Literature Review for the Additive Cox Model

Lin, D. Y., & Ying, Z. (1997). Additive hazards regression models for survival data. In Proceedings of the first Seattle symposium in Biostatistics (pp. 185-198). Springer, New York, NY. (https://dlin.web.unc.edu/wp-content/uploads/sites/1568/2013/04/LinYing97.pdf)

The article is about additive hazards models, and hence not read thoroughly.

Wu, J., & Witten, D. (2019). Flexible and Interpretable Models for Survival Data. Journal of Computational and Graphical Statistics, 28(4), 954-966.

The article extends the trend filtering additive model to the Cox proportional hazard diagram. Trend filtering additive functions are piece-wise polynomials with adaptively chosen knots. The likelihood function consists of a trend filtering penalty for knots selection and a group lasso penalty for functional selection. A second tuning parameter, $\alpha$, is used to control the tradeoff between two penalties. Model fitting is achieved by the proximal gradient descent algorithm and hence is capable of high-dimensional data analysis. An R package tfCox is developed. One of the problems for this approach is that the estimated curve is not smooth, or even continuous depending on the choice of trend filtering funciton.

Cui, E., Crainiceanu, C. M., & Leroux, A. (2021). Additive functional Cox model. Journal of Computational and Graphical Statistics, 30(3), 780-793.

The article is about multivariate functional predictors and doesn't apply to high-dimensional data analysis. A good place to find other "low-dimensional" additive Cox models. Could be used in the discussion section

Bender, A., Groll, A., & Scheipl, F. (2018). A generalized additive model approach to time-to-event analysis. Statistical Modelling, 18(3-4), 299-321.

The author demonstrated using generalized additive model infrastructure to model time-to-event outcome via piece-wise exponential model. This modeling approach increases the utility, allowing spatial(-temporal) random effects and time-dependent covariates. The authors also introduced a utility R-package that does pre-process step of data before fitting to a generalized model. The article doesn't directly relate to the current work as not in the Cox paradigm, but supplies arguments for introduction and discussion.

Marra, G., Farcomeni, A., & Radice, R. (2021). Link-based survival additive models under mixed censoring to assess risks of hospital-acquired infections. Computational Statistics & Data Analysis, 155, 107092.

The authors propose a flexible survival additive models that is link-based to model time-to-event with mixed censoring. Different link functions can be used to achieve different interpretations of the beta coefficients. While the model provides alternative utility for modeling time-to-event outcomes in comparison to the Cox model or Accelerated failure time model, high-dimensionality of the predictors could be addressed under this framework as sparsity penalty was not imposed. An R package GJRM is provided.

Appendix Section

add appendix rendering in the pipeline

Contents include:

Bug report for cosso and acosso
Number of Failures in simulation

New Bacoxph model problem with the new simulation setting

offset induce probelm

Adjust Survival Simulation Functions

Read the Simulation Functions of BhGLM to understand what Dr. Yi meant abt effect variance decomposition.
Adjust the simulation error, such that the baseline AUC (mgcv model result) is around 0.75