A Bayesian Approach for the Cox Proportional Hazards Model with Covariates Subject to Detection Limit
Bibliographic record
Abstract
The research on biomarkers has been limited in its effectiveness because biomarker levels can only be measured within the thresholds of assays and laboratory instruments, a challenge referred to as a detection limit (DL) problem. In this paper, we propose a Bayesian approach to the Cox proportional hazards model with explanatory variables subject to lower, upper, or interval DLs. We demonstrate that by formulating the time-to-event outcome using the Poisson density with counting process notation, implementing the proposed approach in the OpenBUGS and JAGS is straightforward. We have conducted extensive simulations to compare the proposed Bayesian approach to the other four commonly used methods and to evaluate its robustness with respect to the distribution assumption of the biomarkers. The proposed Bayesian approach and other methods were applied to an acute lung injury study, in which a panel of cytokine biomarkers was studied for the biomarkers' association with ventilation-free survival.
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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 | 0.032 | 0.376 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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; both teacher heads agree on what is shown here.
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".