PTCMGH R package

Promotion Time Cure Models with a General Hazard structure

The PTCMGH R package implements promotion time cure models of the type:

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

If a vector of covariates ${\bf x} \in {\mathbb R}^p$ are available, these can be incorporated into the two different components of the PTCM.

1. Let ${\bf w} \subseteq {\bf x}$, and consider the log-link $\theta({\bf w}) = \exp({\bf w}^{\top}{\boldsymbol{\alpha}})$.

2. Let ${\bf z} \subseteq {\bf x}$, and consider the hazard structure $\tilde{H}(t \mid {\bf z})$. Then, we can define

$\tilde{F}(t \mid {\bf z}) = 1 - \exp[-\tilde{H}(t \mid {\bf z})].$

The PTCMGH R package provides functions for simulating survival times from PTCMs with proportional hazards, accelerated failure time, and general hazard structures under a log-link for $\theta$, as well as for performing maximum likelihood estimation of these models. The hazard structure used for modelling $\tilde{F}$ can include the proportional hazards, the accelerated failure time, or more general hazard structures.

• General Hazard (GH) model.

• Accelerated Failure Time (AFT) model.

• Proportional Hazards (PH) model.

• Accelerated Hazards (AH) model.

These models are fitted using the R commands nlminb and optim. Thus, the user needs to specify the initial points and to check the convergence of the optimisation step, as usual.

The current version of the PTCMGH R package implements the following parametric baseline hazards for the models discussed in the previous section, using the command PTCMMLE.

• Power Generalised Weibull (PGW) distribution.

• Exponentiated Weibull (EW) distribution.

• Generalised Gamma (GenGamma) distribuiton.

• Gamma (Gamma) distribution.

• Lognormal (LogNormal) distribution.

• Log-logistic (LogLogistic) distribution.

• Weibull (Weibull) distribution. (only for AFT, PH, and AH models)

All positive parameters are transformed into the real line using a log link (reparameterisation).

The package depends on functions from the HazReg R package, which must also be installed and loaded.

library(devtools)
install_github("FJRubio67/HazReg")
install_github("FJRubio67/PTCMGH")

library(HazReg)
library(PTCMGH)
?simPTCMGH
?PTCMMLE

See also:

• PTCMGH R package: Promotion Time Cure Models with a General Hazard structure