Model diagnostics for censored regression via randomized survival probabilities
Why this work is in the frame
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Bibliographic record
Abstract
Residuals in normal regression are used to assess a model's goodness-of-fit (GOF) and discover directions for improving the model. However, there is a lack of residuals with a characterized reference distribution for censored regression. In this article, we propose to diagnose censored regression with normalized randomized survival probabilities (RSP). The key idea of RSP is to replace the survival probability (SP) of a censored failure time with a uniform random number between 0 and the SP of the censored time. We prove that RSPs always have the uniform distribution on (0, 1) under the true model with the true generating parameters. Therefore, we can transform RSPs into normally distributed residuals with the normal quantile function. We call such residuals by normalized RSP (NRSP residuals). We conduct simulation studies to investigate the sizes and powers of statistical tests based on NRSP residuals in detecting the incorrect choice of distribution family and nonlinear effect in covariates. Our simulation studies show that, although the GOF tests with NRSP residuals are not as powerful as a traditional GOF test method, a nonlinear test based on NRSP residuals has significantly higher power in detecting nonlinearity. We also compared these model diagnostics methods with a breast-cancer recurrent-free time dataset. The results show that the NRSP residual diagnostics successfully captures a subtle nonlinear relationship in the dataset, which is not detected by the graphical diagnostics with CS residuals and existing GOF tests.
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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 | 0.002 | 0.129 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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