Using fractional polynomials to model the effect of cumulative duration of exposure on outcomes: applications to cohort and nested case‐control designs
Bibliographic record
Abstract
PURPOSE: Determining the nature of the relationship between cumulative duration of exposure to an agent and the hazard of an adverse outcome is an important issue in environmental and occupational epidemiology, public health and clinical medicine. The Cox proportional hazards regression model can incorporate time-dependent covariates. An important class of continuous time-dependent covariates is that denoting cumulative duration of exposure. METHODS: We used fractional polynomial methods to describe the association between cumulative duration of exposure and adverse outcomes. We applied these methods in a cohort study to examine the relationship between cumulative duration of use of the antiarrhythmic drug amiodarone and the risk of thyroid dysfunction. We also used these methods with a conditional logistic regression model in a nested case-control study to examine the relationship between cumulative duration of use of bisphosphonate medication and the risk of atypical femur fracture. RESULTS: Using a cohort design and a Cox proportional hazards model, we found a non-linear relationship between cumulative duration of use of the antiarrhythmic drug amiodarone and the risk of thyroid dysfunction. The risk initially increased rapidly with increasing cumulative use. However, as cumulative duration of use increased, the rate of increase in risk attenuated and eventually levelled off. Using a nested case-control design and a conditional logistic regression model, we found evidence of a linear relationship between duration of use of bisphosphonate medication and risk of atypical femur fractures. CONCLUSIONS: Fractional polynomials allow one to model the relationship between cumulative duration of medication use and adverse outcomes.
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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 | 0.049 | 0.104 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".