Comparison of Aalen's additive and Cox proportional hazards models for breast cancer survival: analysis of population- based data from British Columbia, Canada.
Bibliographic record
Abstract
BACKGROUND: Regression models for survival data have traditionally been based on the Cox regression model. However, its validity relies heavily on assumption of proportional hazards. Another restriction of the Cox model is insufficiency in dealing with time-varying covariate effects, since the regression coefficients are assumed constant. These weaknesses have generated interest in alternative approaches and with Aalen's additive model, the effect of the covariates acts on an absolute rather than a relative scale. We here fit the Cox and Aalen's additive models to breast cancer data for comparison through practical application. METHODS: The data related to 14,826 women diagnosed with breast cancer in BC during 1990-1999 and followed to 2010. Plots of the Martingale Residual Process and Arja's Plot was used to assess the fit of the additive model. The Cox-Snell residuals, Martingale residuals and scaled Schoenfeld residuals were used to check the Cox model. RESULTS: In the category of patients younger than 65 years the proportional hazard assumption was satisfied. In this category, by the Cox model, the variables "stage", "surgery", "radiotherapy", "chemotherapy", "hormone therapy" and interaction between "stage" and "surgery" proved significant. In the same category, by the Aalen's additive model, similar significant variables are selected except for "hormone therapy". The sign of estimated coefficients from survival functions based on the both Cox and Aalen's additive models were alike although estimated coefficients in the two models differed from the viewpoint of magnitude. In the category of patients older than 65 years, the proportional hazard assumption was not satisfied, and the Stratified Cox model and Aalen's additive model gave similar results. CONCLUSIONS: Based on our findings, if the proportional hazard assumption is not satisfied, the Aalen's additive model is an appropriate alternative for the Cox model. If the proportional hazard assumption is satisfied, both models are appropriate. Generally, the two models give different pieces of information.
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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 | 0.040 | 0.060 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".