Survival Analysis for Recurrent Event Data

Estimation of the survival function of inter-occurrence times for recurrent event data, using the estimators of Peña, Strawderman and Hollander (2001) and Wang and Chang (1999) , and maximum likelihood estimation under a gamma frailty model. Includes bootstrap comparison of survival quantiles between groups.

survrec

Survival analysis for recurrent event data.

survrec estimates the survival function of the time between occurrences of a recurrent event — repeated hospitalizations, tumour relapses, successive failures of a machine — from censored gap-time data. It implements three estimators: the generalized product-limit estimator of Peña, Strawderman and Hollander (2001), valid for independent gap times; the estimator of Wang and Chang (1999), which remains consistent when gap times are correlated within subjects; and maximum likelihood estimation under a gamma frailty model. Survival quantiles can be compared between groups through several bootstrap schemes.

Version 2.0.0 is a complete rewrite of the package: the Fortran 77 core has been replaced by C++ (validated against the original implementation), the bootstrap is reproducible with set.seed() and runs in parallel, and the package gains ggplot2 graphics, the mean cumulative function and formal bootstrap comparisons of survival quantiles. The last Fortran-based version is preserved as the v1.2-5 release.

Installation

Development version:

# install.packages("remotes")
remotes::install_github("isglobal-brge/survrec")

Usage

library(survrec)
data(colon)

# survival of the rehospitalization gap times, by Dukes stage
fit <- survfitr(Survr(hc, time, event) ~ as.factor(dukes),
                data = colon, type = "wang-chang")

fit                                    # summary per group
quantile(fit, probs = c(0.25, 0.5))    # survival quantiles
autoplot(fit)                          # survival curves with confidence bands

The three estimators can be compared on the same data — the natural check for within-subject correlation:

x <- Survr(colon$hc, colon$time, colon$event)
plotEstimators(x)
mlefrailty_fit(x)$alpha   # small alpha = strong association between gap times

Beyond estimation, the package provides the mean cumulative function of the events (mcf()), and bootstrap comparisons of survival quantiles between groups with percentile intervals and p-values:

b <- survdiffr(Survr(hc, time, event) ~ as.factor(dukes),
               data = colon, q = 0.5, seed = 1)
summary(b)
autoplot(b)

The vignette walks through a complete analysis:

vignette("survrec")

References

Peña, E.A., Strawderman, R. and Hollander, M. (2001). Nonparametric estimation with recurrent event data. Journal of the American Statistical Association, 96(456), 1299–1315. doi:10.1198/016214501753381922

Wang, M.-C. and Chang, S.-H. (1999). Nonparametric estimation of a recurrent survival function. Journal of the American Statistical Association, 94(445), 146–153. doi:10.1080/01621459.1999.10473831

González, J.R. and Peña, E.A. (2003). Bootstrapping median survival with recurrent event data. IX Conferencia Española de Biometría, A Coruña, Spain.