  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 non-collapsible 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.
