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 t riads of genotyped cases plus both parents to test for linkage disequilibri um in the presence of population stratification. Based on the work of Weinb erg (1999ab) and Schaid and Li (1997) with dichotomous outcomes, we discuss how additional tests for maternal or parent-of-origin effects can be perfo rmed and incomplete subject-parent triads can be used in situations where t he outcome is a quantitative variable. This is achieved using a finite mixt ure model where class membership is known for complete triads and unknown f or incomplete triads. Simulations were performed assuming different genetic models and various amounts of missing parental genotypes. Results showed t hat the tests resulted in accurate Type I errors, recovered much of the los s in information caused by missing genotypes, and yielded unbiased paramete r estimates. Extensions of the model to nuclear families, multiple loci, an d multiple outcome variables are briefly discussed.