Estimation of genotype relative risks from pedigree data by retrospective likelihoods

Pedigrees collected for linkage studies are a valuable resource that could be used to estimate genetic relative risks (RRs) for genetic variants recently discovered in case-control genome wide association studies. To estimate RRs from highly ascertained pedigrees, a pedigree "retrospective likelihood" can be used, which adjusts for ascertainment by conditioning on the phenotypes of pedigree members. We explore a variety of approaches to compute the retrospective likelihood, and illustrate a Newton-Raphson method that is computationally efficient particularly for single nucleotide polymorphisms (SNPs) modeled as log-additive effect of alleles on the RR. We also illustrate, by simulations, that a naïve "composite likelihood" method that can lead to biased RR estimates, mainly by not conditioning on the ascertainment process - or as we propose - the disease status of all pedigree members. Applications of the retrospective likelihood to pedigrees collected for a prostate cancer linkage study and recently reported risk-SNPs illustrate the utility of our methods, with results showing that the RRs estimated from the highly ascertained pedigrees are consistent with odds ratios estimated in case-control studies. We also evaluate the potential impact of residual correlations of disease risk among family members due to shared unmeasured risk factors (genetic or environmental) by allowing for a random baseline risk parameter. When modeling only the affected family members in our data, there was little evidence for heterogeneity in baseline risks across families.