Estimating causal effects of rare treatments on binary outcomes: addressing sample size requirements and bias correction.

backgroundInverse probability weighting (IPW) is a widely used method to estimate the causal effect of an exposure on the outcome of interest in epidemiological observational studies. IPW estimators derived from estimated propensity scores (PS) for a binary exposure are unbiased and consistent under some identifiability conditions. However, the properties of IPW estimators have not been extensively studied for rare binary exposures, specifically in settings with a low events per variable (EPV) in the PS model, where the EPV is often used to quantify the rareness of a binary exposure.

methodsGiven the EPV value related to sample size and exposure prevalence, this study investigates the performance of the IPW estimator under varying EPV conditions through simulations, aiming to (i) determine the minimum EPV required for obtaining a consistent IPW estimator of the average causal effect (IPW-ATE) and (ii) evaluate bootstrap-based bias correction for low EPV cases. We have conducted two separate simulation series (one for each case) under various simulation scenarios, varying the outcome prevalence, sample size, number of baseline covariates, and PS model misspecification or overfitting case.

resultsThe simulation results show that the IPW-ATE estimator generally produced consistent estimates of the ATE when the propensity score (PS) model was correctly specified, with both bias and the robust standard error (robSE) decreasing as sample size and EPV increased. However, at low EPV values (EPV [Formula: see text]), the estimator does not exhibit consistent behavior for either the ATE or its robSE. Its performance under an overfitted PS model was similar to that under correct specification, suggesting that overfitting did not materially affect consistency. In contrast, PS model misspecification leads to persistent inconsistency of the IPW estimator, even at higher EPV values. Moreover, in low-EPV settings and under correct PS specification, bootstrap bias correction improves finite-sample performance and promotes convergence toward the true ATE. An application of the method to estimate the causal effect of low birth weight on malnutrition among children under five supports simulation findings and provides an intuitive interpretation.

conclusionThe findings of this study suggest some practical guidance for applied settings. When estimating IPW-based ATEs for causal interpretation, it may be helpful for researchers to evaluate treatment prevalence, sample size, and the number of baseline covariates to determine the EPV value for the PS model. Standard IPW-ATE estimates with robust standard errors generally perform reasonably well when EPV[Formula: see text], provided that the PS model is correctly specified. In settings with lower EPV (EPV [Formula: see text]), bootstrap bias-corrected IPW-ATE estimates can be considered a supplementary approach to help reduce potential bias.