Optimal Statistical Decisions for Hospital Report Cards
Bibliographic record
Abstract
PURPOSE: Hospital report cards provide information designed to help patients and providers to make decisions. The purpose of this study was to place the design of hospital report cards into a decision-theoretic framework. The authors' objectives were 2-fold: 1st, to determine what the choice of significance level implies about the relative value of the different types of misclassifications that can arise. Second, to determine optimal significance levels for specific cost functions describing the relative costs associated with different types of misclassifications. METHODS: Using a previously published theoretical model for hospital mortality, the authors computed false positive (i.e., falsely classified as providing poor-quality care) and false negative (falsely classified as providing good-quality care) rates. First, they determined the cost functions for false negatives and false positives that are implicitly associated with the use of significance levels of 0.05 and 0.01 for identifying hospitals with higher than average mortality. Second, they determined the levels of statistical significance that should be chosen to minimize predefined cost functions, thus minimizing costs associated with misclassifying hospitals. RESULTS: The lower the statistical significance level required for identifying hospitals with higher than average mortality, the lower the implicit cost of false negatives compared to false positives. For a given significance level, the greater the number of patients treated at each hospital or the greater the proportion of truly poorly performing hospitals, the lower the value of the implicit cost incurred by a false negative compared to that for a false positive. For cost functions that put a high relative penalty on false negatives compared to false positives, the use of significance levels of 0.05 or 0.01 does not result in optimal decisions across expected number of patients treated at each hospital or proportions of truly poor-quality care. CONCLUSIONS: Hospital report cards that use significance levels of either 0.05 or 0.01 to identify hospitals that have statistically significantly higher than average mortality make implicit assumptions about cost functions, and the values of the optimal cost function vary across scenarios.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.048 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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; both teacher heads agree on what is shown here.
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".