Speaker: Jiacheng Wu, Graduate Student, UW Biostatistics
Abstract: Mixed effects models are widely used to model heterogeneity. Under these models, it is often of interest to test the null hypothesis that both fixed-effects parameters and random-effects variance components are zero. Examples include testing the existence of effects in meta-analysis, whether a set of single-nucleotide polymorphisms (SNPs) are associated with disease outcomes in genetic variant association studies, and whether there is a time-varying treatment effect in survival analysis. Except for a few special cases, the asymptotic distribution of the likelihood ratio test is complicated and intractable, which motivates us to use score tests because of the computational simplicity. We consider a general mixed-effects framework where we propose a novel construction of independent score statistics from fixed-effects parameters and random-effects variance components. We consider the linear combinations of two score statistics. We show that the null and alternative distributions of this linear combination have tractable asymptotic distribution and are easy to approximate by a non-central chi-squared random variable, which facilitates fast power computation. We illustrate the power trade-off between linear combination weights and propose to choose the weight based on Bayes and Minimax criteria so that power can be balanced well across the alternative space. In comprehensive simulation studies, we compare our method to existing non-linear methods of combining independent score statistics.