Shrinkage estimators for semi-parametric proportional hazards mixture cure models
Bibliographic record
Abstract
Survival analysis is essential for modelling time-to-event data, particularly in medical research. Mixture cure models are widely used methods to study patients' latency and incidence components. This research focuses on mixture model properties in the semi-parametric estimation of the Cox proportional hazard models in the presence of the multicollinearity problem, where the explanatory variables are linearly dependent so that the input design matrix is ill-conditioned. In the mixture of cure models, the multicollinearity issue can happen in both latency and incidence components, where the commonly used least squares (LS) method may lead to unreliable estimates for the coefficients of the underlying model. To address this issue, we propose shrinkage methods to estimate the coefficient of the underlying model. To do so, we developed new expectation-maximization (EM) algorithms to incorporate the shrinkage methods for both components. Through various simulations, we show that the proposed shrinkage methods cope with the multicollinearity problem in latency and incidence components and lead to more reliable estimates in semi-parametric settings. Our findings indicate that Ridge and Liu-type (LT) shrinkage methods provide more reliable parameter estimates and outperform the LS estimation method in scenarios with high multicollinearity. The developed methods are finally applied to a dataset on breast cancer, analyzing the disease prognosis and survival rates of patients with 10 or more positive lymph nodes. The results consistently show that the Ridge and LT methods offer better estimation and survival results compared to the LS method. Our numerical studies show the practical advantages of our proposed shrinkage methods in medical research.
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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 | 0.011 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".