Two-Phase Sampling Designs for Gene Hunting

In studies of disease inheritance, it is more convenient to collect family data by first locating an affected individual and then enquiring about the status of his or her relatives. In the situation of a putative recessive genetic disease, the most typical mechanism for the entry of a sibship into a study is after diagnosis of a sibling for the disease and confirmation of the absence of that disease in the parents. With this approach two problems arise. One problem is that all the offspring of two disease carriers can be normal, undifferentiable from a sibship of normal parents, and thus the sibship goes undetected. The other problem is that a sibship could be selected for study more than once with the frequency dependent on the number of siblings. A two-phase sampling procedure that adjusts for these two problems will be presented. The choice of sampling fractions to minimize cost for this procedure will be discussed with respect to the estimation of a genetic parameter. A third problem that arises with data of this sort is that the sampling distribution of sibship sizes is typically ignored. An approach to modeling this sampling variability with a branching process will be presented. Finally, implications for complex genetic diseases, that are assumed to be characterized by 2 to 30 genes, will be discussed.