The impact of moderator by confounder interactions in the assessment of treatment effect modification: a simulation study

BACKGROUND: When performed in an observational setting, treatment effect modification analyses should account for all confounding, where possible. Often, such studies only consider confounding between the exposure and outcome. However, there is scope for misspecification of the confounding adjustment when estimating moderation as the effects of the confounders may themselves be influenced by the moderator. The aim of this study was to investigate bias in estimates of treatment effect modification resulting from failure to account for an interaction between a binary moderator and a confounder on either treatment receipt or the outcome, and to assess the performance of different approaches to account for such interactions. METHODS: The theory behind the reason for bias and factors that impact the magnitude of bias is explained. Monte Carlo simulations were used to assess the performance of different propensity scores adjustment methods and regression adjustment where the adjustment 1) did not account for any moderator-confounder interactions, 2) included moderator-confounder interactions, and 3) was estimated separately in each moderator subgroup. A real-world observational dataset was used to demonstrate this issue. RESULTS: Regression adjustment and propensity score covariate adjustment were sensitive to the presence of moderator-confounder interactions on outcome, whilst propensity score weighting and matching were more sensitive to the presence of moderator-confounder interactions on treatment receipt. Including the relevant moderator-confounder interactions in the propensity score (for methods using this) or the outcome model (for regression adjustment) rectified this for all methods except propensity score covariate adjustment. For the latter, subgroup-specific propensity scores were required. Analysis of the real-world dataset showed that accounting for a moderator-confounder interaction can change the estimate of effect modification. CONCLUSIONS: When estimating treatment effect modification whilst adjusting for confounders, moderator-confounder interactions on outcome or treatment receipt should be accounted for. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-022-01519-7.