simuDataYP {ELYP}

Generate random times that follow the YP model with the Given Parameters th1, th2, and alphaX.

Description

This function is for simulations. It generates data from Yang-Prentice model with given/known parameters and may be used later to see how well some estimation procedure works on them. th1 = exp(beta1), th2 = exp(beta2), alphaX = $a' X$. There is always a covariate Z that indicates the two samples, and the hazards of the two treatments follows the Yang–Prentice model. The baseline hazard of sample one (where Z=0) is taken to be exponential.

Usage

simuDataYP(n1, n2, th1, th2, cens, alphaX)

Arguments

n1

sample size of first arm.

n2

sample size of second arm.

th1

the parameter of th1=exp(beta1). Short term.

th2

the parameter of th2=exp(beta2). Long term.

cens

logical, Either TRUE or FALSE.

alphaX

a vector of length n1+n2. It is the inner product of alpha and covariates X....the part that is proportional hazards. This way, alpha can be p dimensional, However alpha times X is always a vector of length n1+n2.

Details

The hazard of the generated survival times, Y, have hazard function that is proportional to exp( alphaX ).

The hazard of arm 1 is constant, just exp( alphaX ). The hazard of arm 2 is given as exp(alphaX) / [ 1/th1 S_0(t) + 1/th2 F_0(t) ]

where S_0 and F_0 are survival function and CDF of a standard exponential random variable.

Value

A list with the following components:

Y

The survival times, possibly right censored.

d

The censoring status.

Zmat

the covariates used in generating random times.

Author(s)

Mai Zhou

References

Yang and Prientice. (2005). Semiparametric analysis of short term/long term hazard ratios with two sample survival data. Biometrika

Examples

## generate data and covariates.
X <- -99:100/50        ## the covariate for alpha, 200 long
temp <- simuDataYP(n1=100, n2=100, th1=exp(1), th2=exp(-1), cens=TRUE, alphaX = -0.5*X)
## this generate a sample of censored data with n=200. beta1=1, beta2=-1, alpha= -0.5.
## and the design matrix or covariance matrix is 
Zmat <- cbind(X, temp$Zmat)