CoxFindL2 {ELYP}

Find the Wilks Confidence Interval Lower Bound for Efun based on the Empirical Likelihood Ratio Function CoxEL

Description

This function uses simple search to find the lower level (default 95%) Wilks confidence limits based on the CoxEL( ) likelihood function.

Usage

CoxFindL2(BetaMLE, StepSize, Hfun, Efun, y, d, Z, level=3.84)

Arguments

BetaMLE

a scalar: the NPMLEs: beta1 hat.

StepSize

a vector of length 2. Approximate length of the 2 confidence intervals: beta1, and lambda.

Hfun

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

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 lower value. The two input variables must be named beta and theta.

y

the censored survival times.

d

vector of 0, and 1, censoring indicator

Z

matrix of 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:

Lower

the lower confidence bound.

maxParameterNloglik

Final values of the 3 parameters, and the log likelihood.

Author(s)

Mai Zhou

References

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

Examples

## We find 95% lower limit of theta= \Lambda_0(300) exp(\beta)
## where \Lambda and \beta are inside a Cox model.
## First we define a function (Hfun) = I[t <= 300], so that
## the baseline feature is \Lambda_0(300). The second function
## we need to define is (Efun) = what we called theta above.

data(smallcell)
myHfun <- function(t){as.numeric(t <= 300)}
myEfun <- function(beta, theta){theta*exp(beta)}

myy <- smallcell$survival
myd <- smallcell$indicator
myZ <- smallcell$arm

CoxFindL2(BetaMLE=0.5337653, StepSize=c(0.1, 3), 
          Hfun=myHfun, Efun=myEfun, y=myy, d=myd, Z=myZ)