Small Sample Kernel Association Tests for Human Genetic and Microbiome Association Studies

Kernel machine based association tests (KAT) have been increasingly used in testing the association between an outcome and a set of biological measurements due to its power to combine multiple weak signals of complex relationship with the outcome through the specification of a relevant kernel. Human genetic and microbiome association studies are two important applications of KAT. However, the classic KAT framework relies on large sample theory, and conservativeness has been observed for small sample studies, especially for microbiome association studies. The common approach for addressing the small sample problem relies on computationally intensive resampling methods. Here, we derive an exact test for KAT with continuous traits, which resolve the small sample conservatism of KAT without the need for resampling. The exact test has significantly improved power to detect association for microbiome studies. For binary traits, we propose a similar approximate test, and we show that the approximate test is very powerful for a wide range of kernels including common variant- and microbiome-based kernels, and the approximate test controls the type I error well for these kernels. In contrast, the sequence kernel association tests have slightly inflated genomic inflation factors after small sample adjustment. Extensive simulations and application to a real microbiome association study are used to demonstrate the utility of our method.