The time-varying effects model is a flexible and powerful tool for modeling the dynamic changes of covariate effects. However, in survival analysis, its computational burden increases quickly as the number of sample sizes or predictors grows. Traditional methods that perform well for moderate sample sizes and low-dimensional data do not scale to massive data. We propose a block-wise steepest ascent procedure by leveraging the block structure of parameters inherent from the basis expansions for each coefficient function. The algorithm iteratively updates the optimal block-wise search direction, along which the increment of the partial likelihood is maximized. The proposed method can be interpreted from the perspective of the Minorization-Maximization algorithm and increases the partial likelihood until convergence.

Survival modeling with time-varying coefficients has proven useful in analyzing time-to-event data with one or more distinct failure types. Existing methods suffer from numerical instability due to ill-conditioned second-order information. The estimation accuracy deteriorates further with multiple competing risks. To address these issues, we propose a proximal Newton algorithm with a shared-memory parallelization scheme and tests of significance and nonproportionality for the time-varying effects. A simulation study shows that our scalable approach reduces the time and memory costs by orders of magnitude and enjoys improved estimation accuracy compared with alternative approaches.

This project is to train a deep learning model in Survival Analysis. However, we allow user to incorporate prior information, which can be either statistical models or other neural networks. KL divergence is used for incorporating, which measures the difference between prior information and local information. The weights of prior and local information are selected by hyperparameter tuning and higher weights of prior model mean the model tends to believe more prior information than the local information, which means the quality local data may not be so satisfactory. Besides, we also do an extension from single-risk to competing risk case, which means our software can also handle competing risk data.

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.