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

Abstract

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.

How to perform prespecified subgroup analyses when using propensity score methods in the case of imbalanced subgroups

“…Our simulation study showed that the two “across subsets” and “within subsets” strategies achieve similar results in terms of bias and variance, provided that interaction terms between the subset variable and other covariates influencing the choice of treatment are incorporated. Otherwise, the omission of these interaction terms based on the “across subsets” strategy induced an important bias, regardless of the PS-based method used, which confirms previous results [ 33 , 34 ]. This bias led to the identification of an interaction that was not found with the other two strategies in our illustrative example.…”

“…The “within subsets” strategy was also slightly more robust than the “across subsets” strategy in this case. Although previous studies on this topic focused on PS matching without replacement [ 14 – 16 , 33 – 37 ], compared to the other methods, this method achieved a bias in the estimation of the treatment effect in our setting of large differences between subsets. This bias has been previously named the “unmatched patient bias” [ 38 ].…”

“…We first used propensity score matching, in line with recent works that used Monte Carlo simulations to evaluate propensity score matching with data from complex sample surveys [ 42 ], when dealing with clustered data [ 43 ], or when a confounder has missing data [ 44 ]. Other PS-based methods could have been used, such as the inverse probability treatment weighting (IPTW), which is commonly used in subset analyses [ 16 , 33 , 36 , 37 ]. This method has been reported to achieve better performance than PS matching in the case of right-censored outcomes [ 16 ].…”

A Tutorial for Propensity Score Weighting for Moderation Analysis With Categorical Variables

“…In this model specification, we assume the absence of interactions between covariates bold-italicX and Z for illustrative purposes. If such interactions exist, it is best to control for these additional interaction terms in the final outcome model as well as to assess the balance of the interaction between X and Z . 67 We also assume only 1 moderator of interest; if interest lies in the estimation of multiple M-ATEs, it is possible to repeat this procedure independently for each candidate moderator. In such a case, care should be taken to adjust for multiple hypothesis testing when estimating the additional models.…”

Methodological perspectives on the study of the health effects of unemployment – reviewing the mode of unemployment, the statistical analysis method and the role of confounding factors

“…Propensity score methods and traditional regression modelling, such as G-computation, tend to yield similar results [11], but this has yet to be investigated within our field of interest. Simulation studies have revealed that the variable selection has a bearing on the result when using propensity scores [12][13][14][15], but for unemployment and health this have not previously been investigated.…”