A two‐level copula joint model for joint analysis of longitudinal and competing risks data
Why this work is in the frame
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Bibliographic record
Abstract
In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.
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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 | 0.003 | 0.021 |
| 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 | 0.000 |
| 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