Evaluation of Cox's model and logistic regression for matched case‐control data with time‐dependent covariates: a simulation study
Bibliographic record
Abstract
Case-control studies are typically analysed using the conventional logistic model, which does not directly account for changes in the covariate values over time. Yet, many exposures may vary over time. The most natural alternative to handle such exposures would be to use the Cox model with time-dependent covariates. However, its application to case-control data opens the question of how to manipulate the risk sets. Through a simulation study, we investigate how the accuracy of the estimates of Cox's model depends on the operational definition of risk sets and/or on some aspects of the time-varying exposure. We also assess the estimates obtained from conventional logistic regression. The lifetime experience of a hypothetical population is first generated, and a matched case-control study is then simulated from this population. We control the frequency, the age at initiation, and the total duration of exposure, as well as the strengths of their effects. All models considered include a fixed-in-time covariate and one or two time-dependent covariate(s): the indicator of current exposure and/or the exposure duration. Simulation results show that none of the models always performs well. The discrepancies between the odds ratios yielded by logistic regression and the 'true' hazard ratio depend on both the type of the covariate and the strength of its effect. In addition, it seems that logistic regression has difficulty separating the effects of inter-correlated time-dependent covariates. By contrast, each of the two versions of Cox's model systematically induces either a serious under-estimation or a moderate over-estimation bias. The magnitude of the latter bias is proportional to the true effect, suggesting that an improved manipulation of the risk sets may eliminate, or at least reduce, the bias.
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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 | 0.088 | 0.160 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 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".