1. Epidemiology and Global Health
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Risk factors relate to the variability of health outcomes as well as the mean: a GAMLSS tutorial

  1. David Bann  Is a corresponding author
  2. Liam Wright
  3. Tim J Cole
  1. University College London, United Kingdom
Research Article
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Cite this article as: eLife 2022;11:e72357 doi: 10.7554/eLife.72357


Background: Risk factors or interventions may affect the variability as well as the mean of health outcomes. Understanding this can aid aetiological understanding and public health translation, in that interventions which shift the outcome mean and reduce variability are typically preferable to those which affect only the mean. However, most commonly used statistical tools do not test for differences in variability. Tools that do have few epidemiological applications to date, and fewer applications still have attempted to explain their resulting findings. We thus provide a tutorial for investigating this using GAMLSS (Generalised Additive Models for Location, Scale and Shape).

Methods: The 1970 British birth cohort study was used, with body mass index (BMI; N=6,007) and mental wellbeing (Warwick-Edinburgh Mental Wellbeing Scale; N=7,104) measured in midlife (42-46 years) as outcomes. We used GAMLSS to investigate how multiple risk factors (sex, childhood social class and midlife physical inactivity) related to differences in health outcome mean and variability.

Results: Risk factors were related to sizable differences in outcome variability-for example males had marginally higher mean BMI yet 28% lower variability; lower social class and physical inactivity were each associated with higher mean and higher variability (6.1% and 13.5% higher variability, respectively). For mental wellbeing, gender was not associated with the mean while males had lower variability (-3.9%); lower social class and physical inactivity were each associated with lower mean yet higher variability (7.2% and 10.9% higher variability, respectively).

Conclusions: The results highlight how GAMLSS can be used to investigate how risk factors or interventions may influence the variability in health outcomes. This underutilised approach to the analysis of continuously distributed outcomes may have broader utility in epidemiologic, medical, and psychological sciences. A tutorial and replication syntax is provided online to facilitate this (https://osf.io/5tvz6/).

Funding: DB is supported by the Economic and Social Research Council (grant number ES/M001660/1), The Academy of Medical Sciences / Wellcome Trust ('Springboard Health of the Public in 2040' award: HOP001/1025); DB and LW are supported by the Medical Research Council (MR/V002147/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data availability

All data are available to download from the UK Data Archive: https://beta.ukdataservice.ac.uk/datacatalogue/series/series?id=200001

Article and author information

Author details

  1. David Bann

    Centre for Longitudinal Studies, Social Research Institute, University College London, london, United Kingdom
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6454-626X
  2. Liam Wright

    Centre for Longitudinal Studies, Social Research Institute, University College London, london, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.
  3. Tim J Cole

    Great Ormond Street Institute of Child Health, University College London, london, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.


Medical Research Council (MR/V002147/1)

  • David Bann
  • Liam Wright

Economic and Social Research Council (ES/M001660/1)

  • Liam Wright

Wellcome Trust (HOP001/1025)

  • David Bann

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.


Human subjects: This paper uses secondary data analysis using data from a cohort study which has been followed-up since birth in 1970. Cohort members provided informed consent, and the study received full ethical approval - most recently from the NRES Committee South East Coast-Brighton and Sussex.

Reviewing Editor

  1. Belinda Nicolau, McGill University, Canada

Publication history

  1. Received: July 20, 2021
  2. Accepted: January 4, 2022
  3. Accepted Manuscript published: January 5, 2022 (version 1)


© 2022, Bann et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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