CoxEL {ELYP}

Compute Empirical Likelihood and Partial Likelihood of Cox model for Testing the beta and Baseline Jointly.

Description

This function compute empirical likelihood and partial likelihood for the purpose of testing (jointly) the beta (the regression parameter) and a baseline hazard feature, which is defined by lam and fun.

Usage

CoxEL(y, d, Z, beta, lam, fun)

Arguments

y

a vector containing the survival times

d

censoring status: 1 - uncensored; 0 - censored.

Z

a matrix of covariates, size nxk; Z=(Z_1i, ..., Z_ki)

beta

a vector =(beta1, ... betak)

lam

a scalar, used in the constraint of baseline: int f(t)dH(t)= Mulam. It is sometime called the tilting amount.

fun

a function in the int f(t)dH(t). Together with lam, it defines the feature of the baseline hazard H(t).

Details

This function compute the likelihood when we impose both restriction on beta and on baseline. The restriction on beta is simply by setting beta equal to the given value in the CoxEL input. The restriction on the baseline is via a finite dimensional feature.

lam controls the amount of tilting for the baseline, in the direction of the feature defined by int f(t) dH(t). When lam = 0 means no tilting.

Value

It returns a list containing: (1)logEmpLik: log empirical likelihood value; (2)logPlik: log partial likelihood value; (3)Hazw: the constrained baseline estimator (the jumps); (4)mu: the value of the constraint, int f(t)dH(t)= Mulam i.e., the feature value.

Author(s)

Mai Zhou

References

Zhou, M. (2016). Empirical Likelihood Method in Survival Analysis. Zhou, M. (2005). Cox model with restriction on the baseline hazard. Tech Report, Univ. of Kentucky, Dept of Statistics

Examples

## censored regression with one right censored observation.
## we check the estimation equation, with the MLE inside myfun7. 
y <- c(3, 5.3, 6.4, 9.1, 14.1, 15.4, 18.1, 15.3, 14, 5.8, 7.3, 14.4)
x <- c(1, 1.5, 2,   3,   4,    5,    6,    5,    4,  1,   2,   4.5)
d <- c(1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0)