Threshold regression for survival data with time‐varying covariates
Why this work is in the frame
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Bibliographic record
Abstract
Time-to-event data with time-varying covariates pose an interesting challenge for statistical modeling and inference, especially where the data require a regression structure but are not consistent with the proportional hazard assumption. Threshold regression (TR) is a relatively new methodology based on the concept that degradation or deterioration of a subject's health follows a stochastic process and failure occurs when the process first reaches a failure state or threshold (a first-hitting-time). Survival data with time-varying covariates consist of sequential observations on the level of degradation and/or on covariates of the subject, prior to the occurrence of the failure event. Encounters with this type of data structure abound in practical settings for survival analysis and there is a pressing need for simple regression methods to handle the longitudinal aspect of the data. Using a Markov property to decompose a longitudinal record into a series of single records is one strategy for dealing with this type of data. This study looks at the theoretical conditions for which this Markov approach is valid. The approach is called threshold regression with Markov decomposition or Markov TR for short. A number of important special cases, such as data with unevenly spaced time points and competing risks as stopping modes, are discussed. We show that a proportional hazards regression model with time-varying covariates is consistent with the Markov TR model. The Markov TR procedure is illustrated by a case application to a study of lung cancer risk. The procedure is also shown to be consistent with the use of an alternative time scale. Finally, we present the connection of the procedure to the concept of a collapsible survival model.
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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 | 0.013 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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