Length-Biased Sampling With Right Censoring
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
When survival data arise from prevalent cases ascertained through a cross-sectional study, it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases. Length-biased data have been treated both unconditionally and conditionally in the literature. In the latter case, where length bias is viewed as being induced by random left truncation of the survival times, the truncating distribution is assumed to be unknown. Conditioning on the observed truncation times hence causes very little loss of information. In many instances, however, it can be supposed that the truncating distribution is uniform, and it has been pointed out that under these circumstances, an unconditional analysis will be more informative. There are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator (NPMLE) of the unbiased survivor function in the presence of censoring. This article fills that gap by giving this NPMLE and its accompanying asymptotic properties when the data are purely length biased. An example of survival with dementia is presented in which the conditional and unconditional estimators are compared.
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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 | 0.011 |
| 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