Using an uncertainty-coding matrix in Bayesian regression models for haplotype-specific risk detection in family association studies

Abstract

Haplotype association studies based on family genotype data can provide more biological information than single marker association studies. Difficulties arise, however, in the inference of haplotype phase determination and in haplotype transmission/non-transmission status. Incorporation of the uncertainty associated with haplotype inference into regression models requires special care. This task can get even more complicated when the genetic region contains a large number of haplotypes. To avoid the curse of dimensionality, we employ a clustering algorithm based on the evolutionary relationship among haplotypes and retain for regression analysis only the ancestral core haplotypes identified by it. To integrate the three sources of variation, phase ambiguity, transmission status and ancestral uncertainty, we propose an uncertainty-coding matrix which combines these three types of variability simultaneously. Next we evaluate haplotype risk with the use of such a matrix in a Bayesian conditional logistic regression model. Simulation studies and one application, a schizophrenia multiplex family study, are presented and the results are compared with those from other family based analysis tools such as FBAT. Our proposed method (Bayesian regression using uncertainty-coding matrix, BRUCM) is shown to perform better and the implementation in R is freely available.

Figure 1. Boxplots of haplotype effects under additive models.

Boxplots of 1000 replications for additive model under  = 1.2 (1st column), 1.5 (2nd column) and 2.0 (3rd column). The first row contains posterior mean effects of , the second is for its bias, and the last is for the posterior probability of susceptibility . Red plots correspond to the risk haplotypes.

Figure 2. Performance evaluation under different genetic models and relative risk ratios.

The performance evaluation based on AUC, overall accuracy, sensitivity, and specificity. The three columns are results under  = 1.2, 1.5, and 2.0, respectively. The three rows are simulations from additive (top), dominance (middle), and recessive models (bottom), respectively. The shaded bars in the left are under the hierarchical model with independent priors on regression coefficients, and the right bars contain results from FBAT.

Figure 3. LD information for the schizophrenia study.

LD blocks of the 28 SNPs on chromosome 6p for the schizophrenia multiplex family study. The genotype data from the largest block (3rd block) were selected for analysis.

Figure 4. Boxplots and posterior density plots for the schizophrenia study.

Boxplots and density plots of the posterior distributions of 's (top two plots) and (bottom two plots) for schizophrenia study.