A Simplified Stochastic EM Algorithm for Cure Rate Model with Negative Binomial Competing Risks: An Application to Breast Cancer Data

TL;DR

This paper introduces a simplified stochastic EM algorithm for cure rate models with negative binomial competing risks, improving computational efficiency and performance in analyzing breast cancer survival data.

Contribution

It develops a novel stochastic EM algorithm tailored for cure rate models with negative binomial risks, simplifying calculations and enabling independent maximization of parameters.

Findings

SEM outperforms EM in simulations

Algorithm effectively handles over- and under-dispersion

Application to breast cancer data demonstrates practical utility

Abstract

In this paper, a long-term survival model under competing risks is considered. The unobserved number of competing risks is assumed to follow a negative binomial distribution that can capture both over- and under-dispersion. Considering the latent competing risks as missing data, a variation of the well-known expectation maximization (EM) algorithm, called the stochastic EM algorithm (SEM), is developed. It is shown that the SEM algorithm avoids calculation of complicated expectations, which is a major advantage of the SEM algorithm over the EM algorithm. The proposed procedure also allows the objective function to be split into two simpler functions, one corresponding to the parameters associated with the cure rate and the other corresponding to the parameters associated with the progression times. The advantage of this approach is that each simple function, with lower parameter dimension, can be maximized independently. An extensive Monte Carlo simulation study is carried out to compare the performances of the SEM and EM algorithms. Finally, a breast cancer survival data is analyzed and it is shown that the SEM algorithm performs better than the EM algorithm.