Power calculations for familial aggregation studies

Family studies are frequently undertaken as the first step in the search for genetic determinants of disease. Significant familial aggregation of disease is suggestive of a genetic etiology for the disease, and may lead to more focused genetic analyses. Many methods have been proposed in the literature for the analysis of family studies. One model that is appealing for its simplicity of computation and the conditional interpretation of its parameters is the quadratic exponential model (e.g., Zhao and Prentice [1990] Biometrika 77:642-648; Betensky and Whittemore [1996] Appl. Stat. 45:422-429; Hudson et al. [2001a] Am. J. Epidemiol. 153:500-514). However, a limiting factor in its application, as well as that of the other proposed methods, is that power and sample size calculations have not been derived. These calculations are essential for investigators who are designing family studies. Here we derive analytic approximations for power for testing for familial aggregation, for both randomly sampled and nonrandomly sampled families. We also present simulation studies of power for both single- and two-disease cases, both under random and nonrandom sampling.