Cox Non-Proportional Hazards Model with Time-Varying Coefficients.
surtvep
surtvep is an R package for fitting Cox non-proportional hazards models with time-varying coefficients. Both unpenalized procedures (Newton and proximal Newton) and penalized procedures (P-splines and smoothing splines) are included using B-spline basis functions for estimating time-varying coefficients. For penalized procedures, cross validations, mAIC, TIC or GIC are implemented to select tuning parameters. Utilities for carrying out post-estimation visualization, summarization, point-wise confidence interval and hypothesis testing are also provided.
Introduction
Large-scale time-to-event data derived from national disease registries arise rapidly in medical studies. Detecting and accounting for time-varying effects is particularly important, as time-varying effects have already been reported in the clinical literature. However, there are currently no formal R packages for estimating the time-varying effects without pre-assuming the time-dependent function. Inaccurate pre-assumptions can greatly influence the estimation, leading to unreliable results. To address this issue, we developed a time-varying model using spline terms with penalization that does not require pre-assumption of the true time-dependent function, and implemented it in R.
Our package offers several benefits over traditional methods. Firstly, traditional methods for modeling time-varying survival models often rely on expanding the original data into a repeated measurement format. However, even with moderate sample sizes, this leads to a large and computationally burdensome working dataset. Our package addresses this issue by proposing a computationally efficient Kronecker product-based proximal algorithm, which allows for the evaluation of time-varying effects in large-scale studies. Additionally, our package allows for parallel computing and can handle moderate to large sample sizes more efficiently than current methods.
In our statistical software tutorial, we address a common issue encountered when analyzing data with binary covariates with near-zero variation. For example, in the SEER prostate cancer data, only 0.6% of the 716,553 patients had their tumors regional to the lymph nodes. In such cases, the associated observed information matrix of a Newton-type method may have a minimum eigenvalue close to zero and a large condition number. Inverting this nearly singular matrix can lead to numerical instability and the corresponding Newton updates may be confined within a small neighborhood of the initial value, resulting in estimates that are far from the optimal solutions. To address this problem, our proposed Proximal-Newtown method utilizes a modified Hessian matrix, which allows for accurate estimation in these scenarios.
Installation
Note:This package is still in its early stages of development, so please don't hesitate to report any problems you may experience.
The package only works for R 4.1.0+.
You can install 'surtvep' via:
install.packages("devtools")
install.packages("remotes")
remotes::install_github("UM-KevinHe/surtvep")
We recommand to start with tutorial, as it provides an overview of the package's usage, including preprocessing, model training, selection of penalization parameters, and post-estimation procedures.
Detailed tutorial
For detailed tutorial and model paramter explaination, please go to here.
Getting Help:
If you encounter any problems or bugs, please contact us at: [email protected]{.email}, [email protected]{.email}, [email protected]{.email}
References
[1] Gray, R. J. (1992). Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. Journal of the American Statistical Association, 87(420), 942–951. https://doi.org/10.2307/2290630
[2] Gray, R. J. (1994). Spline-based tests in survival analysis. Biometrics, 50(3), 640–652. https://doi.org/10.2307/2532779
[3] He, K., Zhu, J., Kang, J., & Li, Y. (2022). Stratified Cox models with time-varying effects for national kidney transplant patients: A new blockwise steepest ascent method. Biometrics, 78(3), 1221–1232. https://doi.org/10.1111/biom.13473
[4] Luo, L., He, K., Wu, W., & Taylor, J. M. (2023). Using information criteria to select smoothing parameters when analyzing survival data with time-varying coefficient hazard models. Statistical Methods in Medical Research, in press. https://doi.org/10.1177/09622802231181471
[5] Wu, W., Taylor, J. M., Brouwer, A. F., Luo, L., Kang, J., Jiang, H., & He, K. (2022). Scalable proximal methods for cause-specific hazard modeling with time-varying coefficients. Lifetime Data Analysis, 28 (2), 194–218. https://doi.org/10.1007/s10985-021-09544-2