Healthcare Cost Regressions: Going Beyond the Mean to Estimate the Full Distribution
Bibliographic record
Abstract
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 distribution such as tail probabilities. We conduct a quasi-Monte Carlo experiment using the English National Health Service inpatient data to compare 14 approaches in modelling the distribution of healthcare costs: nine of which are parametric and have commonly been used to fit healthcare costs, and five others are 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.063 | 0.304 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".