Bayesian spatial modeling of haplotype associations

We review methods for relating the risk of disease to a collection of single nucleotide polymorphisms (SNPs) within a small region. Association studies using case-control designs with unrelated individuals could be used either to test for a direct effect of a candidate gene and characterize the responsible variant(s), or to fine map an unknown gene by exploiting the pattern of linkage disequilibrium (LD). We consider a flexible class of logistic penetrance models based on haplotypes and compare them with an alternative formulation based on unphased multilocus genotypes. The likelihood for haplotype-based models requires summation over all possible haplotype assignments consistent with the observed genotype data, and can be fitted using either Expectation-Maximization (E-M) or Markov chain Monte Carlo (MCMC) methods. Subtleties involving ascertainment correction for case-control studies are discussed. There has been great interest in methods for LD mapping based on the coalescent or ancestral recombination graphs as well as methods based on haplotype sharing, both of which we review briefly. Because of their computational complexity, we propose some alternative empirical modeling approaches using techniques borrowed from the Bayesian spatial statistics literature. Here, space is interpreted in terms of a distance metric describing the similarity of any pair of haplotypes to each other, and hence their presumed common ancestry. Specifically, we discuss the conditional autoregressive model and two spatial clustering models: Potts and Voronoi. We conclude with a discussion of the implications of these methods for modeling cryptic relatedness, haplotype blocks, and haplotype tagging SNPs, and suggest a Bayesian framework for the HapMap project.     

Estimation with correlated censored survival data with missing covariates

Incomplete covariate data are a common occurrence in studies in which the outcome is survival time. Further, studies in the health sciences often give rise to correlated, possibly censored, survival data. With no missing covariate data, if the marginal distributions of the correlated survival times follow a given parametric model, then the estimates using the maximum likelihood estimating equations, naively treating the correlated survival times as independent, give consistent estimates of the relative risk parameters Lipsitz et al. 1994 50, 842-846. Now, suppose that some observations within a cluster have some missing covariates. We show in this paper that if one naively treats observations within a cluster as independent, that one can still use the maximum likelihood estimating equations to obtain consistent estimates of the relative risk parameters. This method requires the estimation of the parameters of the distribution of the covariates. We present results from a clinical trial Lipsitz and Ibrahim (1996b) 2, 5-14 with five covariates, four of which have some missing values. In the trial, the clusters are the hospitals in which the patients were treated.     

Variable selection in regression-based estimation of dynamic treatment regimes

Dynamic treatment regimes (DTRs) consist of a sequence of decision rules, one per stage of intervention, that aim to recommend effective treatments for individual patients according to patient information history. DTRs can be estimated from models which include interactions between treatment and a (typically small) number of covariates which are often chosen a priori. However, with increasingly large and complex data being collected, it can be difficult to know which prognostic factors might be relevant in the treatment rule. Therefore, a more data-driven approach to select these covariates might improve the estimated decision rules and simplify models to make them easier to interpret. We propose a variable selection method for DTR estimation using penalized dynamic weighted least squares. Our method has the strong heredity property, that is, an interaction term can be included in the model only if the corresponding main terms have also been selected. We show our method has both the double robustness property and the oracle property theoretically; and the newly proposed method compares favorably with other variable selection approaches in numerical studies. We further illustrate the proposed method on data from the Sequenced Treatment Alternatives to Relieve Depression study.     

Sample size estimation for survival outcomes in cluster-randomized studies with small cluster sizes

We present a method for computing sample size for cluster-randomized studies involving a large number of clusters with relatively small numbers of observations within each cluster. For multivariate survival data, only the marginal bivariate distribution is assumed to be known. The validity of this assumption is also discussed.     

To identify associations with rare variants, just WHaIT: Weighted haplotype and imputation-based tests

Empirical evidences suggest that both common and rare variants contribute to complex disease etiology. Although the effects of common variants have been thoroughly assessed in recent genome-wide association studies (GWAS), our knowledge of the impact of rare variants on complex diseases remains limited. A number of methods have been proposed to test for rare variant association in sequencing-based studies, a study design that is becoming popular but is still not economically feasible. On the contrary, few (if any) methods exist to detect rare variants in GWAS data, the data we have collected on thousands of individuals. Here we propose two methods, a weighted haplotype-based approach and an imputation-based approach, to test for the effect of rare variants with GWAS data. Both methods can incorporate external sequencing data when available. We evaluated our methods and compared them with methods proposed in the sequencing setting through extensive simulations. Our methods clearly show enhanced statistical power over existing methods for a wide range of population-attributable risk, percentage of disease-contributing rare variants, and proportion of rare alleles working in different directions. We also applied our methods to the IFIH1 region for the type 1 diabetes GWAS data collected by the Wellcome Trust Case-Control Consortium. Our methods yield p values in the order of 10⁻³, whereas the most significant p value from the existing methods is greater than 0.17. We thus demonstrate that the evaluation of rare variants with GWAS data is possible, particularly when public sequencing data are incorporated.     

Microsatellite linkage analysis, single-nucleotide polymorphisms, and haplotype associations with ECB21 in the COGA data

This study, part of the Genetic Analysis Workshop 14 (GAW14), explored real Collaborative Study on the Genetics of Alcoholism data for linkage and association mapping between genetic polymorphisms (microsatellite and single-nucleotide polymorphisms (SNPs)) and beta (16.5-20 Hz) oscillations of the brain rhythms (ecb21). The ecb21 phenotype underwent the statistical adjustments for the age of participants, and for attaining a normal distribution. A total of 1,000 subjects' available phenotypes were included in linkage analysis with microsatellite markers. Linkage analysis was performed only for chromosome 4 where a quantitative trait locus with 5.01 LOD score had been previously reported. Previous findings related this location with the gamma-aminobutyric acid type A (GABAA) receptor. At the same location, our analysis showed a LOD score of 2.2. This decrease in the LOD score is the result of a drastic reduction (one-third) of the available GAW14 phenotypic data. We performed SNP and haplotype association analyses with the same phenotypic data under the linkage peak region on chromosome 4. Seven Affymetrix and two Illumina SNPs showed significant associations with ecb21 phenotype. A haplotype, a combination of SNPs TSC0044171 and TSC0551006 (the latter almost under the region of GABAA genes), showed a significant association with ecb21 (p = 0.015) and a relatively high frequency in the sample studied. Our results affirmed that the GABA region has potential of harboring genes that contribute quantitatively to the beta oscillation of the brain rhythms. The inclusion of the remaining 614 subjects, which in the GAW14 had missing data for the ecb21, can improve the strength of the associations as they have already shown that they contribute quite important information in the linkage analysis.     

Boosting method for nonlinear transformation models with censored survival data

We propose a general class of nonlinear transformation models for analyzing censored survival data, of which the nonlinear proportional hazards and proportional odds models are special cases. A cubic smoothing spline-based component-wise boosting algorithm is derived to estimate covariate effects nonparametrically using the gradient of the marginal likelihood, that is computed using importance sampling. The proposed method can be applied to survival data with high-dimensional covariates, including the case when the sample size is smaller than the number of predictors. Empirical performance of the proposed method is evaluated via simulations and analysis of a microarray survival data.     

The association of H-2 haplotype with implantation,survival, and growth of murine embryos

Using three congenic strains, C57BL/10Sn (H-2 ^b), B10.A/SnSg (H-2 ^a), and B10.D2/nSn (H-2 ^d), we sought to investigate the possible association of H-2 haplotype with the number of implants, fetal survival, and fetal weight, as well as to analyze the possible effects of hybrid vigor and maternal-fetal histoincompatibility in primigravidae mice. The results of this study indicate a significant association between genes at or near the H-2 complex and both fetal loss and fetal weight, but not the number of implants. Haplotype variation accounted for 14 percent of the variation in fetal loss and 20 percent of the variation in fetal weight. With the exception of fetal loss, there was no evidence of a maternal effect. There was also no clear evidence of hybrid vigor or histoincompatibility effects for any of the three variables studied. In summary, the data suggests that particular allelic variants at or near the H-2 complex confer some selective advantage as measured by differential fetal survival and fetal growth.