Likelihoods and TDT for the Case-Parents Design
Daniel J. Schaid
Genetic Epidemiology ,
16(3):250-260 (1999).
Abstract
Association studies using diseased cases and their parents avoid biases due to
population stratification, and the transmission/disequilibrium test (TDT) is a
popular method of analysis. Sample size and power calculations for the TDT
method have been reported, but often for the special situation of
multiplicative effects of alleles on the genotype relative risks.
Furthermore, some of the
proposed calculations ignore the dependence of transmitted alleles from a pair
of heterozygous parents when the effects are not multiplicative, which can
lead to erroneous sample size calculations. We demonstrate how to calculate
sample size and power for the TDT method for general genotype relative risks.
As an alternative to the TDT method, we present likelihood methods for a
variety of genotype relative risk models. Exact likelihood methods are
presented to allow for accurate small-sample analyses. We demonstrate by
numerical comparisons: (1) that the TDT method is inefficient for recessive
patterns of relative risks, (2) for alleles that are not rare, falsely
assuming a
multiplicative model can lead to gross underestimation of the required sample
size for the TDT statistic, and (3) for common alleles, if the true genotype
relative risks have an approximately dominant pattern, then the TDT method
can be grossly inefficient compared to likelihood methods. An alternative
likelihood ratio statistic, based on two degrees of freedom, tends to be robust
for a wide range of genotype relative risk models. Finally, we discuss how to
use standard software for conditional logistic regression to accurately assess
effects of alleles as well as genotype-environment interaction.
Association Studies