Supplementary Material for: Rare-Variant Kernel Machine Test for Longitudinal Data from Population and Family Samples

<b><i>Objective:</i></b> The kernel machine (KM) test reportedly performs well in the set-based association test of rare variants. Many studies have been conducted to measure phenotypes at multiple time points, but the standard KM methodology has only been available for phenotypes at a single time point. In addition, family-based designs have been widely used in genetic association studies; therefore, the data analysis method used must appropriately handle familial relatedness. A rare-variant test does not currently exist for longitudinal data from family samples. Therefore, in this paper, we aim to introduce an association test for rare variants, which includes multiple longitudinal phenotype measurements for either population or family samples. <b><i>Methods:</i></b> This approach uses KM regression based on the linear mixed model framework and is applicable to longitudinal data from either population (L-KM) or family samples (LF-KM). <b><i>Results:</i></b> In our population-based simulation studies, L-KM has good control of Type I error rate and increased power in all the scenarios we considered compared with other competing methods. Conversely, in the family-based simulation studies, we found an inflated Type I error rate when L-KM was applied directly to the family samples, whereas LF-KM retained the desired Type I error rate and had the best power performance overall. Finally, we illustrate the utility of our proposed LF-KM approach by analyzing data from an association study between rare variants and blood pressure from the Genetic Analysis Workshop 18 (GAW18). <b><i>Conclusion:</i></b> We propose a method for rare-variant association testing in population and family samples using phenotypes measured at multiple time points for each subject. The proposed method has the best power performance compared to competing approaches in our simulation study.