npSurv2 {mhazard}

Nonparametric estimates of the survival function for bivariate failure time data

Description

Computes the survival function for bivariate failure time data using one of three possible estimators, including Dabrowska, Volterra and Prentice-Cai estimators. Optionally (bootstrap) confidence intervals for the survival function may also be computed.

Usage

npSurv2(
  Y1,
  Y2,
  Delta1,
  Delta2,
  newT1 = NULL,
  newT2 = NULL,
  estimator = c("dabrowska", "volterra", "prentice-cai"),
  conf.int = FALSE,
  R = 1000,
  ...
)

Arguments

Y1, Y2

Vectors of event times (continuous).

Delta1, Delta2

Vectors of censoring indicators (1=event, 0=censored).

newT1, newT2

Optional vectors of times at which to estimate the survival function (which do not need to be subsets of Y1/Y2). Defaults to the unique values in Y1/Y2 if not specified.

estimator

Which estimator of the survival function should be used. Possible values include "dabrowska", "volterra", and "prentice-cai". Defaults to "dabrowska".

conf.int

Should bootstrap confidence intervals be computed?

R

Number of bootstrap replicates. This argument is passed to the boot function. Defaults to 1000. Ignored if conf.int is FALSE.

...

Additional arguments to the boot function.

Value

A list containing the following elements:

T1:

Unique uncensored Y1 values

T2:

Unique uncensored Y2 values

Fhat:

Estimated bivariate survival function (computed at T1, T2)

Fhat.lci:

Lower 95% confidence bounds for Fhat

Fhat.uci:

Upper 95% confidence bounds for Fhat

Fmarg1.est:

Estimated marginal survival function for T1 (computed at newT1)

Fmarg1.lci:

Lower 95% confidence bounds for Fmarg1

Fmarg1.uci:

Upper 95% confidence bounds for Fmarg1

Fmarg2.est:

Estimated marginal survival function for T2 (computed at newT2)

Fmarg2.lci:

Lower 95% confidence bounds for Fmarg2

Fmarg2.uci:

Upper 95% confidence bounds for Fmarg2

F.est:

Estimated survival function (computed at newT1, newT2)

F.est.lci:

Lower 95% confidence bounds for F.est

F.est.uci:

Upper 95% confidence bounds for F.est

CR:

Estimated cross ratio (computed at T1, T2)

KT:

Estimated Kendall\'s tau (computed at T1, T2)

CR.est:

Estimated cross ratio (computed at newT1, newT2)

KT.est:

Estimated Kendall\'s tau (computed at newT1, newT2)

Details

If conf.int is TRUE, confidence intervals will be computed using the boot function in the boot package. Currently only 95% confidence intervals computed using the percentile method are implemented. If conf.int is FALSE, confidence intervals will not be computed, and confidence bounds will not be returned in the output.

References

Prentice, R., Zhao, S. "Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan–Meier estimator", Lifetime Data Analysis (2018) 24:3-27. Prentice, R., Zhao, S. "The statistical analysis of multivariate failure time data: A marginal modeling approach", CRC Press (2019). pp. 52-60.

See Also

boot

Examples

x <- genClayton2(100, 0, 1, 1, 2, 2)
x.npSurv2 <- npSurv2(x$Y1, x$Y2, x$Delta1, x$Delta2)
x.npSurv2.ci <- npSurv2(x$Y1, x$Y2, x$Delta1, x$Delta2,
conf.int=TRUE)
x.npSurv2.volt <- npSurv2(x$Y1, x$Y2, x$Delta1, x$Delta2,
estimator="volterra")
x.npSurv2.t <- npSurv2(x$Y1, x$Y2, x$Delta1, x$Delta2,
newT1=-1*log(c(0.55, 0.7, 0.7, 0.85, 0.85, 0.85)),
newT2=-1*log(c(0.55, 0.55, 0.7, 0.55, 0.7, 0.85)))