The standard design used for the TDT is to ascertain families composed of two parents and one affected offpring ("parent-offspring trios"). Typically, parent-offspring trios are ascertained with disregard to the disease status of other relatives.
Whittaker and Lewis (1998) showed that when the only genetic contribution to disease liability is the test locus itself (i.e. background heritability Va = 0), the power of the TDT can dramatically increase by selecting parent-offspring trios conditional on having another affected first-degree relative (e.g. a parent). However, the assumption that Va = 0 is clearly unrealistic for common, complex diseases.
Indeed, Risch (2001) later showed that for diseases with high heritability, there may be little advantage in ascertaining families with multiple affected offspring as opposed to families with one affected offspring only.
We developed an analytical approach to estimate the power of the TDT for different ascertainment strategies and family structure, while accounting for the effects of residual polygenic and environmental factors on disease liability. This approach accounts for the non-independence of parental transmissions to affected offspring and so it is valid for any modes of inheritance and number of affected offspring used in the TDT. The power estimates derived from this approach match to the second decimal place the empirical power obtained through the analysis of simulated datasets (for 100,000 replicates).
We used this approach to show that for most common diseases, ascertainment of parent-offspring trios conditional on family history often decreases the power of the TDT. We also introduced a simplified extension to the TDT (parenTDT) that may help to recover power in these situations.
Both methods - the analytical approach to estimate the power of the TDT and the parenTDT - are described in Ferreira et al. (submitted). The reference section describes the input and output parameters for the TDT power calculator.