Survival function estimator for recurrence time data using the estimator developed by Wang and Chang.

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Description

Estimation of survival function for correlated or i.i.d. recurrence time data by means of the product limit estimator (PLE) method developed by Wang and Chang. The resulting object of class "survfitr" is plotted by ‘plot.survfitr’, before it is returned.

Usage

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wc.fit(x,tvals) 

Arguments

x

a survival recurrent event object.

tvals

vector of times where the survival function can be estimated.

Details

Wang and Chang (1999) proposed an estimator of the common marginal survivor function in the case where within-unit interrocurence times are correlated. The correlation structure considered by Wang and Chang (1999) is quite general and contains, in particular, both the i.i.d. and multiplicative (hence gamma) frailty model as special cases.

This estimator removes the bias noted for the produc-limit estimator developed by Pea, Strawderman and Hollander (PSH, 2001) when interrocurence times are correlated within units. However, when applied to i.i.d. interocurrence times, this estimator is not expected to perform as well as the PSH estimator, especially with regard to efficiency.

Value

n

number of unit or subjects observed.

m

vector of number of recurrences in each subject (length n).

failed

vector of number of recurrences in each subject (length n*m). Vector ordered (e.g. times of first unit, times of second unit, ..., times of n-unit)

censored

vector of times of censorship for each subject (length n).

numdistinct

number of distinct failures times.

distinct

vector of distinct failures times.

AtRisk

matrix of number of persons-at-risk at each distinct time and for each subject.

survfunc

vector of survival estimated in distinct times.

tvals

copy of argument.

PSHpleAttvals

vector of survival estimated in tvals times.

Note

The mantainer wishes to thank Professors Chiung-Yu Huang and Shu-Hui Chang for their help for providing us with the Fortran code which computes standard errors of Wang and Chang's estimator.

References

Wang, M.-C. and Chang, S.-H. (1999). Nonparametric Estimation of a Recurrent Survival Function. J. Amer. Statist. Assoc 94, 146-153.

See Also

survfitr Survr

Examples

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data(MMC)

fit<-wc.fit(Survr(MMC$id,MMC$time,MMC$event))
fit
plot(fit,conf.int=FALSE)

# compare with pena-straderman-hollander

fit<-psh.fit(Survr(MMC$id,MMC$time,MMC$event))
fit
lines(fit,lty=2)

# and with MLE frailty

fit<-mlefrailty.fit(Survr(MMC$id,MMC$time,MMC$event))
fit
lines(fit,lty=3)