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Challenges in interpreting results from ‘multiple regression’ when there is interaction between covariates

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.