🤖 AI Summary
This study addresses causal effect estimation with count-valued exposure variables under missing data, systematically evaluating five inverse probability of treatment weighting (IPTW) approaches—multinomial binning, covariate balancing propensity score (CBPS and its nonparametric extension npCBPS), generalized boosted models (GBM), and energy balancing weights—combined with multiple imputation and Rubin’s rules. Results show that all IPTW methods perform well under complete data and missing completely at random (MCAR) scenarios. However, under missing at random (MAR) conditions, substantial bias emerges, primarily due to limitations in the imputation models’ ability to adequately capture the right-truncated, overdispersed nature of count data, rather than inherent flaws in the IPTW estimators themselves. The findings offer practical guidance on weighting strategies and method selection for causal inference with high-dimensional count exposures.
📝 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.