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Primary care
Challenges in interpreting results from ‘multiple regression’ when there is interaction between covariates
  1. Ian Shrier1,2,
  2. Annabelle Redelmeier3,
  3. Mireille E Schnitzer4,
  4. Russell J Steele3
  1. 1 Epidemiology, Lady Davis Institute for Medical Research, Montreal, Québec, Canada
  2. 2 Lady Davis Institute, McGill University, Montreal, Québec, Canada
  3. 3 Mathematics and Statistics, McGill University, Montreal, Québec, Canada
  4. 4 Faculté de Pharmacie et École de Santé Publique, Universite de Montreal, Montreal, Québec, Canada
  1. Correspondence to Dr Ian Shrier, Epidemiology, Lady Davis Institute for Medical Research, Montreal, QC H3T 1E2, Canada; ian.shrier{at}


Properly interpreting research results is the foundation of evidence-based medicine. Most observational studies use multiple regression and report adjusted effects. In randomised trials, adjusted effects are often provided when there are chance baseline imbalances. The estimates for the exposure of interest (eg, treatment) from these adjusted analyses are usually interpreted as population average causal effects (PACEs); for example, what would be the difference in the mean outcome if everyone in the population was treated versus untreated? In this paper, we show this interpretation is incorrect when there is an interaction between treatment and other variables with respect to the outcome. We provide the appropriate methods to calculate the PACE from regression analyses and also introduce alternative methods that have gained popularity over the last 20 years. Finally, we explain why researchers should be cautious when excluding interaction terms based on p values.

  • regression
  • inverse probability treatment weighting
  • marginal estimates
  • conditional estimates

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  • Contributors Each of the authors contributed to the development of ideas and the writing of this paper. IS is the guarantor of the article. He is a primary care physician and epidemiologist working in the fields of evidence synthesis, injury epidemiology and causal inference. AR was a Masters student when the project began and has since graduated. She was instrumental in developing and editing the early drafts of the manuscript. MES and RJS are statisticians with expertise in causal inference and were essential in ensuring that the technical details of the manuscript were correct and that the English correctly conveyed the mathematical analyses.

  • Competing interests None declared.

  • Patient consent for publication Not required.

  • Provenance and peer review Not commissioned; externally peer reviewed.