The impact of the number and the size of clusters on prediction performance of the stratified and the conditional shared gamma frailty Cox proportional hazards models
Bibliographic record
Abstract
Researchers in biomedical research often analyse data that are subject to clustering. Development and validation of risk prediction models generally assumes independence of observations. For survival outcomes, the Cox proportional hazards regression model is commonly used to estimate an individual's risk at fixed time horizons. The stratified Cox proportional hazards and the shared gamma frailty Cox proportional hazards regression models are two common approaches to account for the presence of clustering in the data. The accuracy of the predictions of these two approaches has not been examined. We conducted a set of Monte Carlo simulations to assess the impact of the number of clusters, the size of the clusters, and the within-cluster correlation in outcomes on the accuracy of the conditional predictions developed using the stratified and the shared gamma frailty Cox proportional hazards regression model. We compared the accuracy of the predictions in terms of discrimination, calibration and overall performance metrics. We found that the stratified and the shared gamma frailty model had similar performance, especially for larger size and higher number of clusters. For small cluster size, we observed slightly better discrimination and overall performance for the stratified model and better calibration for the shared gamma frailty model at shorter prediction horizons. The utility of the stratified Cox proportional hazards model for risk prediction is limited especially for high within-cluster correlation and when clusters are small, and at longer prediction horizons. Our results were accompanied with two applications using open source data on myelodysplastic syndrome and bladder cancer.
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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 | 0.026 | 0.082 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".