On power and efficiency robust linkage tests for affected sibs

For diseases that do not follow a clear Mendelian pattern of inheritance nonparametric tests applied to affected sibs have been shown to be robust to the inherent uncertainty about the precise underlying genetic model. It is known that the weights optimizing the power of tests using IBD alleles shared by affected sib pairs or triples depend on the underlying model. We show how efficiency robustness techniques, used in other areas of statistics, provide a systematic approach for constructing a robust linear combination of the statistics that are optimal for the individual members of a family of plausible genetic models. The method depends on the correlation matrix of the optimal tests as these correlations reflect how different the models are. When the minimal correlation is less than 0.5, an alternate robust procedure is proposed. The methods apply to combining data from sibships of different sizes.