Variable selection when estimating effects in external target populations

Abstract

External validity is an important part of epidemiologic research. To validly estimate effects in specific external target populations using a chosen effect measure (ie, "transport"), some methods require that one account for all effect measure modifiers (EMMs). However, little is known about how including other variables that are not EMMs (ie, non-EMMs) in adjustment sets affects estimates. Using simulations, we evaluated how inclusion of non-EMMs affected estimation of the transported risk difference (RD) by assessing the impacts of covariates that (1) differ (or not) between the trial and the target, (2) are associated with the outcome (or not), and (3) modify the RD (or not). We assessed variation and bias when covariates with each possible combination of these factors were used to transport RDs using outcome modeling or inverse odds weighting. Inclusion of variables that differed in distribution between the populations but were non-EMMs reduced precision, regardless of whether they were associated with the outcome. However, non-EMMs associated with selection did not amplify bias resulting from omission of necessary EMMs. Including all variables associated with the outcome may result in unnecessarily imprecise estimates when estimating treatment effects in external target populations.

Keywords: external validity; generalizability; odds weights; standardization; transportability.

Figure 1

Causal relationships defining 6 types of variables when considering a randomized trial of the effect of a treatment X on an outcome Y conducted in a population P = 0 targeting an external population P = 1. Variables modifying the effect of X on Y are shown in red (Z₀₁₁ and Z₁₁₁) on the lowest line.