CoxFindU3 {ELYP}

Find the Wilks Confidence Interval Upper Bound from the Given Empirical Likelihood Ratio Function

Description

This program uses simple search to find the upper 95% Wilks confidence limits based on the log likelihood function supplied.

Usage

CoxFindU3(BetaMLE, StepSize, Hfun, Efun, y, d, Z, level=3.84)

Arguments

BetaMLE

a vector containing the two NPMLEs: beta1 hat and beta2 hat.

StepSize

a vector of length 3. Approximate length of the 3 confidence intervals: beta1, beta2 and lambda.

Hfun

a function that defines the baseline feature: mu.

Efun

a function that takes the input of 3 parameter values (beta1, beta2 and Mulam) and returns a parameter that we wish to find the confidence Interval Upper Value. The input variables must be in the form: beta = c(beta1, beta2) and theta = Mulam.

y

a matrix.

d

a vector of 0 and 1

Z

covariates

level

confidence level using chi-square(df=1), but calibration possible.

Details

Basically we repeatedly testing the value of the parameter, until we find those which the -2 log likelihood value is equal to 3.84 (or other level, if set differently).

Value

A list with the following components:

Upper

the upper confidence bound.

maxParameterNloglik

Final values of the 4 parameters (beta1, beta2, Mulam, lam), and the log likelihood.

Author(s)

Mai Zhou

References

Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. JCGS

Examples

## Here Mulam is the value of int g(t) d H(t) = Mulam
## For example g(t) = I[ t <= 2.0 ]; look inside myLLfun(). 

data(GastricCancer)

# The following will take about 0.5 min to run.
# findU3(NPmle=c(1.816674, -1.002082), ConfInt=c(1.2, 0.5, 10),   
#        LogLikfn=myLLfun, Pfun=Pfun, dataMat=GastricCancer)