Risk factors relate to the variability of health outcomes as well as the mean: A GAMLSS tutorial.

David Bann,Tim J Cole,Liam Wright

doi:10.7554/elife.72357

Abstract

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). The 1970 British birth cohort study was used, with body mass index (BMI; N = 6007) and mental wellbeing (Warwick-Edinburgh Mental Wellbeing Scale; N = 7104) 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. 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). 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/). 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.

Highlights

What is health? Contrary to simplistic notions of its being defined as the absence of disease, it is increasingly understood that most outcomes of public health significance are continuous in nature.[1]This applies to both physical and mental health outcomes.[2 3]
We provide a worked example of the use and interpretation of GAMLSS
We examined if the binary split of risk factors influenced the inferences drawn—additional analyses were conducted with them coded instead as categorical variables

Summary

Introduction

What is health? Contrary to simplistic notions of its being defined as the absence of disease, it is increasingly understood that most outcomes of public health significance are continuous in nature.[1]This applies to both physical and mental health outcomes.[2 3]. Contrary to simplistic notions of its being defined as the absence of disease, it is increasingly understood that most outcomes of public health significance are continuous in nature.[1]. Analysing the determinants of health using continuous rather than binary outcomes is beneficial both practically (with more statistical power and less information loss) and substantively (greater aetiological understanding). Those at high risk of a developing an illness may comprise a minority of those who succumb.[4]. Studies into the effect on continuous outcomes of exposures, be they risk factors in observational studies or interventions in randomised trials,[3] typically focus on mean differences in the outcome, using linear regression. We provide a tutorial for investigating this using GAMLSS (Generalised Additive Models for Location, Scale and Shape)

Methods

Results

Conclusion