geecure2 {geecure}

Semiparametric marginal proportional hazards mixture cure model

Description

Fit the semiparametric marginal proportional hazards mixture cure (PHMC) model for clustered failure time data. The function is based on the methods proposed by Peng et al. (2007) and Niu and Peng (2013).

Usage

geecure2(formula, cureform, data, id, corstr = c("independence", "exchangeable"), 
Var = TRUE, stdz = FALSE, boots = FALSE, nboot = 100, esmax = 100, eps = 1e-06)

Arguments

formula

a formula expression, of the form response ~ predictors. The response is a Surv object with right censoring. It is used to specify the covariate effects on the failure time of uncured subjects. See the documentation for survreg, Surv for details. The expression to the right of the "~" specifies the effect of covariates on the failure time of uncured patients.

cureform

a formula expression, of the form cureform ~ predictors. It is used to specify the effects of covariates on the cure rate. A covariate may be used in both formula and cureform.

data

a data frame in which to interpret the variables named in the formula and the cureform.

id

a vector which identifies the clusters. The length of id should be the same as the number of observations.

corstr

a character string specifying the correlation structure. The following are permitted: independence and exchangeable.

Var

If it is TRUE, the program returns Std.Error by the sandwich method. By default, Var = TRUE.

stdz

If it is TRUE, all the covariates in the formula and cureform are standardized. By default, stdz = FALSE.

boots

If it is TRUE, the program returns Std.Error by the bootstrap method. By default, boots = FALSE.

nboot

the number of bootstrap samples. The default is nboot = 100.

esmax

specifies the maximum iteration number. If the convergence criterion is not met, the ES iteration will be stopped after esmax iterations and the estimates will be based on the last ES iteration. The default esmax = 100.

eps

tolerance for convergence. The default is eps = 1e-6. Iteration stops once the relative change in deviance is less than eps.

Details

The semiparametric marginal PHMC model is considered in this function. For cure rate, a logistic regression model is employed and the probability of being cured is given by (1+\exp(\gamma Z))^{(-1)}. For uncured subject, the failure time is modeled by the semiparametric proportional hazards model. A covariate can be used either in formula or in cureform or in both. When corstr = independence, the model parameters are estimated by the expectation-maximization (EM) algorithm and the standard error estimates are obtained from sandwich variance formula based on Peng et al. (2007). When corstr = exchangeable, stdz = TRUE and boots = TRUE, the model parameters are estimated by the expectation-solution (ES) algorithm and the standard error estimates are obtained from bootstrap variance formula based on and Niu et al. (2013).

Value

An object of class geecure2 is returned. It can be examined by print.geecure2().

References

Peng, Y., Taylor, J. M. G., and Yu, B. (2007) A marginal regression model for multivariate failure time data with a surviving fraction. Lifetime Data Analysis, 13: 351-369.

Niu, Y. and Peng, Y. (2013) A semiparametric marginal mixture cure model for clustered survival data. Statistics in Medicine, 32: 2364-2373.

Examples

# Example. Fit the marginal semiparametric PHMC model for the bmt data.
data(bmt)
geebmtind2 <- geecure2(Surv(T2, d3) ~ Z8, cureform = ~ Z8, data = bmt, id = bmt$Z9, 
              corstr= "independence")           
geebmtexch2 <- geecure2(Surv(T2, d3) ~ Z8, cureform = ~ Z8, data = bmt, id = bmt$Z9, 
               corstr= "exchangeable", stdz = TRUE, Var = FALSE)