Hidden linkage: a comparison of the affected sib pair (ASP) test and transmission/disequilibrium test (TDT)

I compare the transmission/disequilibrium test (TDT) and affected sib pair (ASP) test under a general algebraic model describing a bi-allelic disease locus. Assuming linkage to a bi-allelic marker, I derive two binomial probabilities, one for parental allele 'transmission' (Pt) which determines the magnitude of the TDT chi 2 statistic (chi 2tdt), and a second for identity-by-descent (ibd) marker allele 'sharing' (Ps) which determines the magnitude of the ASP test statistic (chi 2asp). I also consider the ASP test applied to a completely polymorphic marker and demonstrate that the probability of ASP marker allele sharing (Ps) is identical to Ps observed for a bi-allelic marker in equilibrium with the disease locus. I present a general framework for determining the power of the TDT and ASP test based on expressions for Pt, Ps and the proportion (H/F) of ascertained parents who are informative at the marker. Two previous analytic investigations of TDT power based on the work of Ott (1989), and Risch & Merikangas (1996) are shown to be special cases of this general framework. In addition, I show the relationship between the framework I present and a third analytic investigation of TDT power for multi-allelic markers based on the work of Sham & Curtis (1995).