No "bias" toward the null hypothesis in most conventional multipoint nonparametric linkage analyses.

To the Editor: We would like to comment on the Schork and Green-wood (2004) article dealing with the inherent " bias " toward the null hypothesis in the context of nonpara-metric linkage analysis. The authors point out that, in certain situations, a loss of evidence for linkage can result from the practice of assigning expected allele-sharing values to affected relative pairs that are uninformative for their identity-by-descent (IBD) status. They explained this by setting up a likelihood function and studying its properties by simulation, clearly illustrating the negative impact of using expected IBD values for un-informative pairs. However, we would like to point out that their likelihood does not reflect how the majority of nonparametric linkage analysis programs compute statistics in practice. Indeed, the " problem " has been known and well discussed for years. Some of the concerns we discuss here have also been raised by Cordell (2004). Schork and Greenwood (2004) set up the likelihood formulation as follows. Let n i be the number of sib pairs sharing i alleles IBD (, 1, or 2). If all families had i p 0 unambiguous IBD sharing, then the LOD score evaluated at the sharing vector (p 0 , p 1 , p 2) is calculated as n n n 0 1 2 p p p 0 1 2 LOD p log 10 { } n n n 0 1 2 0.25 0.50 0.25 () () p n log 4p ϩ n log 2p ϩ n log (4p). (1) 0 1 0 0 1 1 0 1 2 1 0 2 In their model, Schork and Greenwood (2004) said that fully uninformative sibling pairs contribute 0.25, 0.50, and 0.25, respectively, to the counts n 0 , n 1 , and n 2 used in equation (1). If so, then the presence of uninformative sib pairs can lower the LOD score. However, in most software implementations, expected allele-sharing values are not used to compute nonparametric LOD scores. For example, consider the maximum LOD score (MLS) statistic proposed by Risch (1990). Let w i be the probability of the observed marker phenotypes of the pair, given that they share i alleles IBD (, 1, or 2). Then, i p 0 the likelihood of the observed marker data for the pair is given by 2 L p w p ͸ i i , ip0 where p i is the posterior probability that the …