CoxFindL3 {ELYP}

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

Description

This program uses simple search to find the Lower 95% (or other)Wilks confidence limits based on the log likelihood function (CoxEL) supplied.

Usage

CoxFindL3(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 used to 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 Lower Value. The input variables must be called beta and theta. beta: in the form of a 2-d vector (i.e., the beta1, beta2) and theta: (=Mulam)

y

a vector of censored survival time.

d

a vector of 0 and 1, censoring indicator

Z

covariates of the Cox model.

level

confidence level

Details

Basically we repeatedly testing the value of the parameter (defined by Efun), try to go to lower and lower values 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:

Lower

the lower confidence bound.

maxParameterNloglik

Final values of the 4 parameters, 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)