Cross-Validatory Z-Residual for Diagnosing Shared Frailty Models
Bibliographic record
Abstract
Accurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance residuals lack a well-characterized reference distribution for censored regression, making numerical statistical tests based on these residuals challenging. Recently, the introduction of Z-residuals for diagnosing survival models addresses this limitation. However, concerns arise from conventional methods that use the entire dataset for both model parameter estimation and residual assessment, which may cause optimistic biases. This article introduces cross-validatory Z-residuals as an innovative approach to address these limitations. Employing a cross-validation (CV) framework, the method systematically partitions the dataset into training and testing sets to reduce the optimistic bias. Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful (e.g., power increased from 0.2 to 0.6). and more discriminative (e.g., AUC increased from 0.58 to 0.85) than Z-residuals without CV. We also compare the performance of Z-residuals with and without CV in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers, which Z-residuals without CV fail to identify. The CV Z-residual is a more powerful tool than the No-CV Z-residual for checking survival models, particularly in goodness-of-fit tests and outlier detection. We have published a generic function, which is collected in an R package called Zresidual, for computing CV Z-residual for the output of the widely used survival R package.
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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 | 0.028 | 0.094 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".