Stationarity in a prevalent cohort study with follow-up
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Bibliographic record
Abstract
In a prevalent cohort study with follow-up, the incidence process is not directly observed since only the onset times of prevalent cases can be ascertained. Several important consequences follow if one can establish stationarity of the incidence process: (1) The useful epidemiological relationship between prevalence, incidence, and mean duration holds, (2) There is improved efficiency when estimating the underlying survivor function from a prevalent cohort study with follow-up, (3) The constancy of the incidence rate is established, and (4) The constant incidence rate can be estimated using data from a prevalent cohort study. We propose a formal test for stationarity using data from a prevalent cohort study with follow-up, and establish new characterizations of stationarity, and of useful types of departure from stationarity. A dual to the problem of establishing stationarity by comparing the backward and forward recurrence times is addressed. Assuming stationarity of the underlying incidence process, we use the backward and forward recurrence times to verify whether the underlying survival distribution is independent of the date of onset. In doing so, we characterize specific types of dependence of the underlying survival distribution on calendar time. If the data are consistent with stationarity of the incidence rate, then a natural next step is to estimate the (constant) incidence rate. We derive the nonparametric maximum likelihood estimator of the constant incidence rate, prove that the estimator is weakly consistent, and show how one may construct an asymptotic confidence interval for the incidence rate. One main advantage of our procedure is that it only requires the completion of a single prevalent cohort study with follow-up. We apply our test for stationarity to data obtained as part of the Canadian Study of Health and Aging to verify that the incidence rate of dementia amongst the elderly in Canada has remained constant. Upon concluding that this constancy is, plausible, we estimate the incidence rate.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it