Oxford genome screen for asthma-associated traits

Incorporating covariates in mapping heterogeneous traits: a hierarchical model using empirical Bayes estimation

Complex genetic traits are inherently heterogeneous, i.e., they may be caused by different genes, or non-genetic factors, in different individuals. So, for mapping genes responsible for these diseases using linkage analysis, heterogeneity must be accounted for in the model. Heterogeneity across different families can be modeled using a mixture distribution by letting each family have its own heterogeneity parameter denoting the probability that its disease-causing gene is linked to the marker map under consideration. A substantial gain in power is expected if covariates that can discriminate between the families of linked and unlinked types are incorporated in this modeling framework. To this end, we propose a hierarchical Bayesian model, in which the families are grouped according to various (categorized) levels of covariate(s). The heterogeneity parameters of families within each group are assigned a common prior, whose parameters are further assigned hyper-priors. The hyper-parameters are obtained by utilizing the empirical Bayes estimates. We also address related issues such as evaluating whether the covariate(s) under consideration are informative and grouping of families. We compare the proposed approach with one that does not utilize covariates and show that our approach leads to considerable gains in power to detect linkage and in precision of interval estimates through various simulation scenarios. An application to the asthma datasets of Genetic Analysis Workshop 12 also illustrates this gain in a real data analysis. Additionally, we compare the performances of microsatellite markers and single nucleotide polymorphisms for our approach and find that the latter clearly outperforms the former.

Evaluations of maximization procedures for estimating linkage parameters under heterogeneity

Locus heterogeneity is a major problem plaguing the mapping of disease genes responsible for complex genetic traits via linkage analysis. A common feature of several available methods to account for heterogeneity is that they involve maximizing a multidimensional likelihood to obtain maximum likelihood estimates. The high dimensionality of the likelihood surface may be due to multiple heterogeneity (mixing) parameters, linkage parameters, and/or regression coefficients corresponding to multiple covariates. Here, we focus on this nontrivial computational aspect of incorporating heterogeneity by considering several likelihood maximization procedures, including the expectation maximization (EM) algorithm and the stochastic expectation maximization (SEM) algorithm. The wide applicability of these procedures is demonstrated first through a general formulation of accounting for heterogeneity, and then by applying them to two specific formulations. Furthermore, our simulation studies as well as an application to the Genetic Analysis Workshop 12 asthma datasets show that, among other observations, SEM performs better than EM. As an aside, we illustrate a limitation of the popular admixture approach for incorporating heterogeneity, proved elsewhere. We also show how to obtain standard errors (SEs) for EM and SEM estimates, using methods available in the literature. These SEs can then be combined with the corresponding estimates to provide confidence intervals of the parameters.