npSurv3 function

Nonparametric estimates of the survival function for trivariate failure time data

Computes the survival function for a trivariate failure time data. The survival function for trivariate failure time data is analogous to the Kaplan-Meier estimator for a univariate failure time data and Dabrowska estimator for bivariate failure time data. Optionally (bootstrap) confidence intervals for the survival function may also be computed.

npSurv3(
  Y1,
  Y2,
  Y3,
  Delta1,
  Delta2,
  Delta3,
  newT1 = NULL,
  newT2 = NULL,
  newT3 = NULL,
  conf.int = FALSE,
  R = 1000,
  ...
)

Arguments

• Y1, Y2, Y3: Vectors of event times (continuous).
• Delta1, Delta2, Delta3: Vectors of censoring indicators (1=event, 0=censored).
• newT1, newT2, newT3: Optional vectors of times at which to estimate the survival function (which do not need to be subsets of Y1/Y2/Y3). Defaults to the unique values in Y1/Y2/Y3 if not specified.
• 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.

Returns

A list containing the following elements:

• T1:: Unique values of Y1 at which Fhat was computed
• T2:: Unique values of Y2 at which Fhat was computed
• T3:: Unique values of Y3 at which Fhat was computed
• Fhat:: Estimated survival function (computed at T1, T2, T3)
• Fhat.lci:: Lower 95% confidence bounds for Fhat
• Fhat.uci:: Upper 95% confidence bounds for Fhat
• Fmarg1.est:: Estimated marginal survival function for T11 (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
• Fmarg3.est:: Estimated marginal survival function for T3 (computed at newT3)
• Fmarg3.lci:: Lower 95% confidence bounds for Fmarg3
• Fmarg3.uci:: Upper 95% confidence bounds for Fmarg3
• F.est:: Estimated survival function (computed at newT1, newT2, newT3)
• F.est.lci:: Lower 95% confidence bounds for F.est
• F.est.uci:: Upper 95% confidence bounds for F.est
• C110:: Pairwise marginal cross ratio estimator C110 (computed at newT1, newT2, newT3)
• C101:: Pairwise marginal cross ratio estimator C101 (computed at newT1, newT2, newT3)
• C011:: Pairwise marginal cross ratio estimator C011 (computed at new T1, newT2, newT3)
• C111:: Trivariate dependency estimator C111 (computed at newT1, newT2, newT3)

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.

Examples

x <- genClayton3(25, 0, 0.5, 0.5, 0.5)
x.npSurv3 <- npSurv3(x$Y1, x$Y2, x$Y3, x$Delta1, x$Delta2, x$Delta3)
x.npSurv3.ci <- npSurv3(x$Y1, x$Y2, x$Y3, x$Delta1, x$Delta2,
x$Delta3, conf.int=TRUE, R=500)

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. 120-123.

See Also

boot