Z-residual diagnostic tool for assessing covariate functional form in shared frailty models
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Bibliographic record
Abstract
Survival analysis often involves modeling hazard functions while considering frailty to account for unobserved cluster-level factors in clustered survival data. Shared frailty models have gained popularity for this purpose, but assessing covariate functional form in these models presents unique challenges. Martingale and deviance residuals are commonly used for visually assessing covariate functional form against continuous covariates. Nevertheless, their subjective nature and lack of a reference distribution make it challenging to derive numerical statistical tests from these residuals. To address these limitations, we propose 'Z-residuals', a novel diagnostic tool designed for shared frailty models, leveraging the concept of randomized survival probability and introducing both graphical and numerical tests. To implement this approach, we develop an R package to compute Z-residuals for shared frailty models. Through extensive simulation studies, we demonstrate the high power of our derived numerical test for assessing the functional form of covariates. To validate the effectiveness of our method, we apply it to a real data application concerning the modelling of survival time for acute myeloid leukemia patients. Our Z-residual diagnosis results reveal the inadequacy of log-transformation of the covariate, highlighting the limitations of other diagnostic methods for effectively assessing covariate functional form in shared frailty models.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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