The Multitime Case-control Design for Time-varying Exposures
Bibliographic record
Abstract
BACKGROUND: The conventional approach to improve precision of the odds ratio in a case-control study is to increase the number of controls per case. With time-varying exposures, an alternative is to increase the number of observations per control. METHOD: We present the multitime case-control design, which uses multiple control person-moments of exposure within each control subject. The point and variance estimators of the odds ratio are corrected for within-subject correlation. We illustrate this approach using case-control data from studies of the effects of respiratory medications. RESULTS: Simulations show that, with uncorrelated exposures, it is possible to reduce the variance of the odds ratio by around 30% by increasing the number of control person-moments per subject. With correlated exposures, an accurate variance can be obtained by correcting for within-subject correlation. The corrected variance increases with increasing correlation, depending on the number of control person-moments. The first illustration shows that the rate ratio (RR) of cardiac death associated with β-agonist use, not estimable with 1 control per case (30 cases) and 1 control person-moment, was 4.2 (95% confidence interval = 0.4-49) with 12 control person-moments. The second example finds a rate ratio of acute myocardial infarction associated with antibiotics of 2.00 (1.16-3.44) with 1 control per case, which improves in precision with 10 control subjects per case (RR = 2.13 [1.48-3.05]) but also with 1 control per case and 10 control person-moments per control subject (1.99 [1.36-2.90]). CONCLUSION: When dealing with time-varying exposures, the multitime case-control design can increase the efficiency of conventional case-control studies without additional control subjects.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.048 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".