Case‐sibling gene‐association studies for diseases with variable age at onset

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Abstract
Studies which compare cases to disease‐free siblings are useful for assessing association between a genetic locus and a phenotypic trait, as they eliminate the possibility of confounding by population stratification. Many analytic methods for such family‐based studies are based on a binary disease model. However, complex diseases have variable age at onset. Consequently, binary‐outcome methods can be inefficient or biased. We review methods for analysing censored age‐at‐onset data from family studies, including stratified Cox regression and genotype‐decomposition regression, an unstratified procedure which regresses age‐at‐onset on between‐ and within‐family genotype components. We also introduce a retrospective likelihood for censored age‐at‐onset data, which requires an external estimate of the baseline hazard. Stratified Cox regression does not use controls who have not attained the age of their case sibling(s), potentially leading to a loss of efficiency. Both genotype‐decomposition regression and the retrospective likelihood use these younger controls. We assess the performance of these methods via simulation studies. Stratified Cox regression and the retrospective likelihood have appropriate type I error rates in almost all situations studied; genotype‐decomposition regression is often anti‐conservative. Away from the null, confidence intervals for the relative risk derived from stratified Cox regression are anti‐conservative when the disease is rare and case‐rich families are sampled. The retrospective likelihood is more efficient than stratified Cox regression and its confidence intervals have correct coverage when the disease is rare or the estimate of the baseline hazard is reasonably accurate. These results suggest that when estimating genotype relative risks is the principal analytic goal, stratified Cox regression is appropriate as long as the disease is common; when the disease is rare, the retrospective likelihood may be more appropriate. Copyright © 2004 John Wiley & Sons, Ltd.