Likelihood-ratio affected sib-pair tests applied to multiply affected sibships: issues of power and type I error rate

"All-pairs" likelihood-ratio analyses, such as those performed by MAPMAKER/SIBS [Kruglyak and Lander, 1995], require that a sibship containing N affected siblings be split into N(N - 1)/2 sibships, each containing a different pair of affected sibs, before analysis. Each of these N(N - 1)/2 sibships may also contain the other affected sibs from the original sibship, coded as unaffected, to infer missing parental genotypes, as is done automatically in MAPMAKER/SIBS. Then, the use of the same individuals both as affecteds to test for linkage and, elsewhere, as unaffecteds to infer missing parental genotypes leads to negative correlations in the estimated identity by descent sharing among affected pairs from the same original multiplex sibship. This gives a conservative test of linkage, even when no downweighting is applied. Conversely, if the other affected sibs from the original sibship are omitted, the correlations are positive and the linkage test is anticonservative in the absence of weighting. True type I error probability also depends on marker informativity, typed parents, number of affected sibs included in the analysis, and the weighting scheme. This suggests the use of simulation, rather than asymptotic theory, to assess significance levels. The power of multiplex sibships relative to affected pairs increases with increasing phenocopy percentage, but the presence of typed unaffected sibs improves the relative power of multiplex sibships greatly only when penetrance is high. It was found that the 2/N weighting proposed by Suarez and Hodge [1979] increased power over an unweighted analysis in many situations, provided significance levels were adjusted appropriately by simulation.