Smoothing Techniques for the Bivariate Kaplan–Meier Estimator
Bibliographic record
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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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 | 0.009 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".