Causal Inference
Addressing nonpositivity using statistical and mathematical models Paul Zivich* Paul Zivich Jessie K Edwards Bonnie Shook-Sa Eric Lofgren Justin Lessler Stephen R Cole
Transportability methods can be considered when the desired target population and available study population differ on measured covariates. Most transportability methods rely on a positivity assumption, such that all relevant covariate patterns in the target population are also observed in the secondary population from which the available data was selected. Strict eligibility criteria, particularly in the context of randomized trials, may lead to violations of this assumption. Common approaches to nonpositivity are to restrict the target population, restrict the adjustment set, or extrapolate from a statistical model. Instead, we propose a synthesis of statistical (e.g., g-methods) and mathematical (e.g., microsimulation, mechanistic) models that avoids limitations of the alternative methods. Briefly, a statistical model is fit for the regions where positivity holds, and a mathematical model is used to fill-in, or impute, across the nonpositive regions. To implement our approach, we propose two estimators, one based on a marginal structural model and the other on the conditional average causal effect. The proposed synthesis method is illustrated by transporting the effect of antiretroviral therapy on CD4 cell count from the AIDS Clinical Trial Group (ACTG) 175 to the Women’s Interagency HIV Study. Due to inclusion criteria in ACTG 175, nonpositivity occurs by baseline CD4 cell count. Using the synthesis approach and contemporaneous information on the conditional average causal effect, bounds on the effect of antiretroviral therapy are estimated for the nonpositive regions. Our results indicate that two-drug ART would have been beneficial on short-term CD4 cell counts in the target population without relying on the more restrictive assumptions of the other non-synthesis approaches. The synthesis approach sheds light on a way to address positivity violations and unifies different methodological areas to address a single scientific question.
