  When estimating an effect of an action with a randomized or observational
study, that study is often not a random sample of the desired target
population. Instead, estimates from that study can be transported to the target
population. However, transportability methods generally rely on a positivity
assumption, such that all relevant covariate patterns in the target population
are also observed in the study sample. Strict eligibility criteria,
particularly in the context of randomized trials, may lead to violations of
this assumption. Two common approaches to address positivity violations are
restricting the target population and restricting the relevant covariate set.
As neither of these restrictions are ideal, we instead propose a synthesis of
statistical and simulation models to address positivity violations. We propose
corresponding g-computation and inverse probability weighting estimators. The
restriction and synthesis approaches to addressing positivity violations are
contrasted with a simulation experiment and an illustrative example in the
context of sexually transmitted infection testing uptake. In both cases, the
proposed synthesis approach accurately addressed the original research question
when paired with a thoughtfully selected simulation model. Neither of the
restriction approaches were able to accurately address the motivating question.
As public health decisions must often be made with imperfect target population
information, model synthesis is a viable approach given a combination of
empirical data and external information based on the best available knowledge.
