mHR2.LF {mhazard}

Bivariate regression survival function and marginal hazards estimation

Description

Estimates the survival function F and the marginal hazards Lambda11 for a bivariate Cox regression model. F and Lambda11 are estimated at two specified values of the covariates. If desired, (bootstrap) confidence intervals or confidence bounds for F and Lambda11 may also be computed.

Usage

mHR2.LF(
  mHR2.obj,
  X0_out,
  X1_out,
  T1_out,
  T2_out,
  confidence = c("none", "CI", "CB"),
  n.boot = 100
)

Arguments

mHR2.obj

Output from the mHR2 function.

X0_out, X1_out

Two possible sets of values for the covariates. F and Lambda will be estimated at X=X0_out and X=X1_out.

T1_out, T2_out

Vector of time points at which F and Lambda11 should be estimated. If confidence="CB", then both vectors must have length 3.

confidence

Type of confidence estimate to be computed. Possible values include "none", "CI" (to compute confidence intervals), and "CB" (to compute confidence bands). Defaults to "none".

n.boot

Number of bootstrap iterations for computing the confidence intervals/bands. Defaults to 100. Ignored if confidence="none".

Value

A list containing the following elements:

n10, n01:

Total number of events for the first/second outcome

n11:

Total number of double events

beta10, beta01, beta11:

Regression coefficient estimates

lambda10, lambda01, lambda11:

Baseline hazard estimates

Lambda11_out_Z0, Lambda11_out_Z1:

Estimates of Lambda11 at T1_out, T2_out for X=X0_out and X=X1_out

F_out_X0, F_out_X1:

Estimates of F at T1_out, T2_out for X=X0_out and X=X1_out

CI_Lambda11_X0.lb, CI_Lambda11_X0.ub:

Lower and upper bounds for Lambda11 at X=X0_out

CI_Lambda11_X1.lb, CI_Lambda11_X1.ub:

Lower and upper bounds for Lambda11 at X=X1_out

CI_F_X0.lb, CI_F_X0.ub:

Lower and upper bounds for F at X=X0_out

CI_F_X1.lb, CI_F_X1.ub:

Lower and upper bounds for F at X=X1_out

CB1_Lambda11_X0.lb, CB1_Lambda11_X0.ub, CB2_Lambda11_X0.lb, CB2_Lambda11_X0.ub, CB3_Lambda11_X0.lb, CB3_Lambda11_X0.ub:

Lower and upper bounds for Lambda11 at X=X0_out, at three T1_out, T2_out combinations

CB1_Lambda11_X1.lb, CB1_Lambda11_X1.ub, CB2_Lambda11_X1.lb, CB2_Lambda11_X1.ub, CB3_Lambda11_X1.lb, CB3_Lambda11_X1.ub:

Lower and upper bounds for Lambda11 at X=X1_out, at three T1_out, T2_out combinations

CB1_F_X0.lb, CB1_F_X0.ub, CB2_F_X0.lb, CB2_F_X0.ub, CB3_F_X0.lb, CB3_F_X0.ub:

Lower and upper bounds for F at X=X0_out, at three T1_out, T2_out combinations

CB1_F_X1.lb, CB1_F_X1.ub, CB2_F_X1.lb, CB2_F_X1.ub, CB3_F_X1.lb, CB3_F_X1.ub:

Lower and upper bounds for F at X=X1_out, at three T1_out, T2_out combinations

Details

If confidence="CI" or confidence="CB", then 95% bootstrap confidence bounds are computed by estimating the standard errors of F/Lambda11 based on n.boot bootstrap iterations. Currently confidence bounds can only be computed at three specified T1out/T2out combinations (meaning that T1out and T2out must both have length 3 if confidence="CB"). No confidence measures will be returned if confidence="none".

References

Prentice, R., Zhao, S. "The statistical analysis of multivariate failure time data: A marginal modeling approach", CRC Press (2019). Prentice, R., Zhao, S. "Regression models and multivariate life tables", Journal of the American Statistical Association (2020) In press.

See Also

mHR2

Examples

x <- genClaytonReg(50, 2, 0.5, 1, 1, log(2), log(2), log(8/3), 2, 2)
x.mHR2 <- mHR2(x$Y1, x$Y2, x$Delta1, x$Delta2, x$X)
x.LF <- mHR2.LF(x.mHR2, 0, 1, c(0.25, 0.5, 1), c(0.25, 0.5, 1))
x.LF.CI <- mHR2.LF(x.mHR2, 0, 1, c(0.25, 0.5, 1),
c(0.25, 0.5, 1), confidence="CI")
x.LF.CB <- mHR2.LF(x.mHR2, 0, 1, c(0.25, 0.5, 1),
c(0.25, 0.5, 1), confidence="CB")