Estimating effects of rare haplotypes on failure time using a penalized Cox proportional hazards regression model

Background: This paper describes a likelihood approach to model the relation between failure time and haplotypes in studies with unrelated individuals where haplotype phase is unknown, while dealing with the problem of unstable estimates due to rare haplotypes by considering a penalized log-likelihood. Results: The Cox model presented here incorporates the uncertainty related to the unknown phase of multiple heterozygous individuals as weights. Estimation is performed with an EM algorithm. In the E-step the weights are estimated, and in the M-step the parameter estimates are estimated by maximizing the expectation of the joint log-likelihood, and the baseline hazard function and haplotype frequencies are calculated. These steps are iterated until the parameter estimates converge. Two penalty functions are considered, namely the ridge penalty and a difference penalty, which is based on the assumption that similar haplotypes show similar effects. Simulations were conducted to investigate properties of the method, and the association between IL10 haplotypes and risk of target vessel revascularization was investigated in 2653 patients from the GENDER study. Conclusion: Results from simulations and real data show that the penalized log-likelihood approach produces valid results, indicating that this method is of interest when studying the association between rare haplotypes and failure time in studies of unrelated individuals.