Inverse Probability Weighting of Count Exposures in the Presence of Missing Data: A Simulation Study

TL;DR

This study evaluates various inverse probability weighting methods for count exposures with missing data, demonstrating their bias, coverage, and performance in simulated scenarios based on real cohort data.

Contribution

It provides a comprehensive comparison of IPTW methods for count exposures, highlighting their strengths and limitations in the context of missing data and simulation settings.

Findings

Multinomial, CBPS, GBM, and energy weights showed low bias and good coverage.

npCBPS exhibited bias and poor coverage due to extreme weights.

Performance was consistent under complete and missing data, with bias increasing with missingness.

Abstract

Inverse probability of treatment weighting (IPTW) is widely used to estimate causal effects, but guidance is limited for count exposures. It is also unclear how IPTW performs when combined with multiple imputation in this context. In this study, we evaluated five IPTW methods applied to count exposures: multinomial binning, parametric and non-parametric covariate balancing propensity scores (CBPS, npCBPS), generalised boosted models (GBM), and energy balancing. Our simulations were informed by an example using data from the 1970 British Cohort Study, aiming to estimate the effect of psychological distress, measured as a count of symptoms at age 34, on self-reported longstanding illness at age 42. We compared these approaches on bias, coverage, effective sample size, and other metrics under truncated negative binomial and Poisson exposure distributions. We also assessed the performance of Rubin's rules under different missingness mechanisms. Under complete data, multinomial, CBPS, GBM, and energy weights produced low bias and near-nominal coverage, whereas npCBPS resulted in bias and poor coverage due to extreme weights. When data were missing completely at random, similar performance patterns were observed for IPTW with multiple imputation. Under missing at random, bias increased with higher missingness, but this was present for both IPTW and covariate-adjusted regression, possibly reflecting a limitation of the imputation model rather than a failure of IPTW. Overall, these findings support the use of multinomial, CBPS, GBMs, and energy weights for count exposures in similar settings while highlighting trade-offs between these methods and the need for imputation models accommodating right-truncated overdispersed counts.