ELYP (version 0.7-1)

CoxFindU2: Find the Wilks Confidence Interval Upper Bound for Efun from the Empirical Likelihood Ratio Function CoxEL( ).

Description

This function uses simple search to find the upper 95% Wilks confidence limits based on the log likelihood function supplied. A sister function to CoxFindL2().

Usage

CoxFindU2(BetaMLE, StepSize, Hfun, Efun, y, d, Z, level=3.84)

Arguments

BetaMLE

a scalar: the NPMLE beta1 hat.

StepSize

a vector of length 2. Approx. length of the 2 conf. intervals: beta1, and lambda.

Hfun

a function that defines the baseline feature: mu.

Efun

a function that takes the input of 2 parameter values (beta1, and Mulam) and returns a parameter that we wish to find the confidence Interval Upper Value.

y

a vector of censored survival times.

d

a vector of 0 and 1

Z

covariates for the Cox model

level

Confidence Level. Use chi-square(df=1), but calibration possible.

Value

• A list with the following components:
• Upper
  the upper confidence bound.
• maxParameterNloglik
  Final values of the 4 parameters, and the log likelihood.

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).

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)