Decision-making in familial database searching: KI alone or not alone?

We consider the comparison of hypotheses "parent-child" or "full siblings" against the alternative of "unrelated" for pairs of individuals for whom DNA profiles are available. This is a situation that occurs repeatedly in familial database searching. A decision rule that uses both the kinship index (KI), also known as the likelihood ratio, and the identity-by-state statistic (IBS) was advocated in a recent report as superior to the use of KI alone. Such proposal appears to conflict with the Neyman-Pearson Lemma of statistics, which states that the likelihood ratio alone provides the most powerful criterion for distinguishing between any two simple hypotheses. We therefore performed a simulation study that was two orders of magnitude larger than in the previous report, and our results corroborate the theoretical expectation that KI alone provides a better decision rule than KI combined with IBS.