Exploiting excess sharing: a more powerful test of linkage for affected sib pairs than the transmission/disequilibrium test

The transmission/disequilibrium test (TDT) is a popular, simple, and powerful test of linkage, which can be used to analyze data consisting of transmissions to the affected members of families with any kind pedigree structure, including affected sib pairs (ASPs). Although it is based on the preferential transmission of a particular marker allele across families, it is not a valid test of association for ASPs. Martin et al. devised a similar statistic for ASPs, T(sp), which is also based on preferential transmission of a marker allele but which is a valid test of both linkage and association for ASPs. It is, however, less powerful than the TDT as a test of linkage for ASPs. What I show is that the differences between the TDT and T(sp) are due to the fact that, although both statistics are based on preferential transmission of a marker allele, the TDT also exploits excess sharing in identity-by-descent transmissions to ASPs. Furthermore, I show that both of these statistics are members of a family of 'TDT-like' statistics for ASPs. The statistics in this family are based on preferential transmission but also, to varying extents, exploit excess sharing. From this family of statistics, we see that, although the TDT exploits excess sharing to some extent, it is possible to do so to a greater extent - and thus produce a more powerful test of linkage, for ASPs, than is provided by the TDT. Power simulations conducted under a number of disease models are used to verify that the most powerful member of this family of TDT-like statistics is more powerful than the TDT for ASPs