Vertical modeling: analysis of competing risks data with a cure proportion

TL;DR

This paper extends the vertical modeling approach to competing risks survival data by incorporating a cured fraction, allowing for covariate effects on cure probability, failure risk, and cause-specific risks, using an EM-algorithm.

Contribution

It introduces a natural extension of the semi-parametric mixture cure model to competing risks, enabling cause-specific analysis with a cured proportion.

Findings

Method performs well in simulation studies

Application to melanoma data demonstrates practical utility

Estimates of cure and risk components are interpretable

Abstract

In this paper, we extend the vertical modeling approach for the analysis of survival data with competing risks to incorporate a cured fraction in the population, that is, a proportion of the population for which none of the competing events can occur. The proposed method has three components: the proportion of cure, the risk of failure, irrespective of the cause, and the relative risk of a certain cause of failure, given a failure occurred. Covariates may affect each of these components. An appealing aspect of the method is that it is a natural extension to competing risks of the semi-parametric mixture cure model in ordinary survival analysis; thus, causes of failure are assigned only if a failure occurs. This contrasts with the existing mixture cure model for competing risks of Larson and Dinse, which conditions at the onset on the future status presumably attained. Regression parameter estimates are obtained using an EM-algorithm. The performance of the estimators is evaluated in a simulation study. The method is illustrated using a melanoma cancer data set.