ELYP (version 0.7-3)

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. This is 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. Approximate length of the 2 confidence intervals: beta1, and lambda. It is the initial search step size.

Hfun

a function that defines the baseline feature: mu=int f(t) dH(t).

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. The two input variables must be called beta and theta.

y

a vector of censored survival times.

d

a vector of 0 and 1, censoring indicator.

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

# NOT RUN {
## See example in CoxFindL2.
## Here Mulam is the value of int g(t) d H(t) = Mulam
## For example g(t) = I[ t <= 2.0 ]; look inside myLLfun(). 
# }