jointSurroTKendall {frailtypack}

Kendall's \tau estimation using numerical integration methods

Description

This function estimate the Kendall's \tau based on the joint surrogate model described in jointSurroPenal (Sofeu et al., 2018), for the evaluation of a candidate surrogate endpoints, at the individual-level . We used the Monte-carlo and the gaussian Hermite quadrature methods for numerical integration. in the event of Gaussian Hermite quadrature, it is better to choose at least 20 quadature nodes for better results. The actual value of nodes used is the maximum between 20 and nb.gh

Usage

jointSurroTKendall(object = NULL, theta, gamma, alpha = 1, zeta = 1, 
                   sigma.v = matrix(rep(0,4),2,2), int.method = 0, 
                   nb.MC.kendall = 10000, nb.gh = 32, 
                   random.generator = 1, random = 0, 
                   random.nb.sim = 0, seed = 0, ui = 1)

Arguments

object

An object inheriting from jointSurroPenal class. The default is NULL

theta

Variance of the individual-level random effect, \omega_ij. Required if object is set to NULL

gamma

Variance of the trial-level random effect associated with the baseline risk, u_i. Required if object is set to NULL. The default is 3.5.

alpha

Power parameter associated with u_i. Required if object is set to NULL. The default is 1.

zeta

Power parameter associated with \omega_ij. Required if object is set to NULL The default is 1.

sigma.v

Covariance matrix of the random effects treatment-by-trial interaction (v_Si, v_Ti)

int.method

A numeric, indicates the integration method: 0 for Monte carlo and 1 for Gaussian-Hermite quadrature. The default is 0

nb.MC.kendall

Number of generated points used with the Monte-Carlo to estimate integrals in the Kendall's \tau formulation. Beter to use at least 4000 points for stable results. The default is 10000.

nb.gh

Number of nodes for the Gaussian-Hermite quadrature. The default is 32.

random.generator

Random number generator to use by the Fortran compiler, 1 for the intrinsec subroutine Random_number and 2 for the subroutine uniran(). The default is 1.

random

A binary that says if we reset the random number generation with a different environment at each call (1) or not (0). If it is set to 1, we use the computer clock as a seed. In the last case, it is not possible to reproduce the generated datesets". The default is 0.

random.nb.sim

If random is set to 1, a binary that indicates the number of generations that will be made.

seed

The seed to use for data (or samples) generation. required if random is set to 0. The default is 0.

ui

A binary, indicates whether one considered trial random effect associated with the baseline risk (1) or not (0). The default is 1.

Value

This function return the estimated Kendall's \tau

Author(s)

Casimir Ledoux Sofeu [e-mail], [e-mail] and Virginie Rondeau [e-mail]

References

Sofeu C.L., Emura T. and Rondeau V. (2018). One-step validation method for surrogate endpoints in multiple randomized cancer clinical trials with failure-time endpoints. Under review

See Also

jointSurrSimul, summary.jointSurroPenal

Examples

Ktau1 <- jointSurroTKendall(theta = 3.5, gamma = 2.5, nb.gh = 32)
Ktau2 <- jointSurroTKendall(theta = 1, gamma = 0.8, alpha = 1, zeta = 1, 
         nb.gh = 32)

###---Kendall's \eqn{\tau} from a joint surrogate model ---###

## Not run: 
data.sim <-jointSurrSimul(n.obs=400, n.trial = 20,cens.adm=549, 
          alpha = 1.5, theta = 3.5, gamma = 2.5, zeta = 1, 
          sigma.s = 0.7, sigma.t = 0.7,cor = 0.8, betas = -1.25, 
          betat = -1.25, full.data = 0, random.generator = 1, 
          seed = 0, nb.reject.data = 0)
          

###---Estimation---###
joint.surrogate <- jointSurroPenal(data = data.sim, nb.mc = 300, 
                   nb.gh = 20, indicator.alpha = 1, n.knots = 6)
                   
 Ktau3 <- jointSurroTKendall(joint.surrogate)
 Ktau4 <- jointSurroTKendall(joint.surrogate,nb.MC.kendall = 4000,
          seed = 1)

## End(Not run)