A weighted Cox model for modelling time‐dependent exposures in the analysis of case–control studies
Bibliographic record
Abstract
Many exposures investigated in epidemiological case-control studies may vary over time. The effects of these exposures are usually estimated using logistic regression, which does not directly account for changes in covariate values over time within individuals. By contrast, the Cox model with time-dependent covariates directly accounts for these changes over time. However, the over-sampling of cases in case-control studies, relative to controls, requires manipulating the risk sets in the Cox partial likelihood. A previous study showed that simple inclusion or exclusion of future cases in each risk set induces an under- or over-estimation bias in the regression parameters, respectively. We investigate the performance of a weighted Cox model that weights subjects according to age-conditional probabilities of developing the disease of interest in the source population. In a simulation study, the lifetime experience of a source population is first generated and a case-control study is then simulated within each population. Different characteristics of exposure are generated, including time-varying intensity. The results show that the estimates from the weighted Cox model are much less biased than the Cox models that simply include or exclude future cases, and are superior to logistic regression estimates in terms of bias and mean-squared error. An application to frequency-matched population-based case-control data on lung cancer illustrates similar differences in the estimated effects of different smoking variables. The investigated weighted Cox model is a potential alternative method to analyse matched or unmatched population-based case-control studies with time-dependent exposures.
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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 | 0.061 | 0.098 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.006 | 0.002 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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".