Leveraging auxiliary data to improve precision in inverse probability-weighted analyses

Abstract

Purpose: To demonstrate improvements in the precision of inverse probability-weighted estimators by use of auxiliary variables, i.e., determinants of the outcome that are independent of treatment, missingness or selection.

Methods: First with simulated data, and then with public data from the National Health and Nutrition Examination Survey (NHANES), we estimated the mean of a continuous outcome using inverse probability weights to account for informative missingness. We assessed gains in precision resulting from the inclusion of auxiliary variables in the model for the weights. We compared the performance of robust and nonparametric bootstrap variance estimators in this setting.

Results: We found that the inclusion of auxiliary variables reduced the empirical variance of inverse probability-weighted estimators. However, that reduction was not captured in standard errors computed using the robust variance estimator, which is widely used in weighted analyses due to the non-independence of weighted observations. In contrast, a nonparametric bootstrap estimator properly captured the precision gain.

Conclusions: Epidemiologists can leverage auxiliary data to improve the precision of weighted estimators by using bootstrap variance estimation, or a closed-form variance estimator that properly accounts for the estimation of the weights, in place of the standard robust variance estimator.

Keywords: auxiliary variable; bootstrap; inverse probability weighting; missing data; precision; robust estimation; simulation; variance estimation.