Smoothing Techniques for the Bivariate Kaplan–Meier Estimator
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Bibliographic record
Abstract
ABSTRACT Bivariate survival time data arise quite often in medical research, and many estimators for the bivariate survival function have been suggested. While there are a lot of smooth estimators for the univariate Kaplan–Meier estimator, smooth versions of bivariate Kaplan–Meier estimator are not discussed yet. In this article, we suggest two smoothing techniques, the kernel smoothing and the Bezier surface smoothing, for the bivariate survival function estimator, especially for the estimator suggested by Lin and Ying (1993 Lin , D. Y. , Ying , Z. ( 1993 ). A simple nonparametric estimator of the bivariate survival function under univariate censoring . Biometrika 80 : 573 – 581 .[Crossref], [Web of Science ®] , [Google Scholar]). Also, asymptotic results for both estimators are derived. Throughout the simulation studies, the Bezier surface smoothing turned out to be very efficient compared to the bivariate Kaplan–Meier estimator and the kernel smoothing estimator. An illustrative example based on a real data set is also given.
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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 | 0.011 | 0.016 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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