Bayes factors based on robust TDT-type tests for family trio design

Adaptive transmission disequilibrium test (aTDT) and MAX3 test are two robust-efficient association tests for case-parent family trio data. Both tests incorporate information of common genetic models including recessive, additive and dominant models and are efficient in power and robust to genetic model specifications. The aTDT uses information of departure from Hardy-Weinberg disequilibrium to identify the potential genetic model underlying the data and then applies the corresponding TDT-type test, and the MAX3 test is defined as the maximum of the absolute value of three TDT-type tests under the three common genetic models. In this article, we propose three robust Bayes procedures, the aTDT based Bayes factor, MAX3 based Bayes factor and Bayes model averaging (BMA), for association analysis with case-parent trio design. The asymptotic distributions of aTDT under the null and alternative hypothesis are derived in order to calculate its Bayes factor. Extensive simulations show that the Bayes factors and the p-values of the corresponding tests are generally consistent and these Bayes factors are robust to genetic model specifications, especially so when the priors on the genetic models are equal. When equal priors are used for the underlying genetic models, the Bayes factor method based on aTDT is more powerful than those based on MAX3 and Bayes model averaging. When the prior placed a small (large) probability on the true model, the Bayes factor based on aTDT (BMA) is more powerful. Analysis of a simulation data about RA from GAW15 is presented to illustrate applications of the proposed methods.