A LOG-LINEAR APPROACH TO CASE-PARENT-TRIAD DATA - ASSESSING EFFECTS OF DISEASE GENES THAT ACT EITHER DIRECTLY OR THROUGH MATERNAL EFFECTS AND THAT MAY BE SUBJECT TO PARENTAL IMPRINTING

We describe a log-linear method for analysis of case-parent-triad data , based on maximum likelihood with stratification on parental mating t ype. The method leads to estimates of association parameters, such as relative risks, for a single allele, and also to likelihood ratio chi( 2) tests (LRTs) of linkage disequilibrium. Hardy-Weinberg equilibrium need not be assumed. Our simulations suggest that the LRT has power si milar to that of the chi(2) ''score'' test proposed by Schaid and Somm er and that both can outperform the transmission/disequilibrium test ( TDT), although the TDT can perform better under an additive model of i nheritance. Because a restricted version of the LRT is asymptotically equivalent to the TDT, the proposed test can be regarded as a generali zation of the TDT. The method that we describe generalizes easily to a ccommodate maternal effects on risk and, in fact, produces powerful an d orthogonal tests of the contribution of fetal versus maternal geneti c factors. We further generalize the model to allow for effects of par ental imprinting. Imprinting effects can be fitted by a simple, iterat ive procedure that relies on the expectation-maximization algorithm an d that uses standard statistical software for the maximization steps. Simulations reveal that LRT tests for detection of imprinting have ver y good operating characteristics. When a single allele is under study, the proposed method can yield powerful tests for detection of linkage disequilibrium and is applicable to a broader array of causal scenari os than is the TDT.