Covariates and length-biased sampling : is there more than meets the eye ?
Bibliographic record
Abstract
It is well known that when subjects with a disease are identified through a cross-sectional survey and then followed forward in time until either failure or censoring, their estimated survival function of the true survival function from onset are biased. This bias, which is caused by the sampling of prevalent rather than incident cases, is termed length bias if the onset time of the disease forms a stationary Poisson process. While authors have proposed different approaches to the analysis of length-biased survival data, there remain a number of issues that have not been fully addressed. The most, important of these is perhaps that of how to include covariates into length-biased lifetime data analysis of the natural history of diseases, that are initiated by cross-sectional sampling of a population. One aspect of that problem, which appears to have been neglected in the literature, concerns the effect of length-bias on the sampling distribution of the covariates. If the covariates have an effect on the survival time, then their marginal distribution in a length-biased sample is also subject to a bias and is informative about the parameters of interest. As is conventional in most regression analyses one conditions on the observed covariate values. By conditioning on the observed covariates in the situation described above, however, one effectively ignores the information contained in the distribution of the covariates in the sample. We present the appropriate likelihood approach that takes into account this information and we establish the consistency and asymptotic normality of the resulting estimators. It is shown that by ignoring the information contained in the sampling distribution of the covariates, one can still obtain, asymptotically, the same point estimates as with the joint likelihood. However, these conditional estimates are less efficient. Our results are illustrated using data on survival with dementia; collected as part of the Canadian Study of Health an 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 | 0.106 | 0.445 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.004 | 0.015 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.009 | 0.007 |
| 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".