Developing prediction models to estimate the risk of two survival outcomes both occurring: A comparison of techniques
Bibliographic record
Abstract
INTRODUCTION: This study considers the prediction of the time until two survival outcomes have both occurred. We compared a variety of analytical methods motivated by a typical clinical problem of multimorbidity prognosis. METHODS: We considered five methods: product (multiply marginal risks), dual-outcome (directly model the time until both events occur), multistate models (msm), and a range of copula and frailty models. We assessed calibration and discrimination under a variety of simulated data scenarios, varying outcome prevalence, and the amount of residual correlation. The simulation focused on model misspecification and statistical power. Using data from the Clinical Practice Research Datalink, we compared model performance when predicting the risk of cardiovascular disease and type 2 diabetes both occurring. RESULTS: Discrimination was similar for all methods. The product method was poorly calibrated in the presence of residual correlation. The msm and dual-outcome models were the most robust to model misspecification but suffered a drop in performance at small sample sizes due to overfitting, which the copula and frailty model were less susceptible to. The copula and frailty model's performance were highly dependent on the underlying data structure. In the clinical example, the product method was poorly calibrated when adjusting for 8 major cardiovascular risk factors. DISCUSSION: We recommend the dual-outcome method for predicting the risk of two survival outcomes both occurring. It was the most robust to model misspecification, although was also the most prone to overfitting. The clinical example motivates the use of the methods considered in this study.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".