A robust mean and variance test with application to high-dimensional phenotypes

James R Staley, Frank Windmeijer, Matthew J Suderman, Matt S Lyon, George Davey Smith, Kate M Tilling*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
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Most studies of continuous health-related outcomes examine differences in mean levels (location) of the outcome by exposure. However, identifying effects on the variability (scale) of an outcome, and combining tests of mean and variability (location-and-scale), could provide additional insights into biological mechanisms. A joint test could improve power for studies of high-dimensional phenotypes, such as epigenome-wide association studies of DNA methylation at CpG sites. One possible cause of heterogeneity of variance is a variable interacting with exposure in its effect on outcome, so a joint test of mean and variability could help in the identification of effect modifiers. Here, we review a scale test, based on the Brown-Forsythe test, for analysing variability of a continuous outcome with respect to both categorical and continuous exposures, and develop a novel joint location-and-scale score (JLSsc) test. These tests were compared to alternatives 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). In simulations, the Brown-Forsythe and JLSsc tests retained correct type I error rates when the outcome was not normally distributed in contrast to the other approaches tested which all had inflated type I error rates. These tests also identified > 7500 CpG sites for which either mean or variability in cord blood methylation differed according to gender or gestational age. The Brown-Forsythe test and JLSsc are robust tests that can be used to detect associations not solely driven by a mean effect.
Original languageEnglish
JournalEuropean Journal of Epidemiology
Early online date15 Oct 2021
Publication statusPublished - 15 Oct 2021

Bibliographical note

Funding Information:
This work was supported by an MRC Methodology Research Grant [grant number MR/M025020/1]. Work was performed in the MRC Integrative Epidemiology Unit [grant numbers MC_UU_00011/1 and MC_UU_00011/3]. The UK Medical Research Council and Wellcome [grant number 217065/Z/19/Z] and the University of Bristol provide core support for ALSPAC. A comprehensive list of grants funding is available on the ALSPAC website ( http://www.bristol.ac.uk/alspac/external/documents/grant-acknowledgements.pdf ). Methylation data in the ALSPAC cohort were initially generated as part of the UK BBSRC funded (BB/I025751/1 and BB/I025263/1) Accessible Resource for Integrated Epigenomic Studies (ARIES, http://www.ariesepigenomics.org.uk ). Subsequent additions were funded by the National Institute of Child and Human Development [grant number R01HD068437], NIH [grant number 5RO1AI121226-02] and CONTAMED EU collaborative Project [grant number 212502]. ARIES is maintained under the auspices of the MRC Integrative Epidemiology Unit which is supported by the University of Bristol and the UK Medical Research Council (MC_UU_00011/5, MC_UU_12013/2, MC_UU_00011/1, MC_UU_00011/3, MC_UU_12013/9). This study was supported by the NIHR Biomedical Research Centre at University Hospitals Bristol and Weston NHS Foundation Trust and the University of Bristol. The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. This publication is the work of the authors and Kate Tilling will serve as the guarantor for the contents of this paper.

Publisher Copyright:
© 2021, The Author(s).


  • Variability test
  • Joint location-and-scale test
  • DNA methylation


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