Generalizing Evidence from Randomized Trials using Inverse Probability of Sampling Weights

Abstract

Results obtained in randomized trials may not easily generalize to target populations. Whereas in randomized trials the treatment assignment mechanism is known, the sampling mechanism by which individuals are selected to participate in the trial is typically not known and assuming random sampling from the target population is often dubious. We consider an inverse probability of sampling weighted (IPSW) estimator for generalizing trial results to a target population. The IPSW estimator is shown to be consistent and asymptotically normal. A consistent sandwich-type variance estimator is derived and simulation results are presented comparing the IPSW estimator to a previously proposed stratified estimator. The methods are then utilized to generalize results from two randomized trials of HIV treatment to all people living with HIV in the United States.

Keywords: Causal inference; External validity/Generalizability; HIV/AIDS; Inverse probability weights; Randomized controlled trial; Target population.

Fig. 1

Comparison of the distributions of within-trial estimator ${\widehat{\mathrm{\Delta }}}_T$, stratified estimator ${\widehat{\mathrm{\Delta }}}_S$, and inverse probability of sampling weighted estimator ${\widehat{\mathrm{\Delta }}}_{\mathit{IPSW}}$, based on 5,000 simulated data sets where the sampling score model is correctly specified and Δ = 2 with one continuous covariate, β = (−7, 0.6) and α = 1 (scenario 4).