  When extending inferences from a randomized trial to a new target population,
the transportability condition for conditional difference effect measures is
invoked to identify the marginal causal mean difference in the target
population. However, many clinical investigators believe that conditional
relative effect measures are more likely to be "transportable" between
populations. Here, we examine the identification and estimation of the marginal
counterfactual mean difference and ratio under the transportability condition
for conditional relative effect measures. We obtain identification results for
two scenarios that often arise in practice when individuals in the target
population (1) only have access to the control treatment, and (2) have access
to the control and other treatments but not necessarily the experimental
treatment evaluated in the trial. We then propose model and rate multiply
robust and nonparametric efficient estimators that allow for the use of
data-adaptive methods to model the nuisance functions. We examine the
performance of the methods in simulation studies and illustrate their use with
data from two trials of paliperidone for patients with schizophrenia. We
conclude that the proposed methods are attractive when background knowledge
suggests that the transportability condition for conditional relative effect
measures is more plausible than alternative conditions.
