The use of mixture models to perform quantitative tests for linkage disequilibrium, maternal effects, and parent-of-origin effects with incomplete subject-parent triads

The transmission disequilibrium test and related methods require complete triads of genotyped cases plus both parents to test for linkage disequilibrium in the presence of population stratification. Based on the work of Weinberg (1999ab) and Schaid and Li (1997) with dichotomous outcomes, we discuss how additional tests for maternal or parent-of-origin effects can be performed and incomplete subject-parent triads can be used in situations where the outcome is a quantitative variable. This is achieved using a finite mixture model where class membership is known for complete triads and unknown for incomplete triads. Simulations were performed assuming different genetic models and various amounts of missing parental genotypes. Results showed that the tests resulted in accurate Type I errors, recovered much of the loss in information caused by missing genotypes, and yielded unbiased parameter estimates. Extensions of the model to nuclear families, multiple loci, and multiple outcome variables are briefly discussed.