PTCMGH: Promotion Time Cure Models with a General Hazard Structure

Overview

PTCMGH is an R package for fitting and simulating from Promotion Time Cure Models (PTCMs) with flexible hazard structures. PTCMs are a class of survival models that explicitly account for a cured fraction of the population — individuals who will never experience the event of interest. The package is built around the General Hazard (GH) structure, which nests the most widely used hazard regression models as special cases, giving users flexibility in how covariates enter both the cure and the survival components of the model.

The population survival function takes the form:

$$S_c(t) = \exp[-\theta \tilde{F}(t)], \quad t \geq 0,$$

where $\theta > 0$ governs the cured fraction and $\tilde{F}(t)$ is a proper cumulative distribution function. Covariates $\mathbf{x} \in \mathbb{R}^p$ can enter through either or both components:

1. Cure component: via the log-link $\theta(\mathbf{w}) = \exp(\mathbf{w}^\top \boldsymbol{\alpha})$, where $\mathbf{w} \subseteq \mathbf{x}$.
2. Survival component: via the hazard structure $\tilde{H}(t \mid \mathbf{z})$, giving $\tilde{F}(t \mid \mathbf{z}) = 1 - \exp[-\tilde{H}(t \mid \mathbf{z})]$, where $\mathbf{z} \subseteq \mathbf{x}$.

Installation

PTCMGH depends on HazReg, which must be installed first:

# install.packages("devtools")
devtools::install_github("FJRubio67/HazReg")
devtools::install_github("FJRubio67/PTCMGH")

library(HazReg)
library(PTCMGH)

Main functions

Function	Description
PTCMMLE	Maximum likelihood estimation for PTCMs
simPTCMGH	Simulation of survival times from PTCMs

For full documentation: ?PTCMMLE, ?simPTCMGH

A PDF manual is also available in the repository: PTCMGH.pdf.

Supported hazard structures

The following hazard models are available for the survival component $\tilde{F}$:

Model	Abbreviation
General Hazard	GH
Proportional Hazards	PH
Accelerated Failure Time	AFT
Accelerated Hazards	AH

Models are fitted by maximum likelihood via nlminb and optim. Users should specify initial values and verify convergence of the optimisation, as is standard practice for these routines.

Supported baseline hazard distributions

All positive parameters are log-transformed for unconstrained optimisation.

Distribution	Key	GH	PH	AFT	AH
Power Generalised Weibull	PGW	✓	✓	✓	✓
Exponentiated Weibull	EW	✓	✓	✓	✓
Generalised Gamma	GenGamma	✓	✓	✓	✓
Gamma	Gamma	✓	✓	✓	✓
Log-normal	LogNormal	✓	✓	✓	✓
Log-logistic	LogLogistic	✓	✓	✓	✓
Weibull	Weibull	—	✓	✓	✓

Tutorial

• PTCMGH: Promotion Time Cure Models with a General Hazard structure — illustrative example on RPubs
• A rendered tutorial is also available in the Tutorial/ folder of this repository.

Related resources

• HazReg — R package for parametric hazard-based regression models (required dependency)
• HazReg.jl — Julia implementation
• Short course on Parametric Survival Analysis

License

This package is licensed under the MIT License.