Abstract 170: Effect of Hospital Case Volume, Number of Hospitals, and the Predictive Accuracy Of Risk-adjustment Models (c-statistic) on the Accuracy of Hospital Report Cards
Bibliographic record
Abstract
Background: The generation of report cards to compare hospital outcomes is increasingly common. Many researchers use the c-statistic of the risk-adjusted logistic regression model as a measure of the accuracy of the report cards, while often ignoring factors such as hospital case volumes and the number of hospitals. Through the use of Monte-Carlo simulations, we assessed the relative importance of these 3 variables (hospital case volume, number of hospitals,and model c-statistic) on the accuracy of hospital report cards. Methods: Using a previously developed 30-day mortality prediction model, we used data from 31,183 patients hospitalized with AMI in 159 Ontario hospitals between 2008 and 2010 to construct a data-generating process that allowed us to generate simulated datasets in which the actual hospital rankings (based on 30-day risk-adjusted mortality) were known with certainty. The simulated datasets had the same variability in case mix as was observed in the 159 hospitals (intra-class correlation ICC= 0.037). Using Monte Carlo simulations we varied the 3 variables across plausible ranges i.e., number of patients per hospital (50, 100, 200), number of hospitals (50, 100, 200), c-statistic (25 values ranging from 0.53 - 0.96), producing 225 different scenarios (i.e., 3 x 3 x 25) and created 500 simulated datasets for each scenario. The observed rank order of hospitals in each simulation was determined by generating observed vs. expected (O-E) ratios using indirect standardization as well as predicted vs. expected (P-E) ratios using hierarchical regression models. We determined the influence of the 3 factors on the accuracy of the report cards by calculating the Spearman-rank correlation (r s ) between the known and observed (O-E and P-E) hospital rank orders. Results: Of the 3 factors examined, only the number of patients per hospital had a meaningful influence on the correlation between known and observed rank order. To illustrate, in one typical simulation, as the case volume increased from 50, to 100, and then to 200 patients, the correlation increased from 0.37, 0.50, and 0.62, respectively. In contrast, the model c-statistic had a very modest impact on the accuracy of hospital report cards; across the full range of the c-statistic (0.53-0.96) correlations increased by <5% in all scenarios. The number of hospitals included in the simulations had no meaningful effect (change in r s ≤1%). The fact that none of the simulations produced correlations >0.70 and many were <0.50, serves to highlight the substantial amount of error that can occur when attempting to profile hospitals, even in the favorable environment of simulated datasets. Conclusions: The c-statistic of a risk-adjustment model should not be used to assess the accuracy of hospital report cards, rather, more attention should be paid to hospital case volumes which directly impact the accuracy of hospital rankings.
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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 | 0.074 | 0.284 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".