Allowing for missing parents in genetic studies of case-parent triads.

In earlier work, my colleagues and I described a log-linear model for genetic data from triads composed of affected probands and their parents. This model allows detection of and discrimination between effects of an inherited haplotype versus effects of the maternal haplotype, which presumably would be mediated by prenatal factors. Like the transmission disequilibrium test (TDT), the likelihood-ratio test (LRT) based on this model is not sensitive to associations that are due to genetic admixture. When used as a method for testing for linkage disequilibrium, the LRT can be regarded as an alternative to the TDT. When one or both parents are missing, the resulting incomplete triad must be discarded to ensure validity of the TDT, thereby sacrificing information. By contrast, when the problem is set in a likelihood framework, the expectation-maximization algorithm allows the incomplete triads to contribute their information to the LRT without invalidation of the analysis. Simulations demonstrate that much of the lost statistical power can be recaptured by means of this missing-data technique. In fact, power is reasonably good even when no triad is complete-for example, when a study is designed to include only mothers of cases. Information from siblings also can be incorporated to further improve the statistical power when genetic data from parents or probands are missing.