Double Bias: Estimation of Causal Effects from Length-Biased Samples in the Presence of Confounding
Bibliographic record
Abstract
Length bias in survival data occurs in observational studies when, for example, subjects with shorter lifetimes are less likely to be present in the recorded data. In this paper, we consider estimating the causal exposure (treatment) effect on survival time from observational data when, in addition to the lack of randomization and consequent potential for confounding, the data constitute a length-biased sample; we hence term this a double-bias problem. We develop estimating equations that can be used to estimate the causal effect indexing the structural Cox proportional hazard and accelerated failure time models for point exposures in double-bias settings. The approaches rely on propensity score-based adjustments, and we demonstrate that estimation of the propensity score must be adjusted to acknowledge the length-biased sampling. Large sample properties of the estimators are established and their small sample behavior is studied using simulations. We apply the proposed methods to a set of, partly synthesized, length-biased survival data collected as part of the Canadian Study of Health and Aging (CSHA) to compare survival of subjects with dementia among institutionalized patients versus those recruited from the community and depict their adjusted survival curves.
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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 | 0.066 | 0.235 |
| 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 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".