  Epidemiologists and applied statisticians often believe that relative effect
measures conditional on covariates, such as risk ratios and mean ratios, are
``transportable'' across populations. Here, we examine the identification of
causal effects in a target population using an assumption that conditional
relative effect measures (e.g., conditional risk ratios or mean ratios) are
transportable from a trial to the target population. We show that
transportability for relative effect measures is largely incompatible with
transportability for difference effect measures, unless the treatment has no
effect on average or one is willing to make even stronger transportability
assumptions, which imply the transportability of both relative and difference
effect measures. We then describe how marginal causal estimands in a target
population can be identified under the assumption of transportability of
relative effect measures, when we are interested in the effectiveness of a new
experimental treatment in a target population where the only treatment in use
is the control treatment evaluated in the trial. We extend these results to
consider cases where the control treatment evaluated in the trial is only one
of the treatments in use in the target population, under an additional partial
exchangeability assumption in the target population (i.e., a partial assumption
of no unmeasured confounding in the target population). We also develop
identification results that allow for the covariates needed for
transportability of relative effect measures to be only a small subset of the
covariates needed to control confounding in the target population. Last, we
propose estimators that can be easily implemented in standard statistical
software.
