General equations for Pt, Ps, and the power of the TDT and the affected-sib-pair test

Several equations are highlighted here, whose algebraic symmetries and generality make them very useful for understanding and comparing the properties of the transmission disequilibrium test (TDT) and affected sib-pair test. Methods using the equations are also presented that yield precise estimates of sample sizes needed for genome scans or for testing a single candidate gene, and these power methods are shown to compare favorably with alternative approaches recently described by Knapp (1999) and by Tu and Whittemore (1999). Simple relationships are also noted that summarize the relative sample sizes required for equivalent power to detect association by the TDT or case-control designs. As single-nucleotide polymorphism (SNP) maps revolutionize the search for disease-causing genes, the equations should prove useful for planning and evaluating studies of linkage and association across a broad range of possible disease models and relationships between markers and linked disease loci.