Entropy balancing versus vector-based kernel weighting for causal inference in categorical treatment settings

Applied health services researchers often use methods that address observed confounding in attempts to estimate causal treatment effects. In prior work, vector-based kernel weighting (VBKW) was shown to minimize bias and maximize efficiency compared to other propensity-score based methods in categorical treatment settings. Entropy balancing (EB) has been shown to outperform other weighting and matching schemes in binary treatment settings. We extend EB to a categorical treatment setting and compare the bias and efficiency of estimates obtained through EB and VBKW in analytic scenarios likely to be encountered by applied researchers. To do so, we followed a simulation design with a known data generating process, allowing variation in the functional form for treatment assignment, sampling distribution, treatment effect heterogeneity, and coefficient magnitude for determining treatment assignment. We investigated 210 unique analytic scenarios using Monte-Carlo simulations with 1000 replications and examined 9 unique estimands. Our results indicate that EB consistently outperformed VBKW on measures of efficiency and bias. EB had lower median absolute mean relative bias (0.007 vs 0.05), smaller median absolute error (0.003 vs 0.031), smaller root mean squared error (0.003 vs 0.048), and a smaller interquartile range of the estimate (0.003 vs 0.060). Despite better performance, we found that as baseline imbalance in covariates (as measured by standardized mean differences in prognostic scores) increased, the likelihood of the EB algorithm failing to converge also increased. We provide guidance to researchers on choosing the most appropriate strategy in applied settings considering the potential tradeoffs.