genClaytonReg {mhazard}

Generates regression data from a bivariate Clayton-Oakes model

Description

Generates simulated survival data from a bivariate Clayton-Oakes model where the hazard depends on a binary coefficient X. This can be used to create example data for bivariate Cox regression. The marginal distributions are exponential with given rate parameters. The joint distribution is defined using a Clayton copula. The censoring times are also exponentially distributed with given rate parameters.

Usage

genClaytonReg(
  n,
  theta,
  Xp,
  lambda10,
  lambda01,
  b10,
  b01,
  b11,
  lambdaC1,
  lambdaC2
)

Arguments

n

Sample size for the simulated data set.

theta

Parameter for the Clayton copula. Must be -1 or larger.

Xp

Probability that the covariate is equal to 1. Must satisfy 0<Xp<1.

lambda10, lambda01

Rate parameters for the (marginal) exponential distributions when X=0.

b10, b01, b11

Regression coefficient values.

lambdaC1, lambdaC2

Rate parameters for the censoring times. No censoring occurs if this parameter is equal to 0.

Value

A data frame containing the following elements:

Y1, Y2:

Survival times for the simulated data

Delta1, Delta2:

Censoring indicators for the simulated data

X

Covariate matrix (of dimension n x 1).

Details

This function simulates data with the following survival function: F(t1,t2) = [F(t1,0)^(-eta) + F(0,t2)^(-eta) - 1]^(-1/eta) (The survival function is defined to be equal to 0 if this quantity is negative.) Here eta=thetaexp(Xb11). The marginal survival functions F(t1,0) and F(0,t2) are exponentially distributed with rate parameters lambda10exp(Xb10) and lambda01exp(Xb01), respectively. After generating survival times Y1 and Y2 (of length n) under this distribution, censoring times C1 and C2 (also of length n) are generated. C1/C2 are generated under an exponential distribution with rate parameters lambdaC1 and lambdaC2. If C1[i]<Y1[i] for a given observation i, then observation i is considered to be censored (i.e., Delta1[i]=0). Delta2 is defined in a similar manner. If lambdaC1 or lambdaC2 is equal to 0, then the corresponding variable is uncensored (meaning that Delta[i]=1 for all i).

References

Clayton, D. "Model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.", Biometrika (1978) 65:141-151. Prentice, R., Zhao, S. "The statistical analysis of multivariate failure time data: A marginal modeling approach", CRC Press (2019).

Examples

x <- genClaytonReg(1000, 2, 0.5, 1, 1, log(2), log(2), log(8/3), 2, 2)