Purely prognostic variables may modify marginal treatment effects for non-collapsible effect measures

In evidence synthesis, effect measure modifiers are typically described as variables that induce treatment effect heterogeneity at the individual level, through treatment-covariate interactions in an outcome model parametrized at such level. As such, effect modification is defined with respect to a conditional measure. However, marginal effect estimates are required for population-level decisions in health technology assessment. For non-collapsible effect measures, purely prognostic variables that do not predict response to treatment at the individual level may modify marginal treatment effects at the population level. This has important implications for recommended practices for evidence synthesis. Firstly, unadjusted indirect comparisons of marginal effects may be biased in the absence of individual-level treatment effect heterogeneity. Secondly, covariate adjustment may be necessary to account for cross-study imbalances in purely prognostic variables. Popular summary measures in meta-analysis such as odds ratios and hazard ratios are non-collapsible. Collapsible measures would facilitate the transportability of marginal effects between studies by: (1) removing dependence on model-based covariate adjustment when there is treatment effect homogeneity at the individual level; and (2) facilitating the selection of baseline characteristics for covariate adjustment when there is heterogeneity.