Using an Uncertainty-Coding Matrix in Bayesian Regression Models for Haplotype-Specific Risk Detection in Family Association Studies

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.