Power calculations for likelihood ratio tests for offspring genotype risks, maternal effects, and parent‐of‐origin (POO) effects in the presence of missing parental genotypes when unaffected siblings are available

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Abstract
Genotype‐based likelihood‐ratio tests (LRT) of association that examine maternal and parent‐of‐origin effects have been previously developed in the framework of log‐linear and conditional logistic regression models. In the situation where parental genotypes are missing, the expectation‐maximization (EM) algorithm has been incorporated in the log‐linear approach to allow incomplete triads to contribute to the LRT. We present an extension to this model which we call the Combined_LRT that incorporates additional information from the genotypes of unaffected siblings to improve assignment of incompletely typed families to mating type categories, thereby improving inference of missing parental data. Using simulations involving a realistic array of family structures, we demonstrate the validity of the Combined_LRT under the null hypothesis of no association and provide power comparisons under varying levels of missing data and using sibling genotype data. We demonstrate the improved power of the Combined_LRT compared with the family‐based association test (FBAT), another widely used association test. Lastly, we apply the Combined_LRT to a candidate gene analysis in Autism families, some of which have missing parental genotypes. We conclude that the proposed log‐linear model will be an important tool for future candidate gene studies, for many complex diseases where unaffected siblings can often be ascertained and where epigenetic factors such as imprinting may play a role in disease etiology.Genet. Epidemiol.