Testing for familial aggregation when the population size is known

We treat the problem of testing for familial aggregation when sampling from a population of a known size. And consider the setting where data from all families in the population containing at least one affected member are obtained. The results are compared to the setting where the population size is unknown and data from a sample of families containing at least one affected member are obtained, and to the setting where the population size is known and data from all families in the population are obtained. Two kinds of local alternatives are considered: one in which a predisposing factor is prevalent but has small penetrance; the other in which the factor is penetrant but has small prevalence. It is found that knowing the population size provides substantial advantage over settings where population size is unknown, but that there is little advantage to settings where data from all families are obtained. The methods are illustrated through an application to data from a child survival study in northeast Brazil reported by Sastry (1997), and reanalyzed by Yu and Zelterman (2002).