Background: Most studies of high-dimensional phenotypes focus on assessing differences in mean levels (location) of the phenotype by exposure, e.g. epigenome-wide association studies of the effect of exposure on mean DNA methylation at CpG sites. However, identifying effects on the variability (scale) of these outcomes could provide additional insights into biological mechanisms. Methods: We introduce a scale test, based on the Brown-Forsythe test, for analysing phenotype variability for both categorical and continuous exposures. We also present a novel joint location-and-scale score test (JLSsc). These tests were compared to the equivalent likelihood-ratio tests and alternative approaches in simulations and used to test associations of mean and variability of DNA methylation with gender and gestational age using data from the Accessible Resource for Integrated Epigenomics Studies (ARIES). Results: The extended Brown-Forsythe test and JLSsc had good statistical properties for both categorical and continuous exposures, without requiring transformation of the methylation levels. All of the other methods assessed had inflated type I error using the raw methylation levels. In ARIES, JLSsc identified 7228 and 340 CpG sites (240 CpGs were associated with methylation variability differences between males and females using the extended Brown-Forsythe test) that were associated with either mean or variability in gender and gestational age in cord blood, respectively. Conclusions: The extended Brown-Forsythe test and JLSsc are robust tests of variability and combined mean and variability effects, respectively. These tests can be used to detect associations not solely driven by a mean effect of the exposure on the outcome.
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