The Genetics Of Alcoholism project. Rémi Kazma 1 , Catherine Bonaďti-Pellié 1 , Emmanuelle Génin 12 INSERM UMR-S535 and Université Paris Sud, Villejuif, 94817, France Keywords: Gene-environment interaction, sibling recurrence risk, exposure correlation Gene-environment interactions may play important roles in complex disease susceptibility but their detection is often difficult. Here we show how gene-environment interactions can be detected by investigating the degree of familial aggregation according to the exposure of the probands. In case of gene-environment interaction, the distribution of genotypes of affected individuals, and consequently the risk in relatives, depends on their exposure. We developed a test comparing the risks in sibs according to the proband exposure. To evaluate the properties of this new test, we derived the formulas for calculating the expected risks in sibs according to the exposure of probands for various values of exposure frequency, relative risk due to exposure alone, frequencies of latent susceptibility genotypes, genetic relative risks and interaction coefficients. We find that the ratio of risks when the proband is exposed and not exposed is a good indicator of the interaction effect. We evaluate the power of the test for various sample sizes of affected individuals. We conclude that this test is valuable for diseases with moderate familial aggregation, only when the role of the exposure has been clearly evidenced. Since a correlation for exposure among sibs might lead to a difference in risks among sibs in the different proband exposure strata, we also add an exposure correlation coefficient in the model. Interestingly, we find that when this correlation is correctly accounted for, the power of the test is not decreased and might even be significantly increased. Andrea Callegaro 1 , Hans J.C. Van Houwelingen 1 , Jeanine Houwing-Duistermaat 13 Dept. of Medical Statistics and Bioinformatics, Leiden University Medical Center, The Netherlands Keywords: Survival analysis, age at onset, score test, linkage analysis Non parametric linkage (NPL) analysis compares the identical by descent (IBD) sharing in sibling pairs to the expected IBD sharing under the hypothesis of no linkage. Often information is available on the marginal cumulative hazards (for example breast cancer incidence curves). Our aim is to extend the NPL methods by taking into account the age at onset of selected sibling pairs using these known marginal hazards. Li and Zhong (2002) proposed a (retrospective) likelihood ratio test based on an additive frailty model for genetic linkage analysis. From their model we derive a score statistic for selected samples which turns out to be a weighed NPL method. The weights depend on the marginal cumulative hazards and on the frailty parameter. A second approach is based on a simple gamma shared frailty model. Here, we simply test whether the score function of the frailty parameter depends on the excess IBD. We compare the performance of these methods using simulated data. Céline Bellenguez 1 , Carole Ober 2 , Catherine Bourgain 14 INSERM U535 and University Paris Sud, Villejuif, France 5 Department of Human Genetics, The University of Chicago, USA Keywords: Linkage analysis, linkage disequilibrium, high density SNP data Compared with microsatellite markers, high density SNP maps should be more informative for linkage analyses. However, because they are much closer, SNPs present important linkage disequilibrium (LD), which biases classical nonparametric multipoint analyses. This problem is even stronger in population isolates where LD extends over larger regions with a more stochastic pattern. We investigate the issue of linkage analysis with a 500K SNP map in a large and inbred 1840-member Hutterite pedigree, phenotyped for asthma. Using an efficient pedigree breaking strategy, we first identified linked regions with a 5cM microsatellite map, on which we focused to evaluate the SNP map. The only method that models LD in the NPL analysis is limited in both the pedigree size and the number of markers (Abecasis and Wigginton, 2005) and therefore could not be used. Instead, we studied methods that identify sets of SNPs with maximum linkage information content in our pedigree and no LD-driven bias. Both algorithms that directly remove pairs of SNPs in high LD and clustering methods were evaluated. Null simulations were performed to control that Zlr calculated with the SNP sets were not falsely inflated. Preliminary results suggest that although LD is strong in such populations, linkage information content slightly better than that of microsatellite maps can be extracted from dense SNP maps, provided that a careful marker selection is conducted. In particular, we show that the specific LD pattern requires considering LD between a wide range of marker pairs rather than only in predefined blocks. Peter Van Loo 1,2,3 , Stein Aerts 1,2 , Diether Lambrechts 4,5 , Bernard Thienpont 2 , Sunit Maity 4,5 , Bert Coessens 3 , Frederik De Smet 4,5 , Leon-Charles Tranchevent 3 , Bart De Moor 2 , Koen Devriendt 3 , Peter Marynen 1,2 , Bassem Hassan 1,2 , Peter Carmeliet 4,5 , Yves Moreau 36 Department of Molecular and Developmental Genetics, VIB, Belgium 7 Department of Human Genetics, University of Leuven, Belgium 8 Bioinformatics group, Department of Electrical Engineering, University of Leuven, Belgium 9 Department of Transgene Technology and Gene Therapy, VIB, Belgium 10 Center for Transgene Technology and Gene Therapy, University of Leuven, Belgium Keywords: Bioinformatics, gene prioritization, data fusion The identification of genes involved in health and disease remains a formidable challenge. Here, we describe a novel bioinformatics method to prioritize candidate genes underlying pathways or diseases, based on their similarity to genes known to be involved in these processes. It is freely accessible as an interactive software tool, ENDEAVOUR, at http://www.esat.kuleuven.be/endeavour. Unlike previous methods, ENDEAVOUR generates distinct prioritizations from multiple heterogeneous data sources, which are then integrated, or fused, into one global ranking using order statistics. ENDEAVOUR prioritizes candidate genes in a three-step process. First, information about a disease or pathway is gathered from a set of known "training" genes by consulting multiple data sources. Next, the candidate genes are ranked based on similarity with the training properties obtained in the first step, resulting in one prioritized list for each data source. Finally, ENDEAVOUR fuses each of these rankings into a single global ranking, providing an overall prioritization of the candidate genes. Validation of ENDEAVOUR revealed it was able to efficiently prioritize 627 genes in disease data sets and 76 genes in biological pathway sets, identify candidates of 16 mono- or polygenic diseases, and discover regulatory genes of myeloid differentiation. Furthermore, the approach identified YPEL1 as a novel gene involved in craniofacial development from a 2-Mb chromosomal region, deleted in some patients with DiGeorge-like birth defects. Finally, we are currently evaluating a pipeline combining array-CGH, ENDEAVOUR and in vivo validation in zebrafish to identify novel genes involved in congenital heart defects. Mark Broom 1 , Graeme Ruxton 2 , Rebecca Kilner 311 Mathematics Dept., University of Sussex, UK 12 Division of Environmental and Evolutionary Biology, University of Glasgow, UK 13 Department of Zoology, University of Cambridge, UK Keywords: Evolutionarily stable strategy, parasitism, asymmetric game Brood parasites chicks vary in the harm that they do to their companions in the nest. In this presentation we use game-theoretic methods to model this variation. Our model considers hosts which potentially abandon single nestlings and instead choose to re-allocate their reproductive effort to future breeding, irrespective of whether the abandoned chick is the host's young or a brood parasite's. The parasite chick must decide whether or not to kill host young by balancing the benefits from reduced competition in the nest against the risk of desertion by host parents. The model predicts that three different types of evolutionarily stable strategies can exist. (1) Hosts routinely rear depleted broods, the brood parasite always kills host young and the host never then abandons the nest. (2) When adult survival after deserting single offspring is very high, hosts always abandon broods of a single nestling and the parasite never kills host offspring, effectively holding them as hostages to prevent nest desertion. (3) Intermediate strategies, in which parasites sometimes kill their nest-mates and host parents sometimes desert nests that contain only a single chick, can also be evolutionarily stable. We provide quantitative descriptions of how the values given to ecological and behavioral parameters of the host-parasite system influence the likelihood of each strategy and compare our results with real host-brood parasite associations in nature. Martin Harrison 114 Mathematics Dept, University of Sussex, UK Keywords: Brood parasitism, games, host, parasite The interaction between hosts and parasites in bird populations has been studied extensively. Game theoretical methods have been used to model this interaction previously, but this has not been studied extensively taking into account the sequential nature of this game. We consider a model allowing the host and parasite to make a number of decisions, which depend on a number of natural factors. The host lays an egg, a parasite bird will arrive at the nest with a certain probability and then chooses to destroy a number of the host eggs and lay one of it's own. With some destruction occurring, either natural or through the actions of the parasite, the host chooses to continue, eject an egg (hoping to eject the parasite) or abandon the nest. Once the eggs have hatched the game then falls to the parasite chick versus the host. The chick chooses to destroy or eject a number of eggs. The final decision is made by the host, choosing whether to raise or abandon the chicks that are in the nest. We consider various natural parameters and probabilities which influence these decisions. We then use this model to look at real-world situations of the interactions of the Reed Warbler and two different parasites, the Common Cuckoo and the Brown-Headed Cowbird. These two parasites have different methods in the way that they parasitize the nests of their hosts. The hosts in turn have a different reaction to these parasites. Arne Jochens 1 , Amke Caliebe 2 , Uwe Roesler 1 , Michael Krawczak 215 Mathematical Seminar, University of Kiel, Germany 16 Institute of Medical Informatics and Statistics, University of Kiel, Germany Keywords: Stepwise mutation model, microsatellite, recursion equation, temporal behaviour We consider the stepwise mutation model which occurs, e.g., in microsatellite loci. Let X(t,i) denote the allelic state of individual i at time t. We compute expectation, variance and covariance of X(t,i), i=1,,,N, and provide a recursion equation for P(X(t,i)=z). Because the variance of X(t,i) goes to infinity as t grows, for the description of the temporal behaviour, we regard the scaled process X(t,i)-X(t,1). The results furnish a better understanding of the behaviour of the stepwise mutation model and may in future be used to derive tests for neutrality under this model. Paul O'Reilly 1 , Ewan Birney 2 , David Balding 117 Statistical Genetics, Department of Epidemiology and Public Health, Imperial, College London, UK 18 European Bioinformatics Institute, EMBL, Cambridge, UK Keywords: Positive selection, Recombination rate, LD, Genome-wide, Natural Selection In recent years efforts to develop population genetics methods that estimate rates of recombination and levels of natural selection in the human genome have intensified. However, since the two processes have an intimately related impact on genetic variation their inference is vulnerable to confounding. Genomic regions subject to recent selection are likely to have a relatively recent common ancestor and consequently less opportunity for historical recombinations that are detectable in contemporary populations. Here we show that selection can reduce the population-based recombination rate estimate substantially. In genome-wide studies for detecting selection we observe a tendency to highlight loci that are subject to low levels of recombination. We find that the outlier approach commonly adopted in such studies may have low power unless variable recombination is accounted for. We introduce a new genome-wide method for detecting selection that exploits the sensitivity to recent selection of methods for estimating recombination rates, while accounting for variable recombination using pedigree data. Through simulations we demonstrate the high power of the Ped/Pop approach to discriminate between neutral and adaptive evolution, particularly in the context of choosing outliers from a genome-wide distribution. Although methods have been developed showing good power to detect selection ,in action', the corresponding window of opportunity is small. In contrast, the power of the Ped/Pop method is maintained for many generations after the fixation of an advantageous variant Sarah Griffiths 1 , Frank Dudbridge 120 MRC Biostatistics Unit, Cambridge, UK Keywords: Genetic association, multimarker tag, haplotype, likelihood analysis In association studies it is generally too expensive to genotype all variants in all subjects. We can exploit linkage disequilibrium between SNPs to select a subset that captures the variation in a training data set obtained either through direct resequencing or a public resource such as the HapMap. These ,tag SNPs' are then genotyped in the whole sample. Multimarker tagging is a more aggressive adaptation of pairwise tagging that allows for combinations of two or more tag SNPs to predict an untyped SNP. Here we describe a new method for directly testing the association of an untyped SNP using a multimarker tag. Previously, other investigators have suggested testing a specific tag haplotype, or performing a weighted analysis using weights derived from the training data. However these approaches do not properly account for the imperfect correlation between the tag haplotype and the untyped SNP. Here we describe a straightforward approach to testing untyped SNPs using a missing-data likelihood analysis, including the tag markers as nuisance parameters. The training data is stacked on top of the main body of genotype data so there is information on how the tag markers predict the genotype of the untyped SNP. The uncertainty in this prediction is automatically taken into account in the likelihood analysis. This approach yields more power and also a more accurate prediction of the odds ratio of the untyped SNP. Anke Schulz 1 , Christine Fischer 2 , Jenny Chang-Claude 1 , Lars Beckmann 121 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany 22 Institute of Human Genetics, University of Heidelberg, Germany Keywords: Haplotype, haplotype sharing, entropy, Mantel statistics, marker selection We previously introduced a new method to map genes involved in complex diseases, using haplotype sharing-based Mantel statistics to correlate genetic and phenotypic similarity. Although the Mantel statistic is powerful in narrowing down candidate regions, the precise localization of a gene is hampered in genomic regions where linkage disequilibrium is so high that neighboring markers are found to be significant at similar magnitude and we are not able to discriminate between them. Here, we present a new approach to localize susceptibility genes by combining haplotype sharing-based Mantel statistics with an iterative entropy-based marker selection algorithm. For each marker at which the Mantel statistic is evaluated, the algorithm selects a subset of surrounding markers. The subset is chosen to maximize multilocus linkage disequilibrium, which is measured by the normalized entropy difference introduced by Nothnagel et al. (2002). We evaluated the algorithm with respect to type I error and power. Its ability to localize the disease variant was compared to the localization (i) without marker selection and (ii) considering haplotype block structure. Case-control samples were simulated from a set of 18 haplotypes, consisting of 15 SNPs in two haplotype blocks. The new algorithm gave correct type I error and yielded similar power to detect the disease locus compared to the alternative approaches. The neighboring markers were clearly less often significant than the causal locus, and also less often significant compared to the alternative approaches. Thus the new algorithm improved the precision of the localization of susceptibility genes. Mark M. Iles 123 Section of Epidemiology and Biostatistics, LIMM, University of Leeds, UK Keywords: tSNP, tagging, association, HapMap Tagging SNPs (tSNPs) are commonly used to capture genetic diversity cost-effectively. However, it is important that the efficacy of tSNPs is correctly estimated, otherwise coverage may be insufficient. If the pilot sample from which tSNPs are chosen is too small or the initial marker map too sparse, tSNP efficacy may be overestimated. An existing estimation method based on bootstrapping goes some way to correct for insufficient sample size and overfitting, but does not completely solve the problem. We describe a novel method, based on exclusion of haplotypes, that improves on the bootstrap approach. Using simulated data, the extent of the sample size problem is investigated and the performance of the bootstrap and the novel method are compared. We incorporate an existing method adjusting for marker density by ,SNP-dropping'. We find that insufficient sample size can cause large overestimates in tSNP efficacy, even with as many as 100 individuals, and the problem worsens as the region studied increases in size. Both the bootstrap and novel method correct much of this overestimate, with our novel method consistently outperforming the bootstrap method. We conclude that a combination of insufficient sample size and overfitting may lead to overestimation of tSNP efficacy and underpowering of studies based on tSNPs. Our novel approach corrects for much of this bias and is superior to the previous method. Sample sizes larger than previously suggested may still be required for accurate estimation of tSNP efficacy. This has obvious ramifications for the selection of tSNPs from HapMap data. Claudio Verzilli 1 , Juliet Chapman 1 , Aroon Hingorani 2 , Juan Pablo-Casas 1 , Tina Shah 2 , Liam Smeeth 1 , John Whittaker 124 Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, UK 25 Division of Medicine, University College London, UK Keywords: Meta-analysis, Genetic association studies We present a Bayesian hierarchical model for the meta-analysis of candidate gene studies with a continuous outcome. Such studies often report results from association tests for different, possibly study-specific and non-overlapping markers (typically SNPs) in the same genetic region. Meta analyses of the results at each marker in isolation are seldom appropriate as they ignore the correlation that may exist between markers due to linkage disequlibrium (LD) and cannot assess the relative importance of variants at each marker. Also such marker-wise meta analyses are restricted to only those studies that have typed the marker in question, with a potential loss of power. A better strategy is one which incorporates information about the LD between markers so that any combined estimate of the effect of each variant is corrected for the effect of other variants, as in multiple regression. Here we develop a Bayesian hierarchical linear regression that models the observed genotype group means and uses pairwise LD measurements between markers as prior information to make posterior inference on adjusted effects. The approach is applied to the meta analysis of 24 studies assessing the effect of 7 variants in the C-reactive protein (CRP) gene region on plasma CRP levels, an inflammatory biomarker shown in observational studies to be positively associated with cardiovascular disease. Cathryn M. Lewis 1 , Christopher G. Mathew 1 , Theresa M. Marteau 226 Dept. of Medical and Molecular Genetics, King's College London, UK 27 Department of Psychology, King's College London, UK Keywords: Risk, genetics, CARD15, smoking, model Recently progress has been made in identifying mutations that confer susceptibility to complex diseases, with the potential to use these mutations in determining disease risk. We developed methods to estimate disease risk based on genotype relative risks (for a gene G), exposure to an environmental factor (E), and family history (with recurrence risk ,R for a relative of type R). ,R must be partitioned into the risk due to G (which is modelled independently) and the residual risk. The risk model was then applied to Crohn's disease (CD), a severe gastrointestinal disease for which smoking increases disease risk approximately 2-fold, and mutations in CARD15 confer increased risks of 2.25 (for carriers of a single mutation) and 9.3 (for carriers of two mutations). CARD15 accounts for only a small proportion of the genetic component of CD, with a gene-specific ,S, CARD15 of 1.16, from a total sibling relative risk of ,S= 27. CD risks were estimated for high-risk individuals who are siblings of a CD case, and who also smoke. The CD risk to such individuals who carry two CARD15 mutations is approximately 0.34, and for those carrying a single CARD15 mutation the risk is 0.08, compared to a population prevalence of approximately 0.001. These results imply that complex disease genes may be valuable in estimating with greater precision than has hitherto been possible disease risks in specific, easily identified subgroups of the population with a view to prevention. Yurii Aulchenko 128 Department of Epidemiology & Biostatistics, Erasmus Medical Centre Rotterdam, The Netherlands Keywords: Compression, information, bzip2, genome-wide SNP data, statistical genetics With advances in molecular technology, studies accessing millions of genetic polymorphisms in thousands of study subjects will soon become common. Such studies generate large amounts of data, whose effective storage and management is a challenge to the modern statistical genetics. Standard file compression utilities, such as Zip, Gzip and Bzip2, may be helpful to minimise the storage requirements. Less obvious is the fact that the data compression techniques may be also used in the analysis of genetic data. It is known that the efficiency of a particular compression algorithm depends on the probability structure of the data. In this work, we compared different standard and customised tools using the data from human HapMap project. Secondly, we investigate the potential uses of data compression techniques for the analysis of linkage, association and linkage disequilibrium Suzanne Leal 1 , Bingshan Li 129 Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, USA Keywords: Consanguineous pedigrees, missing genotype data Missing genotype data can increase false-positive evidence for linkage when either parametric or nonparametric analysis is carried out ignoring intermarker linkage disequilibrium (LD). Previously it was demonstrated by Huang et al (2005) that no bias occurs in this situation for affected sib-pairs with unrelated parents when either both parents are genotyped or genotype data is available for two additional unaffected siblings when parental genotypes are missing. However, this is not the case for consanguineous pedigrees, where missing genotype data for any pedigree member within a consanguinity loop can increase false-positive evidence of linkage. The false-positive evidence for linkage is further increased when cryptic consanguinity is present. The amount of false-positive evidence for linkage is highly dependent on which family members are genotyped. When parental genotype data is available, the false-positive evidence for linkage is usually not as strong as when parental genotype data is unavailable. Which family members will aid in the reduction of false-positive evidence of linkage is highly dependent on which other family members are genotyped. For a pedigree with an affected proband whose first-cousin parents have been genotyped, further reduction in the false-positive evidence of linkage can be obtained by including genotype data from additional affected siblings of the proband or genotype data from the proband's sibling-grandparents. When parental genotypes are not available, false-positive evidence for linkage can be reduced by including in the analysis genotype data from either unaffected siblings of the proband or the proband's married-in-grandparents. Najaf Amin 1 , Yurii Aulchenko 130 Department of Epidemiology & Biostatistics, Erasmus Medical Centre Rotterdam, The Netherlands Keywords: Genomic Control, pedigree structure, quantitative traits The Genomic Control (GC) method was originally developed to control for population stratification and cryptic relatedness in association studies. This method assumes that the effect of population substructure on the test statistics is essentially constant across the genome, and therefore unassociated markers can be used to estimate the effect of confounding onto the test statistic. The properties of GC method were extensively investigated for different stratification scenarios, and compared to alternative methods, such as the transmission-disequilibrium test. The potential of this method to correct not for occasional cryptic relations, but for regular pedigree structure, however, was not investigated before. In this work we investigate the potential of the GC method for pedigree-based association analysis of quantitative traits. The power and type one error of the method was compared to standard methods, such as the measured genotype (MG) approach and quantitative trait transmission-disequilibrium test. In human pedigrees, with trait heritability varying from 30 to 80%, the power of MG and GC approach was always higher than that of TDT. GC had correct type 1 error and its power was close to that of MG under moderate heritability (30%), but decreased with higher heritability. William Astle 1 , Chris Holmes 2 , David Balding 131 Department of Epidemiology and Public Health, Imperial College London, UK 32 Department of Statistics, University of Oxford, UK Keywords: Population structure, association studies, genetic epidemiology, statistical genetics In the analysis of population association studies, Genomic Control (Devlin & Roeder, 1999) (GC) adjusts the Armitage test statistic to correct the type I error for the effects of population substructure, but its power is often sub-optimal. Turbo Genomic Control (TGC) generalises GC to incorporate co-variation of relatedness and phenotype, retaining control over type I error while improving power. TGC is similar to the method of Yu et al. (2006), but we extend it to binary (case-control) in addition to quantitative phenotypes, we implement improved estimation of relatedness coefficients, and we derive an explicit statistic that generalizes the Armitage test statistic and is fast to compute. TGC also has similarities to EIGENSTRAT (Price et al., 2006) which is a new method based on principle components analysis. The problems of population structure(Clayton et al., 2005) and cryptic relatedness (Voight & Pritchard, 2005) are essentially the same: if patterns of shared ancestry differ between cases and controls, whether distant (coancestry) or recent (cryptic relatedness), false positives can arise and power can be diminished. With large numbers of widely-spaced genetic markers, coancestry can now be measured accurately for each pair of individuals via patterns of allele-sharing. Instead of modelling subpopulations, we work instead with a coancestry coefficient for each pair of individuals in the study. We explain the relationships between TGC, GC and EIGENSTRAT. We present simulation studies and real data analyses to illustrate the power advantage of TGC in a range of scenarios incorporating both substructure and cryptic relatedness. References Clayton, D. G.et al. (2005) Population structure, differential bias and genomic control in a large-scale case-control association study. Nature Genetics37(11) November 2005. Devlin, B. & Roeder, K. (1999) Genomic control for association studies. Biometics55(4) December 1999. Price, A. L.et al. (2006) Principal components analysis corrects for stratification in genome-wide association studies. Nature Genetics38(8) (August 2006). Voight, B. J. & Pritchard, J. K. (2005) Confounding from cryptic relatedness in case-control association studies. Public Library of Science Genetics1(3) September 2005. Yu, J.et al. (2006) A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nature Genetics38(2) February 2006. Hervé Perdry 1 , Marie-Claude Babron 1 , Françoise Clerget-Darpoux 133 INSERM U535 and Univ. Paris Sud, UMR-S 535, Villejuif, France Keywords: Modifier genes, case-parents trios, ordered transmission disequilibrium test A modifying locus is a polymorphic locus, distinct from the disease locus, which leads to differences in the disease phenotype, either by modifying the penetrance of the disease allele, or by modifying the expression of the disease. The effect of such a locus is a clinical heterogeneity that can be reflected by the values of an appropriate covariate, such as the age of onset, or the severity of the disease. We designed the Ordered Transmission Disequilibrium Test (OTDT) to test for a relation between the clinical heterogeneity, expressed by the covariate, and marker genotypes of a candidate gene. The method applies to trio families with one affected child and his parents. Each family member is genotyped at a bi-allelic marker M of a candidate gene. To each of the families is associated a covariate value; the families are ordered on the values of this covariate. As the TDT (Spielman et al. 1993), the OTDT is based on the observation of the transmission rate T of a given allele at M. The OTDT aims to find a critical value of the covariate which separates the sample of families in two subsamples in which the transmission rates are significantly different. We investigate the power of the method by simulations under various genetic models and covariate distributions. Acknowledgments H Perdry is funded by ARSEP. Pascal Croiseau 1 , Heather Cordell 2 , Emmanuelle Génin 134 INSERM U535 and University Paris Sud, UMR-S535, Villejuif, France 35 Institute of Human Genetics, Newcastle University, UK Keywords: Association, missing data, conditionnal logistic regression Missing data is an important problem in association studies. Several methods used to test for association need that individuals be genotyped at the full set of markers. Individuals with missing data need to be excluded from the analysis. This could involve an important decrease in sample size and a loss of information. If the disease susceptibility locus (DSL) is poorly typed, it is also possible that a marker in linkage disequilibrium gives a stronger association signal than the DSL. One may then falsely conclude that the marker is more likely to be the DSL. We recently developed a Multiple Imputation method to infer missing data on case-parent trios Starting from the observed data, a few number of complete data sets are generated by Markov-Chain Monte Carlo approach. These complete datasets are analysed using standard statistical package and the results are combined as described in Little & Rubin (2002). Here we report the results of simulations performed to examine, for different patterns of missing data, how often the true DSL gives the highest association score among different loci in LD. We found that multiple imputation usually correctly detect the DSL site even if the percentage of missing data is high. This is not the case for the naďve approach that consists in discarding trios with missing data. In conclusion, Multiple imputation presents the advantage of being easy to use and flexible and is therefore a promising tool in the search for DSL involved in complex diseases. Salma Kotti 1 , Heike Bickeböller 2 , Françoise Clerget-Darpoux 136 University Paris Sud, UMR-S535, Villejuif, France 37 Department of Genetic Epidemiology, Medical School, University of Göttingen, Germany Keywords: Genotype relative risk, internal controls, Family based analyses Family based analyses using internal controls are very popular both for detecting the effect of a genetic factor and for estimating the relative disease risk on the corresponding genotypes. Two different procedures are often applied to reconstitute internal controls. The first one considers one pseudocontrol genotype formed by the parental non-transmitted alleles called also 1:1 matching of alleles, while the second corresponds to three pseudocontrols corresponding to all genotypes formed by the parental alleles except the one of the case (1:3 matching). Many studies have compared between the two procedures in terms of the power and have concluded that the difference depends on the underlying genetic model and the allele frequencies. However, the estimation of the Genotype Relative Risk (GRR) under the two procedures has not been studied. Based on the fact that on the 1:1 matching, the control group is composed of the alleles untransmitted to the affected child and on the 1:3 matching, the control group is composed amongst alleles already transmitted to the affected child, we expect a difference on the GRR estimation. In fact, we suspect that the second procedure leads to biased estimation of the GRRs. We will analytically derive the GRR estimators for the 1:1 and 1:3 matching and will present the results at the meeting. Family based analyses using internal controls are very popular both for detecting the effect of a genetic factor and for estimating the relative disease risk on the corresponding genotypes. Two different procedures are often applied to reconstitute internal controls. The first one considers one pseudocontrol genotype formed by the parental non-transmitted alleles called also 1:1 matching of alleles, while the second corresponds to three pseudocontrols corresponding to all genotypes formed by the parental alleles except the one of the case (1:3 matching). Many studies have compared between the two procedures in terms of the power and have concluded that the difference depends on the underlying genetic model and the allele frequencies. However, the estimation of the Genotype Relative Risk (GRR) under the two procedures has not been studied. Based on the fact that on the 1:1 matching, the control group is composed of the alleles untransmitted to the affected child and on the 1:3 matching, the control group is composed amongst alleles already transmitted to the affected child, we expect a difference on the GRR estimation. In fact, we suspect that the second procedure leads to biased estimation of the GRR. We will analytically derive the GRR estimator for the 1:1 and 1:3 matching and will present the results at the meeting. Luigi Palla 1 , David Siegmund 239 Department of Mathematics,Free University Amsterdam, The Netherlands 40 Department of Statistics, Stanford University, California, USA Keywords: TDT, assortative mating, inbreeding, statistical power A substantial amount of Assortative Mating (AM) is often recorded on physical and psychological, dichotomous as well as quantitative traits that are supposed to have a multifactorial genetic component. In particular AM has the effect of increasing the genetic variance, even more than inbreeding because it acts across loci beside within loci, when the trait has a multifactorial origin. Under the assumption of a polygenic model for AM dating back to Wright (1921) and refined by Crow and Felsenstein (1968,1982), the effect of assortative mating on the power to detect genetic association in the Transmission Disequilibrium Test (TDT) is explored as parameters, such as the effective number of genes and the allelic frequency vary. The power is reflected by the non centrality parameter of the TDT and is expressed as a function of the number of trios, the relative risk of the heterozygous genotype and the allele frequency (Siegmund and Yakir, 2007). The noncentrality parameter of the relevant score statistic is updated considering the effect of AM which is expressed in terms of an ,effective' inbreeding coefficient. In particular, for dichotomous traits it is apparent that the higher the number of genes involved in the trait, the lower the loss in power due to AM. Finally an attempt is made to extend this relation to the Q-TDT (Rabinowitz, 1997), which involves considering the effect of AM also on the phenotypic variance of the trait of interest, under the assumption that AM affects only its additive genetic component. References Crow, & Felsenstein, (1968). The effect of assortative mating on the genetic composition of a population. Eugen.Quart.15, 87,97. Rabinowitz,, 1997. A Transmission Disequilibrium Test for Quantitative Trait Loci. Human Heredity47, 342,350. Siegmund, & Yakir, (2007) Statistics of gene mapping, Springer. Wright, (1921). System of mating.III. Assortative mating based on somatic resemblance. Genetics6, 144,161. Jérémie Nsengimana 1 , Ben D Brown 2 , Alistair S Hall 2 , Jenny H Barrett 141 Leeds Institute of Molecular Medicine, University of Leeds, UK 42 Leeds Institute for Genetics, Health and Therapeutics, University of Leeds, UK Keywords: Inflammatory genes, haplotype, coronary artery disease Genetic Risk of Acute Coronary Events (GRACE) is an initiative to collect cases of coronary artery disease (CAD) and their unaffected siblings in the UK and to use them to map genetic variants increasing disease risk. The aim of the present study was to test the association between CAD and 51 single nucleotide polymorphisms (SNPs) and their haplotypes from 35 inflammatory genes. Genotype data were available for 1154 persons affected before age 66 (including 48% before age 50) and their 1545 unaffected siblings (891 discordant families). Each SNP was tested for association to CAD, and haplotypes within genes or gene clusters were tested using FBAT (Rabinowitz & Laird, 2000). For the most significant results, genetic effect size was estimated using conditional logistic regression (CLR) within STATA adjusting for other risk factors. Haplotypes were assigned using HAPLORE (Zhang et al., 2005), which considers all parental mating types consistent with offspring genotypes and assigns them a probability of occurence. This probability was used in CLR to weight the haplotypes. In the single SNP analysis, several SNPs showed some evidence for association, including one SNP in the interleukin-1A gene. Analysing haplotypes in the interleukin-1 gene cluster, a common 3-SNP haplotype was found to increase the risk of CAD (P = 0.009). In an additive genetic model adjusting for covariates the odds ratio (OR) for this haplotype is 1.56 (95% CI: 1.16-2.10, p = 0.004) for early-onset CAD (before age 50). This study illustrates the utility of haplotype analysis in family-based association studies to investigate candidate genes. References Rabinowitz, D. & Laird, N. M. (2000) Hum Hered50, 211,223. Zhang, K., Sun, F. & Zhao, H. (2005) Bioinformatics21, 90,103. Andrea Foulkes 1 , Recai Yucel 1 , Xiaohong Li 143 Division of Biostatistics, University of Massachusetts, USA Keywords: Haploytpe, high-dimensional, mixed modeling The explosion of molecular level information coupled with large epidemiological studies presents an exciting opportunity to uncover the genetic underpinnings of complex diseases; however, several analytical challenges remain to be addressed. Characterizing the components to complex diseases inevitably requires consideration of synergies across multiple genetic loci and environmental and demographic factors. In addition, it is critical to capture information on allelic phase, that is whether alleles within a gene are in cis (on the same chromosome) or in trans (on different chromosomes.) In associations studies of unrelated individuals, this alignment of alleles within a chromosomal copy is generally not observed. We address the potential ambiguity in allelic phase in this high dimensional data setting using mixed effects models. Both a semi-parametric and fully likelihood-based approach to estimation are considered to account for missingness in cluster identifiers. In the first case, we apply a multiple imputation procedure coupled with a first stage expectation maximization algorithm for parameter estimation. A bootstrap approach is employed to assess sensitivity to variability induced by parameter estimation. Secondly, a fully likelihood-based approach using an expectation conditional maximization algorithm is described. Notably, these models allow for characterizing high-order gene-gene interactions while providing a flexible statistical framework to account for the confounding or mediating role of person specific covariates. The proposed method is applied to data arising from a cohort of human immunodeficiency virus type-1 (HIV-1) infected individuals at risk for therapy associated dyslipidemia. Simulation studies demonstrate reasonable power and control of family-wise type 1 error rates. Vivien Marquard 1 , Lars Beckmann 1 , Jenny Chang-Claude 144 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany Keywords: Genotyping errors, type I error, haplotype-based association methods It has been shown in several simulation studies that genotyping errors may have a great impact on the type I error of statistical methods used in genetic association analysis of complex diseases. Our aim was to investigate type I error rates in a case-control study, when differential and non-differential genotyping errors were introduced in realistic scenarios. We simulated case-control data sets, where individual genotypes were drawn from a haplotype distribution of 18 haplotypes with 15 markers in the APM1 gene. Genotyping errors were introduced following the unrestricted and symmetric with 0 edges error models described by Heid et al. (2006). In six scenarios, errors resulted from changes of one allele to another with predefined probabilities of 1%, 2.5% or 10%, respectively. A multiple number of errors per haplotype was possible and could vary between 0 and 15, the number of markers investigated. We examined three association methods: Mantel statistics using haplotype-sharing; a haplotype-specific score test; and Armitage trend test for single markers. The type I error rates were not influenced for any of all the three methods for a genotyping error rate of less than 1%. For higher error rates and differential errors, the type I error of the Mantel statistic was only slightly and of the Armitage trend test moderately increased. The type I error rates of the score test were highly increased. The type I error rates were correct for all three methods for non-differential errors. Further investigations will be carried out with different frequencies of differential error rates and focus on power. Arne Neumann 1 , Dörthe Malzahn 1 , Martina Müller 2 , Heike Bickeböller 145 Department of Genetic Epidemiology, Medical School, University of Göttingen, Germany 46 GSF-National Research Center for Environment and Health, Neuherberg & IBE-Institute of Epidemiology, Ludwig-Maximilians University München, Germany Keywords: Interaction, longitudinal, nonparametric Longitudinal data show the time dependent course of phenotypic traits. In this contribution, we consider longitudinal cohort studies and investigate the association between two candidate genes and a dependent quantitative longitudinal phenotype. The set-up defines a factorial design which allows us to test simultaneously for the overall gene effect of the loci as well as for possible gene-gene and gene time interaction. The latter would induce genetically based time-profile differences in the longitudinal phenotype. We adopt a non-parametric statistical test to genetic epidemiological cohort studies and investigate its performance by simulation studies. The statistical test was originally developed for longitudinal clinical studies (Brunner, Munzel, Puri, 1999 J Multivariate Anal 70:286-317). It is non-parametric in the sense that no assumptions are made about the underlying distribution of the quantitative phenotype. Longitudinal observations belonging to the same individual can be arbitrarily dependent on one another for the different time points whereas trait observations of different individuals are independent. The two loci are assumed to be statistically independent. Our simulations show that the nonparametric test is comparable with ANOVA in terms of power of detecting gene-gene and gene-time interaction in an ANOVA favourable setting. Rebecca Hein 1 , Lars Beckmann 1 , Jenny Chang-Claude 147 Division of Cancer Epidemiology, German Cancer Research Center (DKFZ) Heidelberg, Germany Keywords: Indirect association studies, interaction effects, linkage disequilibrium, marker allele frequency Association studies accounting for gene-environment interactions (GxE) may be useful for detecting genetic effects and identifying important environmental effect modifiers. Current technology facilitates very dense marker spacing in genetic association studies; however, the true disease variant(s) may not be genotyped. In this situation, an association between a gene and a phenotype may still be detectable, using genetic markers associated with the true disease variant(s) (indirect association). Zondervan and Cardon [2004] showed that the odds ratios (OR) of markers which are associated with the disease variant depend highly on the linkage disequilibrium (LD) between the variant and the markers, and whether the allele frequencies match and thereby influence the sample size needed to detect genetic association. We examined the influence of LD and allele frequencies on the sample size needed to detect GxE in indirect association studies, and provide tables for sample size estimation. For discordant allele frequencies and incomplete LD, sample sizes can be unfeasibly large. The influence of both factors is stronger for disease loci with small rather than moderate to high disease allele frequencies. A decline in D' of e.g. 5% has less impact on sample size than increasing the difference in allele frequencies by the same percentage. Assuming 80% power, large interaction effects can be detected using smaller sample sizes than those needed for the detection of main effects. The detection of interaction effects involving rare alleles may not be possible. Focussing only on marker density can be a limited strategy in indirect association studies for GxE. Cyril Dalmasso 1 , Emmanuelle Génin 2 , Catherine Bourgain 2 , Philippe Broët 148 JE 2492 , Univ. Paris-Sud, France 49 INSERM UMR-S 535 and University Paris Sud, Villejuif, France Keywords: Linkage analysis, Multiple testing, False Discovery Rate, Mixture model In the context of genome-wide linkage analyses, where a large number of statistical tests are simultaneously performed, the False Discovery Rate (FDR) that is defined as the expected proportion of false discoveries among all discoveries is nowadays widely used for taking into account the multiple testing problem. Other related criteria have been considered such as the local False Discovery Rate (lFDR) that is a variant of the FDR giving to each test its own measure of significance. The lFDR is defined as the posterior probability that a null hypothesis is true. Most of the proposed methods for estimating the lFDR or the FDR rely on distributional assumption under the null hypothesis. However, in observational studies, the empirical null distribution may be very different from the theoretical one. In this work, we propose a mixture model based approach that provides estimates of the lFDR and the FDR in the context of large-scale variance component linkage analyses. In particular, this approach allows estimating the empirical null distribution, this latter being a key quantity for any simultaneous inference procedure. The proposed method is applied on a real dataset. Arief Gusnanto 1 , Frank Dudbridge 150 MRC Biostatistics Unit, Cambridge UK Keywords: Significance, genome-wide, association, permutation, multiplicity Genome-wide association scans have introduced statistical challenges, mainly in the multiplicity of thousands of tests. The question of what constitutes a significant finding remains somewhat unresolved. Permutation testing is very time-consuming, whereas Bayesian arguments struggle to distinguish direct from indirect association. It seems attractive to summarise the multiplicity in a simple form that allows users to avoid time-consuming permutations. A standard significance level would facilitate reporting of results and reduce the need for permutation tests. This is potentially important because current scans do not have full coverage of the whole genome, and yet, the implicit multiplicity is genome-wide. We discuss some proposed summaries, with reference to the empirical null distribution of the multiple tests, approximated through a large number of random permutations. Using genome-wide data from the Wellcome Trust Case-Control Consortium, we use a sub-sampling approach with increasing density to estimate the nominal p-value to obtain family-wise significance of 5%. The results indicate that the significance level is converging to about 1e-7 as the marker spacing becomes infinitely dense. We considered the concept of an effective number of independent tests, and showed that when used in a Bonferroni correction, the number varies with the overall significance level, but is roughly constant in the region of interest. We compared several estimators of the effective number of tests, and showed that in the region of significance of interest, Patterson's eigenvalue based estimator gives approximately the right family-wise error rate. Michael Nothnagel 1 , Amke Caliebe 1 , Michael Krawczak 151 Institute of Medical Informatics and Statistics, University Clinic Schleswig-Holstein, University of Kiel, Germany Keywords: Association scans, Bayesian framework, posterior odds, genetic risk, multiplicative model Whole-genome association scans have been suggested to be a cost-efficient way to survey genetic variation and to map genetic disease factors. We used a Bayesian framework to investigate the posterior odds of a genuine association under multiplicative disease models. We demonstrate that the p value alone is not a sufficient means to evaluate the findings in association studies. We suggest that likelihood ratios should accompany p values in association reports. We argue, that, given the reported results of whole-genome scans, more associations should have been successfully replicated if the consistently made assumptions about considerable genetic risks were correct. We conclude that it is very likely that the vast majority of relative genetic risks are only of the order of 1.2 or lower. Clive Hoggart 1 , Maria De Iorio 1 , John Whittakker 2 , David Balding 152 Department of Epidemiology and Public Health, Imperial College London, UK 53 Department of Epidemiology and Public Health, London School of Hygiene and Tropical Medicine, UK Keywords: Genome-wide association analyses, shrinkage priors, Lasso Testing one SNP at a time does not fully realise the potential of genome-wide association studies to identify multiple causal variants of small effect, which is a plausible scenario for many complex diseases. Moreover, many simulation studies assume a single causal variant and so more complex realities are ignored. Analysing large numbers of variants simultaneously is now becoming feasible, thanks to developments in Bayesian stochastic search methods. We pose the problem of SNP selection as variable selection in a regression model. In contrast to single SNP tests this approach simultaneously models the effect of all SNPs. SNPs are selected by a Bayesian interpretation of the lasso (Tibshirani, 1996); the maximum a posterior (MAP) estimate of the regression coefficients, which have been given independent, double exponential prior distributions. The double exponential distribution is an example of a shrinkage prior, MAP estimates with shrinkage priors can be zero, thus all SNPs with non zero regression coefficients are selected. In addition to the commonly-used double exponential (Laplace) prior, we also implement the normal exponential gamma prior distribution. We show that use of the Laplace prior improves SNP selection in comparison with single -SNP tests, and that the normal exponential gamma prior leads to a further improvement. Our method is fast and can handle very large numbers of SNPs: we demonstrate its performance using both simulated and real genome-wide data sets with 500 K SNPs, which can be analysed in 2 hours on a desktop workstation. Mickael Guedj 1,2 , Jerome Wojcik 2 , Gregory Nuel 154 Laboratoire Statistique et Génome, Université d'Evry, Evry France 55 Serono Pharmaceutical Research Institute, Plan-les-Ouates, Switzerland Keywords: Local Replication, Local Score, Association In gene-mapping, replication of initial findings has been put forwards as the approach of choice for filtering false-positives from true signals for underlying loci. In practice, such replications are however too poorly observed. Besides the statistical and technical-related factors (lack of power, multiple-testing, stratification, quality control,) inconsistent conclusions obtained from independent populations might result from real biological differences. In particular, the high degree of variation in the strength of LD among populations of different origins is a major challenge to the discovery of genes. Seeking for Local Replications (defined as the presence of a signal of association in a same genomic region among populations) instead of strict replications (same locus, same risk allele) may lead to more reliable results. Recently, a multi-markers approach based on the Local Score statistic has been proposed as a simple and efficient way to select candidate genomic regions at the first stage of genome-wide association studies. Here we propose an extension of this approach adapted to replicated association studies. Based on simulations, this method appears promising. In particular it outperforms classical simple-marker strategies to detect modest-effect genes. Additionally it constitutes, to our knowledge, a first framework dedicated to the detection of such Local Replications. Juliet Chapman 1 , Claudio Verzilli 1 , John Whittaker 156 Department of Epidemiology and Public Health, London School of Hygiene and Tropical Medicine, UK Keywords: FDR, Association studies, Bayesian model selection As genomewide association studies become commonplace there is debate as to how such studies might be analysed and what we might hope to gain from the data. It is clear that standard single locus approaches are limited in that they do not adjust for the effects of other loci and problematic since it is not obvious how to adjust for multiple comparisons. False discovery rates have been suggested, but it is unclear how well these will cope with highly correlated genetic data. We consider the validity of standard false discovery rates in large scale association studies. We also show that a Bayesian procedure has advantages in detecting causal loci amongst a large number of dependant SNPs and investigate properties of a Bayesian FDR. Peter Kraft 157 Harvard School of Public Health, Boston USA Keywords: Gene-environment interaction, genome-wide association scans Appropriately analyzed two-stage designs,where a subset of available subjects are genotyped on a genome-wide panel of markers at the first stage and then a much smaller subset of the most promising markers are genotyped on the remaining subjects,can have nearly as much power as a single-stage study where all subjects are genotyped on the genome-wide panel yet can be much less expensive. Typically, the "most promising" markers are selected based on evidence for a marginal association between genotypes and disease. Subsequently, the few markers found to be associated with disease at the end of the second stage are interrogated for evidence of gene-environment interaction, mainly to understand their impact on disease etiology and public health impact. However, this approach may miss variants which have a sizeable effect restricted to one exposure stratum and therefore only a modest marginal effect. We have proposed to use information on the joint effects of genes and a discrete list of environmental exposures at the initial screening stage to select promising markers for the second stage [Kraft et al Hum Hered 2007]. This approach optimizes power to detect variants that have a sizeable marginal effect and variants that have a small marginal effect but a sizeable effect in a stratum defined by an environmental exposure. As an example, I discuss a proposed genome-wide association scan for Type II diabetes susceptibility variants based in several large nested case-control studies. Beate Glaser 1 , Peter Holmans 158 Biostatistics and Bioinformatics Unit, Cardiff University, School of Medicine, Heath Park, Cardiff, UK Keywords: Combined case-control and trios analysis, Power, False-positive rate, Simulation, Association studies The statistical power of genetic association studies can be enhanced by combining the analysis of case-control with parent-offspring trio samples. Various combined analysis techniques have been recently developed; as yet, there have been no comparisons of their power. This work was performed with the aim of identifying the most powerful method among available combined techniques including test statistics developed by Kazeem and Farrall (2005), Nagelkerke and colleagues (2004) and Dudbridge (2006), as well as a simple combination of ,2-statistics from single samples. Simulation studies were performed to investigate their power under different additive, multiplicative, dominant and recessive disease models. False-positive rates were determined by studying the type I error rates under null models including models with unequal allele frequencies between the single case-control and trios samples. We identified three techniques with equivalent power and false-positive rates, which included modifications of the three main approaches: 1) the unmodified combined Odds ratio estimate by Kazeem & Farrall (2005), 2) a modified approach of the combined risk ratio estimate by Nagelkerke & colleagues (2004) and 3) a modified technique for a combined risk ratio estimate by Dudbridge (2006). Our work highlights the importance of studies investigating test performance criteria of novel methods, as they will help users to select the optimal approach within a range of available analysis techniques. David Almorza 1 , M.V. Kandus 2 , Juan Carlos Salerno 2 , Rafael Boggio 359 Facultad de Ciencias del Trabajo, University of Cádiz, Spain 60 Instituto de Genética IGEAF, Buenos Aires, Argentina 61 Universidad Nacional de La Plata, Buenos Aires, Argentina Keywords: Principal component analysis, maize, ear weight, inbred lines The objective of this work was to evaluate the relationship among different traits of the ear of maize inbred lines and to group genotypes according to its performance. Ten inbred lines developed at IGEAF (INTA Castelar) and five public inbred lines as checks were used. A field trial was carried out in Castelar, Buenos Aires (34° 36' S , 58° 39' W) using a complete randomize design with three replications. At harvest, individual weight (P.E.), diameter (D.E.), row number (N.H.) and length (L.E.) of the ear were assessed. A principal component analysis, PCA, (Infostat 2005) was used, and the variability of the data was depicted with a biplot. Principal components 1 and 2 (CP1 and CP2) explained 90% of the data variability. CP1 was correlated with P.E., L.E. and D.E., meanwhile CP2 was correlated with N.H. We found that individual weight (P.E.) was more correlated with diameter of the ear (D.E.) than with length (L.E). Five groups of inbred lines were distinguished: with high P.E. and mean N.H. (04-70, 04-73, 04-101 and MO17), with high P.E. but less N.H. (04-61 and B14), with mean P.E. and N.H. (B73, 04-123 and 04-96), with high N.H. but less P.E. (LP109, 04-8, 04-91 and 04-76) and with low P.E. and low N.H. (LP521 and 04-104). The use of PCA showed which variables had more incidence in ear weight and how is the correlation among them. Moreover, the different groups found with this analysis allow the evaluation of inbred lines by several traits simultaneously. Sven Knüppel 1 , Anja Bauerfeind 1 , Klaus Rohde 162 Department of Bioinformatics, MDC Berlin, Germany Keywords: Haplotypes, association studies, case-control, nuclear families The area of gene chip technology provides a plethora of phase-unknown SNP genotypes in order to find significant association to some genetic trait. To circumvent possibly low information content of a single SNP one groups successive SNPs and estimates haplotypes. Haplotype estimation, however, may reveal ambiguous haplotype pairs and bias the application of statistical methods. Zaykin et al. (Hum Hered, 53:79-91, 2002) proposed the construction of a design matrix to take this ambiguity into account. Here we present a set of functions written for the Statistical package R, which carries out haplotype estimation on the basis of the EM-algorithm for individuals (case-control) or nuclear families. The construction of a design matrix on basis of estimated haplotypes or haplotype pairs allows application of standard methods for association studies (linear, logistic regression), as well as statistical methods as haplotype sharing statistics and TDT-Test. Applications of these methods to genome-wide association screens will be demonstrated. Manuela Zucknick 1 , Chris Holmes 2 , Sylvia Richardson 163 Department of Epidemiology and Public Health, Imperial College London, UK 64 Department of Statistics, Oxford Center for Gene Function, University of Oxford, UK Keywords: Bayesian, variable selection, MCMC, large p, small n, structured dependence In large-scale genomic applications vast numbers of markers or genes are scanned to find a few candidates which are linked to a particular phenotype. Statistically, this is a variable selection problem in the "large p, small n" situation where many more variables than samples are available. An additional feature is the complex dependence structure which is often observed among the markers/genes due to linkage disequilibrium or their joint involvement in biological processes. Bayesian variable selection methods using indicator variables are well suited to the problem. Binary phenotypes like disease status are common and both Bayesian probit and logistic regression can be applied in this context. We argue that logistic regression models are both easier to tune and to interpret than probit models and implement the approach by Holmes & Held (2006). Because the model space is vast, MCMC methods are used as stochastic search algorithms with the aim to quickly find regions of high posterior probability. In a trade-off between fast-updating but slow-moving single-gene Metropolis-Hastings samplers and computationally expensive full Gibbs sampling, we propose to employ the dependence structure among the genes/markers to help decide which variables to update together. Also, parallel tempering methods are used to aid bold moves and help avoid getting trapped in local optima. Mixing and convergence of the resulting Markov chains are evaluated and compared to standard samplers in both a simulation study and in an application to a gene expression data set. Reference Holmes, C. C. & Held, L. (2006) Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis1, 145,168. Dawn Teare 165 MMGE, University of Sheffield, UK Keywords: CNP, family-based analysis, MCMC Evidence is accumulating that segmental copy number polymorphisms (CNPs) may represent a significant portion of human genetic variation. These highly polymorphic systems require handling as phenotypes rather than co-dominant markers, placing new demands on family-based analyses. We present an integrated approach to meet these challenges in the form of a graphical model, where the underlying discrete CNP phenotype is inferred from the (single or replicate) quantitative measure within the analysis, whilst assuming an allele based system segregating through the pedigree. [source] ## Contribution of a haplotype in the HLA region to anti,cyclic citrullinated peptide antibody positivity in rheumatoid arthritis, independently of HLA,DRB1 ARTHRITIS & RHEUMATISM, Issue 12 2009Yukinori OkadaObjective To examine the risk of anti,cyclic citrullinated peptide (anti-CCP) antibody positivity in rheumatoid arthritis (RA) patients carrying certain haplotypes in the HLA region. Methods A total of 1,389 Japanese patients with RA were genotyped for 30 single-nucleotide polymorphisms (SNPs) in the HLA region using commercial oligonucleotide arrays (from Perlegen or Affymetrix) as well as for HLA,DRB1 alleles using a sequence-specific polymerase chain reaction method. Stepwise logistic regression was used to select from among the 30 SNPs the ones that represented a risk of anti-CCP antibody positivity. Haplotypes of the selected SNPs were inferred using an expectation-maximization algorithm. Associations of individual SNPs were evaluated with the Cochran-Armitage test for trend. DRB1 alleles and haplotypes were evaluated with the chi-square test. Heterogeneities of risks among the shared epitope (SE) and non-SE HLA,DRB1 alleles were examined using the exact test. Haplotype associations that were independent of individual HLA,DRB1 alleles were evaluated using the likelihood ratio test. Results Significant associations were found for 9 SNPs (smallest P value being 2.4 × 10,8) and in 4 HLA,DRB1 alleles (smallest P value being 2.0 × 10,10 in DRB1*0405). Stepwise logistic regression selected 4 SNPs (rs9262638, rs7775228, rs4713580, and rs9277359). Among the 16 inferred haplotypes of these 4 SNPs, 6 indicated significant associations (smallest P value being 1.9 × 10,11). Risks among SE and non-SE alleles were significantly heterogeneous (P = 0.0095 and P = 9.8 × 10,9, respectively), indicating the importance of stratification with individual DRB1 alleles rather than SE alleles. Conditional analysis of the risk associated with individual DRB1 alleles identified a risk haplotype that was independent of DRB1 (odds ratio 2.00 [95% confidence interval 1.44,2.79], P = 2.6 × 10,5). Conclusion Heterogeneous risks of anti-CCP antibody positivity were confirmed among SE and non-SE alleles in our patient population. A risk haplotype in the HLA region that is independent of HLA,DRB1 was confirmed. [source] ## Association of a specific ERAP1/ARTS1 haplotype with disease susceptibility in ankylosing spondylitis ARTHRITIS & RHEUMATISM, Issue 5 2009W. P. MaksymowychObjective Alterations in antigen processing have been proposed to play a significant role in the pathogenesis of ankylosing spondylitis (AS). A non,major histocompatibility complex gene encoding an endoplasmic reticulum aminopeptidase, ERAP1, has been implicated recently. This study assessed 13 coding single-nucleotide polymorphisms (SNPs) from 5 genes involved in antigen processing (ERAP1, TAP1, TAP2, LMP2, and LMP7) in 3 Canadian cohorts of patients with AS, to address the possibility of gene interactions in disease susceptibility. Methods The study involved 992 AS cases and 1,437 controls from 3 centers (472 cases and 451 controls from Alberta, 138 cases and 392 controls from Newfoundland, and 382 cases and 594 controls from Toronto). Most of the patients with AS and healthy, unrelated controls were Caucasians of northern European descent. Single-marker and haplotype associations were determined using an allelic likelihood ratio test in UNPHASED, version 3.0.12, and the WHAP program, respectively. P values for significance of haplotype associations were calculated using a permutation test. Results A specific ERAP1 haplotype, rs27044/10050860/30187-CCT, was strongly associated with increased risk of AS in all 3 case,control cohorts (pooled odds ratio [OR] 1.81, 95% confidence interval [95% CI] 1.46,2.24; P = 7 × 10,8), while a second specific ERAP1 haplotype, rs30187/26618/26653-CTG, reduced the disease risk (pooled OR 0.77, 95% CI 0.67,0.88; P = 9 × 10,5). Significant associations were also noted for 3 ERAP1 SNP variants (rs10050860, rs30187, and rs26653), although no significant haplotype interaction between ERAP1 and TAP/LMP loci was evident. Conclusion These data indicate that an AS disease locus may reside on a specific ERAP1 haplotype, and its effect is not multiplicative with contributions from TAP and LMP genes. [source] ## POISSON VERSUS BINOMIAL: APPOINTMENT OF JUDGES TO THE U.S. SUPREME COURT AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2010Vassilly VoinovSummary The problem of discriminating between the Poisson and binomial models is discussed in the context of a detailed statistical analysis of the number of appointments of the U.S. Supreme Court justices from 1789 to 2004. Various new and existing tests are examined. The analysis shows that both simple Poisson and simple binomial models are equally appropriate for describing the data. No firm statistical evidence in favour of an exponential Poisson regression model was found. Two attendant results were obtained by simulation: firstly, that the likelihood ratio test is the most powerful of those considered when testing for the Poisson versus binomial and, secondly, that the classical variance test with an upper-tail critical region is biased. [source] ## Testing the Ratio of Two Poisson Rates BIOMETRICAL JOURNAL, Issue 2 2008Kangxia GuAbstract In this paper we compare the properties of four different general approaches for testing the ratio of two Poisson rates. Asymptotically normal tests, tests based on approximate p -values, exact conditional tests, and a likelihood ratio test are considered. The properties and power performance of these tests are studied by a Monte Carlo simulation experiment. Sample size calculation formulae are given for each of the test procedures and their validities are studied. Some recommendations favoring the likelihood ratio and certain asymptotic tests are based on these simulation results. Finally, all of the test procedures are illustrated with two real life medical examples. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## A Comparison of the Three Conditional Exact Tests in Two-way Contingency Tables Using the Unconditional Exact Power BIOMETRICAL JOURNAL, Issue 3 2004Seung-Ho KangAbstract The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi-squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Statistical Inference For Risk Difference in an Incomplete Correlated 2 × 2 Table BIOMETRICAL JOURNAL, Issue 1 2003Nian-Sheng TangAbstract In some infectious disease studies and 2-step treatment studies, 2 × 2 table with structural zero could arise in situations where it is theoretically impossible for a particular cell to contain observations or structural void is introduced by design. In this article, we propose a score test of hypotheses pertaining to the marginal and conditional probabilities in a 2 × 2 table with structural zero via the risk/rate difference measure. Score test-based confidence interval will also be outlined. We evaluate the performance of the score test and the existing likelihood ratio test. Our empirical results evince the similar and satisfactory performance of the two tests (with appropriate adjustments) in terms of coverage probability and expected interval width. Both tests consistently perform well from small- to moderate-sample designs. The score test however has the advantage that it is only undefined in one scenario while the likelihood ratio test can be undefined in many scenarios. We illustrate our method by a real example from a two-step tuberculosis skin test study. [source] ## A Robust Genome-Wide Scan Statistic of the Wellcome Trust Case,Control Consortium BIOMETRICS, Issue 4 2009Jungnam JooSummary In genome-wide association (GWA) studies, test statistics that are efficient and robust across various genetic models are preferable, particularly for studying multiple diseases in the Wellcome Trust Case,Control Consortium (WTCCC, 2007,,Nature,447, 661,678). A new test statistic, the minimum of the p-values of the trend test and Pearson's test, was considered by the WTCCC. It is referred to here as MIN2. Because the minimum of two p-values is no longer a valid p-value itself, the WTCCC only used it to rank single nucleotide polymorphisms (SNPs) but did not report the p-values of the associated SNPs when MIN2 was used for ranking. Given its importance in practice, we derive the asymptotic null distribution of MIN2, study some of its analytical properties related to GWA studies, and compare it with existing methods (the trend test, Pearson's test, MAX3, and the constrained likelihood ratio test [CLRT]) by simulations across a wide range of possible genetic models: the recessive (REC), additive (ADD), multiplicative (MUL), dominant (DOM), and overdominant models. The results show that MAX3 and CLRT have greater efficiency robustness than other tests when the REC, ADD/MUL, and DOM models are possible, whereas Pearson's test and MIN2 have greater efficiency robustness if the possible genetic models also include the overdominant model. We conclude that robust tests (MAX3, MIN2, CLRT, and Pearson's test) are preferable to a single trend test for initial GWA studies. The four robust tests are applied to more than 100 SNPs associated with 11 common diseases identified by the two WTCCC GWA studies. [source] ## Nonparametric Functional Mapping of Quantitative Trait Loci BIOMETRICS, Issue 1 2009Jie YangSummary Functional mapping is a useful tool for mapping quantitative trait loci (QTL) that control dynamic traits. It incorporates mathematical aspects of biological processes into the mixture model-based likelihood setting for QTL mapping, thus increasing the power of QTL detection and the precision of parameter estimation. However, in many situations there is no obvious functional form and, in such cases, this strategy will not be optimal. Here we propose to use nonparametric function estimation, typically implemented with B-splines, to estimate the underlying functional form of phenotypic trajectories, and then construct a nonparametric test to find evidence of existing QTL. Using the representation of a nonparametric regression as a mixed model, the final test statistic is a likelihood ratio test. We consider two types of genetic maps: dense maps and general maps, and the power of nonparametric functional mapping is investigated through simulation studies and demonstrated by examples. [source] ## Comparison of Properties of Tests for Assessing Tumor Clonality BIOMETRICS, Issue 4 2008Irina OstrovnayaSummary In a recent article Begg et al. (2007, Biometrics 63, 522,530) proposed a statistical test to determine whether or not a diagnosed second primary tumor is biologically independent of the original primary tumor, by comparing patterns of allelic losses at candidate genetic loci. The proposed concordant mutations test is a conditional test, an adaptation of Fisher's exact test, that requires no knowledge of the marginal mutation probabilities. The test was shown to have generally good properties, but is susceptible to anticonservative bias if there is wide variation in mutation probabilities between loci, or if the individual mutation probabilities of the parental alleles for individual patients differ substantially from each other. In this article, a likelihood ratio test is derived in an effort to address these validity issues. This test requires prespecification of the marginal mutation probabilities at each locus, parameters for which some information will typically be available in the literature. In simulations this test is shown to be valid, but to be considerably less efficient than the concordant mutations test for sample sizes (numbers of informative loci) typical of this problem. Much of the efficiency deficit can be recovered, however, by restricting the allelic imbalance parameter estimate to a prespecified range, assuming that this parameter is in the prespecified range. [source] |