Uniform confidence bands for hazard functions from censored prevalent cohort survival data
Bibliographic record
Abstract
Prevalent cohort studies are commonly conducted in many areas of research when incident cohort studies are deemed infeasible due to logistic or other constraints. While such studies are cost effective, it is known that survival data collected on prevalent cases do not form a representative sample from the target population. When the incidence (e.g. onset of disease) arise from a stationary Poisson process, it allows developing a more efficient methodology. While the stationarity assumption holds in many applications, to the best of our knowledge, the problem of establishing uniform confidence bands using data arisen in such settings has not been addressed in the current literature. We devise a method for obtaining uniform confidence bands for the cumulative hazard and the survival function built on their nonparametric maximum likelihood estimators (NPMLEs). To attain this objective, we first present results on uniform strong consistency, weak convergence and asymptotic efficiency of the NPMLE of the cumulative hazard function. Given the intractable forms of the limiting processes in this case, the idea is to numerically approximate the functionals of the asymptotic processes of the normalized NPMLEs. Our simulation studies reveal the efficiency of the estimators for finite samples. The proposed procedures are illustrated using a set of real data on patients with dementia from the Canadian Study of Health and Aging.
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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 | 0.071 | 0.379 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.004 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.005 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".