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P82 An illustration of the analytical challenges due to mathematical coupling in health geography research
  1. L Berrie1,2,
  2. PD Norman3,
  3. PD Baxter1,2,
  4. MS Gilthorpe1,2
  1. 1Leeds Institute for Data Analytics, University of Leeds, Leeds, UK
  2. 2Division of Epidemiology and Biostatistics, University of Leeds, Leeds, UK
  3. 3School of Geography, University of Leeds, Leeds, UK


Background It has been acknowledged that the use of ratio variables is problematic in regression analysis where ratios comprise common components and are present in both the dependent and independent constituents of the model, e.g. regression analyses of ratio variables with common population denominators. However, such ratio variables are ubiquitous in health research and their resultant mathematical coupling (MC) has not been investigated extensively in relation to studies in health geography, where common population denominators are frequently encountered. It is common, for instance, that area level measures for health outcomes are considered in relation to area levels of mortality and/or indicators of social deprivation, where the common denominator is the area population. Our study seeks to illustrate this issue and examines the implications of this form of MC from a causal inference perspective.

Methods We examine the impact of MC amongst ratio variables in regression analyses using simulated data based on the correlation structure and distribution of variables derived from the UK census. Specifically, we consider the proportion of limiting long term illness (LLTI) in relation to mortality rates and the Townsend Material Deprivation Score (constructed from percentages of the population of an area that are experiencing pre-defined properties). Simulations are constructed under the null hypothesis, i.e. there is no impact of an area measure of deprivation on the relationship between mortality and proportion of limiting long term illness. A causal framework is introduced utilising directed acyclic graphs (DAGs) to assess variable relationships and to suggest analytical strategies that mitigate any problems arising due to MC.

Results We show that artefactual relationships arise in the regression analyses of composite proportions due to MC: area measures of deprivation appear to influence the relationship between LLTI and mortality when no such influence is present in the simulated data. A DAG aids comprehension of this issue from a causal inference perspective and, depending upon the exact nature of the MC present, the DAG can also point to alternative analytical strategies that are discussed.

Conclusion Mathematical coupling of ratio variables has been recognised and reported on in the past, yet its problems remain pervasive. By setting the problem within a causal framework, we provide a means by which the issue might be more readily identified. Furthermore, using DAGs can help direct alternative analytical strategies to remove bias due to MC from future health research.

  • mathematical coupling
  • ratio variables
  • health geography

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