Transportability of model-based estimands in evidence synthesis

In evidence synthesis, effect 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, but marginal effect estimates are required for population-level decisions in health technology assessment. For noncollapsible measures, purely prognostic variables that are not determinants of treatment response at the individual level may modify marginal effects, even where there is individual-level treatment effect homogeneity. With heterogeneity, marginal effects for measures that are not directly collapsible cannot be expressed in terms of marginal covariate moments, and generally depend on the joint distribution of conditional effect measure modifiers and purely prognostic variables. There are implications for recommended practices in evidence synthesis. Unadjusted anchored indirect comparisons can be biased in the absence of individual-level treatment effect heterogeneity, or when marginal covariate moments are balanced across studies. Covariate adjustment may be necessary to account for cross-study imbalances in joint covariate distributions involving purely prognostic variables. In the absence of individual patient data for the target, covariate adjustment approaches are inherently limited in their ability to remove bias for measures that are not directly collapsible. Directly collapsible measures would facilitate the transportability of marginal effects between studies by: (1) reducing dependence on model-based covariate adjustment where there is individual-level treatment effect homogeneity or marginal covariate moments are balanced; and (2) facilitating the selection of baseline covariates for adjustment where there is individual-level treatment effect heterogeneity.