Sensitivity analysis using bias functions for studies extending inferences from a randomized trial to a target population

Abstract

Extending (i.e., generalizing or transporting) causal inferences from a randomized trial to a target population requires assumptions that randomized and nonrandomized individuals are exchangeable conditional on baseline covariates. These assumptions are made on the basis of background knowledge, which is often uncertain or controversial, and need to be subjected to sensitivity analysis. We present simple methods for sensitivity analyses that directly parameterize violations of the assumptions using bias functions and do not require detailed background knowledge about specific unknown or unmeasured determinants of the outcome or modifiers of the treatment effect. We show how the methods can be applied to non-nested trial designs, where the trial data are combined with a separately obtained sample of nonrandomized individuals, as well as to nested trial designs, where the trial is embedded within a cohort sampled from the target population.

Keywords: bias analysis; double robustness; g-formula; generalizability; inverse probability weighting; sensitivity analysis; transportability.

FIGURE 1

Sensitivity analysis results for transporting inferences between two research centers participating in the HALT-C trial. AIOW2 = augmented inverse odds weighting estimator with normalized weights; IOW2 = inverse odds weighting with normalized weights; OM = outcome model-based estimator. Results are shown as point estimates (black lines) and corresponding 95% confidence intervals (gray lines) for potential outcome means under treatment a = 1 (solid lines) and a = 0 (dashed lines). Results for IOW1 and AIOW1 were similar to IOW2 and AIOW2, respectively, and are shown in the Appendix.

FIGURE 2

Sensitivity analysis results for transporting inferences from the ACTG 175 trial to the target population of trial-eligible women in WIHS. AIOW2 = augmented inverse odds weighting estimator with normalized weights; IOW2 = inverse odds weighting with normalized weights; OM = outcome model-based estimator. Results are shown as point estimates (black lines) and corresponding 95% confidence intervals (gray lines) for potential outcome means under treatment a = 1 (solid lines) and a = 0 (dashed lines). Results for IOW1 and AIOW1 were similar to IOW2 and AIOW2, respectively, and are shown in the Appendix.