Covariate Bias Induced by Length-Biased Sampling of Failure Times
Bibliographic record
Abstract
Although many authors have proposed different approaches to the analysis of length-biased survival data, a number of issues have not been fully addressed. The most important among these issues is perhaps that regarding inclusion of covariates into the analysis of length-biased lifetime data collected through cross-sectional sampling of a population. One aspect of this problem, which appears to have been neglected in the literature, concerns the effect of length bias on the sampling distribution of the covariates. In most regression analyses, it is conventional to condition on the observed covariate values; however, certain covariate values could be preferentially selected into the sample, being linked to the long-term survivors, who themselves are favored by the sampling mechanism. This observation raises two questions: (1) Does the conditional analysis of covariates lead to biased estimators of regression coefficients?; and (2) does inference through the joint l likelihood of covariates and failure times yield more efficient estimators of the regression parameters? We present a joint likelihood approach and study the large-sample behavior of the resulting maximum likelihood estimators (MLEs). We find that these MLEs are more efficient than their conditional counterparts even though the two MLEs are asymptotically equal. Our results are illustrated using data on survival with dementia, collected as part of 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 | 0.092 | 0.347 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".