Supplementary Material for: A Powerful Two-Stage Association Test Using Case-Control and Case-Parents Genotype Data

<i>Objective:</i> The performance of association tests based on case-control or case-parents substudy alone can be improved by jointly using genetic data from two substudies. However, genetic data from different sources may not be combinable due to population stratification. We propose a two-stage association test based on using combinability tests in stage 1 and association tests in stage 2. <i>Methods:</i> The combinability tests are designed for testing that genotype data from different sources have same genotype frequencies and relative risks. The association tests are well known tests in the literature. We propose a method to adjust the significance levels at two stages so that the overall type I error rate of the two-stage test can be controlled at the desired level. <i>Results:</i> The simulation results confirm that the two-stage test has empirical type I error rates approximately equal to the predetermined levels while making substantially fewer false negatives than the usual test based only on case-parents substudy. <i>Conclusion:</i> It is advantageous to combinecase-control and case-parents data into a single analysis.The two-stage test has significant power improvement when the family-based test has weak or moderate power performance and is robust to the effect of population stratification.