A Comparison of Generalized Additive Models to Other Common Modeling Strategies for Continuous Covariates: Implications for Risk Adjustment
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Bibliographic record
Abstract
Common modeling strategies for quantitative covariates include single linear terms, dummy variables on categories, Fractional Polynomials (FP) and cubic smoothing splines in Generalized Additive Models (GAM). The goal of this study was to evaluate the impact of using GAM over other common covariate modeling strategies on risk adjustment. Analyses were based on inter-hospital mortality comparisons in a Canadian provincial trauma system (n=123,732; 59 hospitals). Parameter estimates describing the increase in log odds of mortality for one hospital compared to the reference were adjusted with five quantitative covariates modeled using 1) single linear terms, 2) dummy variables on 2, 3, 4, 5 categories, 3) FP, and 4) GAM. The parameter estimates generated by the first three modeling strategies were compared to that generated by the GAM using mean standardized difference. Mean standardized difference (95% CI) was 71.69 (51.7-91.7) for single linear terms, 21.1 (14.3-28.9); 23.4 (15.6-31.2); 49.6 (28.1-71.1); and 48.5 (28.8-68.2) for dummy variables on 2, 3, 4, and 5 categories, respectively and 12.7 (10.0-15.4) for FP. Results suggest that GAM, FP and at least 4 risk-homogeneous categories provide equivalent risk adjustment to smoothing splines in GAM while single linear terms and less than 4 categories may induce residual confounding.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it