Vector-Based Kernel Weighting: A Simple Estimator for Improving Precision and Bias of Average Treatment Effects in Multiple Treatment Settings

Treatment effect estimation must account for endogeneity, in which factors affect treatment assignment and outcomes simultaneously. By ignoring endogeneity, we risk concluding that a helpful treatment is not beneficial or that a treatment is safe when actually harmful. Propensity score matching or weighting adjusts for observed endogeneity, but matching becomes impracticable with multiple treatments, and weighting methods are sensitive to propensity model misspecification in applied analyses. We used Monte Carlo simulations (1,000 replications) to examine sensitivity of multi-valued treatment inferences to propensity score weighting or matching strategies. We consider four variants of propensity score adjustment: inverse probability of treatment weights (IPTW), kernel weights, vector matching, and a new hybrid that is easily implemented – vector-based kernel weighting (VBKW). VBKW matches observations with similar propensity score vectors, assigning greater kernel weights to observations with similar probabilities within a given bandwidth.

We varied degree of propensity score model misspecification, sample size, treatment effect heterogeneity, initial covariate imbalance, and sample distribution across treatment groups. We evaluated sensitivity of results to propensity score estimation technique (multinomial logit or multinomial probit). Across simulations, VBKW performed equally or better than the other methods in terms of bias, efficiency, and covariate balance measured via prognostic scores. For instance, we tabulated the number of scenarios in which each method led to estimates with less than 40% bias, an indication of situations in which test statistics are likely to perform well. Across 1008 analytic scenarios with a sample size of n=999 and 3 treatment groups, VBKW led to estimates with less than 40% bias in 97% of scenarios, vector matching in 70% of scenarios, kernel weights in 58% of scenarios, and IPTW in 34% of scenarios. Among the estimates with less than 40% bias, VBKW had the lowest root-mean-squared error (0.051), compared to vector matching (0.064), kernel weights (0.064), and IPTW (0.067). VBKW estimates also had the lowest median prognostic score values, indicating good covariate balance after propensity score adjustment.

Our simulations suggest that VBKW is less sensitive to PS model misspecification than other methods used to account for endogeneity in multi-valued treatment analyses. We will illustrate the implications of this for inferences from applied analyses with an example using Medical Expenditure Panel Survey (MEPS) data. Using MEPS data, we will show how inferences differ when we use IPTW, kernel weights, vector matching, and VBKW to estimate associations among potentially inappropriate medication use (none, benzodiazepines, opioids, benzodiazepines + opioids) and next-year health care expenditures among older adults.