Minorization-Maximization-based Steepest Ascent for Large-scale Survival Analysis with Time-Varying Effects: Application to the National Kidney Transplant Dataset

TL;DR

This paper introduces a scalable optimization method based on Minorization-Maximization for estimating time-varying effects in large-scale survival analysis, demonstrated on national kidney transplant data.

Contribution

It develops a novel steepest ascent procedure leveraging block structure for efficient estimation in high-dimensional survival models.

Findings

Method achieves efficient convergence in large datasets.

Successful application to national kidney transplant data.

Outperforms traditional methods in scalability and accuracy.

Abstract

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. Analysis of national kidney transplant data with a massive sample size and large number of predictors defy any existing statistical methods and software. In view of these difficulties, we propose a Minorization-Maximization-based steepest ascent procedure for estimating the time-varying effects. Leveraging the block structure formed by the basis expansions, the proposed procedure iteratively updates the optimal block-wise direction along which the approximate increase in the log-partial likelihood is maximized. The resulting estimates ensure the ascent property and serve as refinements of the previous step. The performance of the proposed method is examined by simulations and applications to the analysis of national kidney transplant data.