| CoxFindU2 {ELYP} | R Documentation |
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. |
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, and the log likelihood. |
Author(s)
Mai Zhou
References
Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. JCGS
Examples
## 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().