Score Tests for Testing Homogeneity of Recurrent Event Times Using Frailty Models
Bibliographic record
Abstract
This thesis presents an overview of frailty models in survival analysis for modelling unobserved heterogeneity in survival times.The frailty model is a generalization of Cox's proportional hazard model, where a shared unobserved quantity called frailty describes a positive correlation among the survival times.The frailty term describes the common risks, acting as a factor on the hazard function.In this thesis, we investigate a score test based on the mixture of chi-square distributions for testing homogeneity of individuals in recurrent event data using a shared frailty model, which is equivalent to testing whether the variance component in a frailty model is zero.Simulation studies are conducted to assess the empirical level and power of the score test under correctly specified and misspecified random effects, and to study the finite-sample properties in terms of biases and mean squared errors of the estimators under both correctly specified and misspecified frailty models.The simulation results indicate that when the sample size is small, the empirical levels of the score tests are generally lower than the nominal 5% level.But they tend to get closer to the nominal level when the sample size is large.Also, for estimating the model parameters, the ML method appears to provide roughly unbiased estimates of the regression parameters and variance components under correctly specified frailty models.However, under misspecified models, the ML method appears to provide estimators with large biases and mean squared errors.An application of the score test for frailty variance component is illustrated by using a i data set of recurrent events of tumours referred to as the bladder cancer data.I am greatly indebted to my supervisor, Dr. Sanjoy Sinha, for kindly providing guidance throughout the development of this thesis.His directions and comments have been of the greatest help at all times.This work could not have been done without his guidance.I extend my sincere thanks to many people in the School of Mathematics and Statistics at Carleton University for their help, continual support, and constructive advice during
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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 | 0.042 | 0.266 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".