Bootstrap confidence intervals for relative risk parameters in affected-sib-pair data

In affected-sib-pair (ASP) studies, parameters such as the locus-specific s ibling relative risk, lambda(s), may be estimated and used to decide whethe r or not to continue the search for susceptibility genes. Typically, a maxi mum likelihood point estimate of lambda(s) is given, but since this estimat e may have substantial variability, it is of interest to obtain confidence limits for the true value of lambda(s). While a variety of methods for doin g this exist, there is considerable uncertainty over their reliability. Thi s is because the discrete nature of ASP data and the imposition of genetic "possible triangle" constraints during the likelihood maximization mean tha t asymptotic results may not apply. In this paper, we use simulation to eva luate the reliability of various asymptotic and simulation-based confidence intervals, the latter being based on a resampling, or bootstrap approach. We seek to identify, from the large pool of methods available, those method s that yield short intervals with accurate coverage probabilities for ASP d ata. Our results show that many of the most popular bootstrap confidence in terval methods perform poorly for ASP data, giving coverage probabilities m uch lower than claimed. The test-inversion, profile-likelihood, and asympto tic methods, however, perform well, although some care is needed in choice of nuisance parameter. Overall, in simulations under a variety of different genetic hypotheses, we find that the asymptotic methods of confidence inte rval evaluation are the most reliable, even in small samples. We illustrate our results with a practical application to a real data set, obtaining con fidence intervals for the sibling relative risks associated with several lo ci involved in type 1 diabetes. Genet. Epidemiol. 18:157-172, 2000. (C) 200 0 Wiley-Liss, Inc.