Multipoint lods provide reliable linkage evidence despite unknown limiting distribution: type I error probabilities decrease with sample size for multipoint lods and mods

Abstract

We investigate the behavior of type I error rates in model‐based multipoint (MP) linkage analysis, as a function of sample size (N ). We consider both MP lods (i.e., MP linkage analysis that uses the correct genetic model) and MP mods (maximizing MP lods over 18 dominant and recessive models). Following Xing and Elston (2006 Genet. Epidemiol , 30: 447–458), we first consider MP linkage analysis limited to a single position; then we enlarge the scope and maximize the lods and mods over a span of positions. In all situations we examined, type I error rates decrease with increasing sample size , apparently approaching zero. We show: (a) For MP lods analyzed only at a single position, well‐known statistical theory predicts that type I error rates approach zero. (b) For MP lods and mods maximized over position, this result has a different explanation, related to the fact that one maximizes the scores over only a finite portion of the parameter range. The implications of these findings may be far‐reaching: Although it is widely accepted that fixed nominal critical values for MP lods and mods are not known, this study shows that whatever the nominal error rates are, the actual error rates appear to decrease with increasing sample size. Moreover, the actual (observed) type I error rate may be quite small for any given study. We conclude that MP lod and mod scores provide reliable linkage evidence for complex diseases, despite the unknown limiting distributions of these MP scores. Genet. Epidemiol . 2008.