nltm {nltm}R Documentation

Fit Non Linear Transformation Model for Analyzing Survival Data

Description

Fits a non-linear transformation (NLT) model for analyzing survival data, see Tsodikov (2003). The class of NLT models includes the following currently supported models Cox proportional hazard and proportional hazard cure models, proportional odds model, proportional hazard - proportional hazard cure model, proportional hazard - proportional odds model, Gamma frailty model, and proportional hazard - proportional odds model.

Usage

nltm(formula=formula(data), data=parent.frame(), subset, na.action,
init, control, model=c("PH","PHC","PO","PHPHC","PHPOC","GFM","PHPO"),
verbose=FALSE, ...)

Arguments

formula A formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function.
data A data.frame in which to interpret the variables named in the formula, or in the subset argument.
subset Expression saying that only a subset of the rows of the data should be used in the fit.
na.action A missing-data filter function, applied to the model.frame, after any subset argument has been used. Default is options()$na.action.
init Vector of initial values for the calculation of the maximum likelihood estimator of the regression parameters. Default initial value is zero.
control Object of class coxph.control specifying iteration limit and other control options. Default is nltm.control(...).
model A character string specifying a non-linear transformation model. Default Proportional Hazards Model.
The conditional survival function S(t|z) given the covariates z of each of the models currently supported are given below. Let S_0(t) be the non-parametric baseline survival function, and theta(z) and eta(z) predictors. We take theta(z)=exp(β_theta z) and eta(z)=exp(β_eta z).
  • Proportional hazard model (PH):

    S(t|z)=S_0(t)^theta(z).

  • Proportional hazard cure model (PHC):

    S(t|z)=exp(-theta(z)(1-S_0(t))).

  • Proportional odds model (PO):

    S(t|z)=frac{theta(z)}{theta(z)-ln(S_0(t)).}

  • Proportional hazard - proportional hazard cure model (PHPHC):

    S(t|z)=exp(-theta(z)(1-S_0^{eta(z)}(t))).

  • Proportional hazard - proportional odds cure model (PHPOC):

    S(t|z)=exp(-theta(z)(1-S_0(t))/(1-(1-eta(z))S_0(t))).

  • Gamma frailty model (GFM):

    S(t|z)=(frac{theta(z)^{eta(z)}} {theta(z)-ln(S_0(t))})^eta(z).

  • Proportional hazard - proportional odds model (PHPO):

    S(t|z)=frac {theta S_0^{eta(z)}(t)} {1-(1-theta)S_0^{eta(z)}(t)}.

verbose If TRUE it stores information from maximization of likelihood and calculation of information matrix in a file. Default is FALSE.
... Other arguments

Value

an object of class "coxph".

Author(s)

Gilda Garibotti (garibott AT math.utah.edu), Alexander Tsodikov

References

Tsodikov AD (2003) "Semiparametric models: a generalized self-consistency approach". Journal of the Royal Statistical Society B, 65, Part 3, 759-774.

Tsodikov AD, Ibrahim JG, Yakovlev AY (2003) "Estimating cure rates from survival data: an alternative to two-component mixture models". Journal of the American Statistical Association, Vol. 98, No. 464, 1063-1078.

Tsodikov AD (2002) "Semi-parametric models of long- and short-term survival: an application to the analysis of breast cancer survival in Utah by age and stage". Statistics in Medicine, 21, 895-920.

Wendland MMM, Tsodikov AD, Glenn MJ, Gaffney DK (2004) "Time interval to the development of breast carcinoma after treatment for Hodgkin disease". Cancer Vol. 101, No. 6, 1275-1282.

See Also

coxph, nltm.control

Examples

## Not run: 
# Simple test data set 
test1 <- list(time=c(10,7,32,23,22,6,16,34,32,25,11,20,19,6,17,35,6,13,9,6,1),
              status=c(1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0),
              size=c(1.79,7.93,2.02,6.89,2.30,7.82,1.25,9.85,6.02,3.43,4.72,7.45,8.83,9.53,1.10,1.06,5.25,5.86,2.03,3.62,3.52),
              age=factor(c(65,65,65,65,99,45,65,99,99,99,65,45,65,55,45,45,55,55,55,99,65)))
nltm(Surv(time,status) ~ size + age, data=test1, model="PO")
## End(Not run)

[Package nltm version 1.1 Index]