Joint estimation of time‐dependent and non‐linear effects of continuous covariates on survival
Bibliographic record
Abstract
In order to yield more flexible models, the Cox regression model, lambda(t;x) = lambda(0)(t)exp(betax), has been generalized using different non-parametric model estimation techniques. One generalization is the relaxation of log-linearity in x, lambda(t;x) = lambda(0)(t)exp[r(x)]. Another is the relaxation of the proportional hazards assumption, lambda(t;x) = lambda(0)(t)exp[beta(t)x]. These generalizations are typically considered independently of each other. We propose the product model, lambda(t;x) = lambda(0)(t)exp[beta(t)r(x)] which allows for joint estimation of both effects, and investigate its properties. The functions describing the time-dependent beta(t) and non-linear r(x) effects are modelled simultaneously using regression splines and estimated by maximum partial likelihood. Likelihood ratio tests are proposed to compare alternative models. Simulations indicate that both the recovery of the shapes of the two functions and the size of the tests are reasonably accurate provided they are based on the correct model. By contrast, type I error rates may be highly inflated, and the estimates considerably biased, if the model is misspecified. Applications in cancer epidemiology illustrate how the product model may yield new insights about the role of prognostic factors.
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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 | 0.029 | 0.075 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".