reReg: Fits Semiparametric Regression Models for Recurrent Event Data

Description

Fits a semiparametric regression model for the recurrent event data. The rate function of the underlying process for the recurrent event process can be specified as a Cox-type model, an accelerated mean model, or a generalized scale-change model. See details for model specifications.

Usage

reReg(formula, data, B = 200, method = c("cox.LWYY", "cox.GL",
  "cox.HW", "am.GL", "am.XCHWY", "sc.XCYH"), se = c("NULL", "bootstrap",
  "resampling"), contrasts = NULL, control = list())

Arguments

formula

a formula object, with the response on the left of a "~" operator, and the predictors on the right. The response must be a recurrent event survival object as returned by function Recur.

data

an optional data frame in which to interpret the variables occurring in the "formula".

a numeric value specifies the number of resampling for variance estimation. When B = 0, variance estimation will not be performed.

method

a character string specifying the underlying model. See Details.

a character string specifying the method for standard error estimation. See Details.

contrasts

an optional list.

control

a list of control parameters.

Details

Suppose the recurrent event process and the failure events are observed in the time interval $t\in[0,\tau]$, for some constant $\tau$. We formulate the rate function, $\lambda(t)$, for the recurrent event process and the hazard function, $h(t)$, for the censoring time under the following model specifications:

Cox-type model:: $$\lambda(t) = Z \lambda_0(t) e^{X^\top\alpha}, h(t) = Z h_0(t)e^{X^\top\beta},$$
Accelerated mean model:: $$\lambda(t) = Z \lambda_0(te^{X^\top\alpha})e^{X^\top\alpha}, h(t) = Z h_0(te^{X^\top\beta})e^{X^\top\beta},$$
Scale-change model:: $$\lambda(t) = Z \lambda_0(te^{X^\top\alpha})e^{X^\top\beta},$$

where $\lambda_0(t)$ is the baseline rate function, $h_0(t)$ is the baseline hazard function, $X$ is a $n$ by $p$ covariate matrix and $\alpha$, $Z$ is an unobserved shared frailty variable, and $\beta$ are unknown $p$-dimensional regression parameters.

The reReg function fits models with the following available methods:

method = "cox.LWYY": assumes the Cox-type model with Z = 1 and requires independent censoring. The returned result is equivalent to that from coxph. See reference Lin et al. (2000).
method = "cox.HW": assumes the Cox-type model with unspecified Z, thus accommodate informative censoring. See the references See reference Wang, Qin and Chiang (2001) and Huang and Wang (2004).
method = "am.GL": assumes the accelerated mean model with Z = 1 and requires independent censoring. See the reference Ghosh and Lin (2003).
method = "am.XCHWY": assumes the accelerated mean model with unspecified Z, thus accommodate informative censoring. See the reference Xu et al. (2017).
method = "sc.XCYH": assumes the generalized scale-change model, and includes the methods "cox.HW" and "am.XCHWY" as special cases. Informative censoring is accounted for through the unspecified frailty variable Z. The methods also provide a hypothesis test of these submodels.

The available methods for variance estimation are:

NULL: variance estimation will not be performed. This is equivalent to setting B = 0.
"resampling": performs the efficient resampling-based sandwich estimator that works with methods "cox.HW", "am.XCHWY" and "sc.XCYH".
"bootstrap": works with all fitting methods.

The control list consists of the following parameters:

tol: absolute error tolerance.
a0, b0: initial guesses used for root search.
solver: the equation solver used for root search. The available options are BB::BBsolve, BB::dfsane, BB:BBoptim, and optim.
parallel: an logical value indicating whether parallel computation will be applied when se = "bootstrap" is called.
parCl: an integer value specifying the number of CPU cores to be used when parallel = TRUE. The default value is half the CPU cores on the current host.

References

Xu, G., Chiou, S.H., Huang, C.-Y., Wang, M.-C. and Yan, J. (2017). Joint Scale-change Models for Recurrent Events and Failure Time. Journal of the American Statistical Association, 112(518): 796--805.

Lin, D., Wei, L., Yang, I. and Ying, Z. (2000). Semiparametric Regression for the Mean and Rate Functions of Recurrent Events. Journal of the Royal Statistical Society: Series B (Methodological), 62: 711--730.

Wang, M.-C., Qin, J., and Chiang, C.-T. (2001). Analyzing Recurrent Event Data with Informative Censoring. Journal of the American Statistical Association, 96(455): 1057--1065.

Ghosh, D. and Lin, D.Y. (2003). Semiparametric Analysis of Recurrent Events Data in the Presence of Dependent Censoring. Biometrics, 59: 877--885.

Huang, C.-Y. and Wang, M.-C. (2004). Joint Modeling and Estimation for Recurrent Event Processes and Failure Time Data. Journal of the American Statistical Association, 99(468): 1153--1165.

Examples

Run this code

# NOT RUN {
fm <- Recur(Time, id, event, status) ~ x1 + x2

## Accelerated Mean Model
set.seed(1)
dat <- simSC(80, c(-1, 1), c(-1, 1), type = "am")
(fit <- reReg(Recur(Time, id, event, status) ~ x1 + x2, 
              data = dat, method = "am.XCHWY", se = "resampling", B = 20))
summary(fit)

## Generalized Scale-Change Model
set.seed(1)
dat <- simSC(100, c(-1, 1), c(-1, 1), type = "sc")
(fit <- reReg(Recur(Time, id, event, status) ~ x1 + x2, 
              data = dat, method = "sc.XCYH", se = "resampling", B = 20))
summary(fit)
# }