Going Beyond the Mean in Healthcare Cost Regressions: a Comparison of Methods for Estimating the Full Conditional Distribution

Understanding the data generating process behind healthcare costs remains a key empirical issue. Although much research to date has focused on the prediction of the conditional mean cost, this can potentially miss important features of the full conditional distribution such as tail probabilities. We conduct a quasi-Monte Carlo experiment using English NHS inpatient data to compare 14 approaches to modelling the distribution of healthcare costs: nine of which are parametric, and have commonly been used to fit healthcare costs, and five others designed specifically to construct a counterfactual distribution. Our results indicate that no one method is clearly dominant and that there is a trade-off between bias and precision of tail probability forecasts. We find that distributional methods demonstrate significant potential, particularly with larger sample sizes where the variability of predictions is reduced. Parametric distributions such as log-normal, generalised gamma and generalised beta of the second kind are found to estimate tail probabilities with high precision, but with varying bias depending upon the cost threshold being considered.