Selecting the Optimal Transformation of a Continuous Covariate in Cox's Regression: Implications for Hypothesis Testing
Why this work is in the frame
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Bibliographic record
Abstract
ABSTRACT Background: Many exposures in epidemiological studies have nonlinear effects and the problem is to choose an appropriate functional relationship between such exposures and the outcome. One common approach is to investigate several parametric transformations of the covariate of interest, and to select a posteriori the function that fits the data the best. However, such approach may result in an inflated Type I error. Methods: Through a simulation study, we generated data from Cox's models with different transformations of a single continuous covariate. We investigated the Type I error rate and the power of the likelihood ratio test (LRT) corresponding to three different procedures that considered the same set of parametric dose-response functions. The first unconditional approach did not involve any model selection, while the second conditional approach was based on a posteriori selection of the parametric function. The proposed third approach was similar to the second except that it used a corrected critical value for the LRT to ensure a correct Type I error. Results: The Type I error rate of the second approach was two times higher than the nominal size. For simple monotone dose-response, the corrected test had similar power as the unconditional approach, while for non monotone, dose-response, it had a higher power. A real-life application that focused on the effect of body mass index on the risk of coronary heart disease death, illustrated the advantage of the proposed approach. Conclusion: Our results confirm that a posteriori selecting the functional form of the dose-response induces a Type I error inflation. The corrected procedure, which can be applied in a wide range of situations, may provide a good trade-off between Type I error and power.
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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 | 0.023 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| 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 it