Abstract
Generalized linear models (GLMs) are widely used in biostatistics, e.g. to model binary responses or counts. For example, when analyzing RNA-Seq data, it is common to fit many GLMs simultaneously. GLMs are often misspecified due to overdispersion and heteroscedasticity. Existing quasi-likelihood methods for testing in misspecified GLMs often do not provide satisfactory type I error rate control. We provide a novel semi-parametric test, based on a permutation-type approach. Our test often provides better type I error control than its competitors. Further, we consider the common scenario that there are multiple response variables. Think for example about RNA-Seq or neuroimaging data. For each of the responses, association with the predictor of interest is tested. The challenge is then to deal with the multiple testing problem in a powerful and reliable way. To achieve this, we combine our approach with powerful permutation-based multiple testing methods.