A general approach to power calculation for relationship testing

This paper is motivated by power considerations in connection with relationship testing. Given the true relationship between a set of individuals, a claimed relationship between the same individuals, and a set of genetic markers, we compute the power of exclusion, i.e., the probability that the genotypes will be incompatible with the claimed relationship. If exclusion is impossible, as will be the case if it is required for instance to distinguish between sibs and half sibs, we rather obtain the distribution of the likelihood ratio. The problem we are addressing can also be seen as a standard way of measuring the ability of a battery of tests to resolve claimed family relationships. In particular, simple exclusion probabilities are regularly calculated worldwide as a part of designing forensic marker sets. Our approach to these problems is guided by a natural way of calculating exclusion probabilities on a computer. We present a user friendly implementation for this as part of the R package paramlink, originally designed by one of the authors (MDV) for pedigree manipulations and likelihood computations. By doing so we are able to handle problems more challenging than we have seen in the literature. Specifically, we deal with complex pedigrees with arbitrary inbreeding and conditioning. We present examples for autosomal as well as X-linked markers and some formulae to validate the results. The examples indicate a wide range of applications. Details are presented for an immigration case where previously reported calculations are extended to account for possible inbreeding and known genotypes. The supplementary material includes a tutorial on how to perform these calculations in paramlink.