EMPIRICAL LIKELIHOOD INFERENCE FOR SURVIVAL RATE
REGRESSION WITH MISSING INFORMATION PRINCIPLE
Abstract: Recently, regression model for the long-term survival probabilities of patients
was proposed, and a semiparametric inference procedure was developed based on
missing information principle. In this paper, we propose an alternative empirical
likelihood method. First, we define an estimated empirical likelihood ratio for the
regression parameter. The limiting distribution of the empirical likelihood ratio is
shown to have a weighted sum of i.i.d. ’s. We also define an adjusted empirical
likelihood ratio for the regression parameter and the adjusted empirical likelihood ratio
is shown to have a central chi-squared limiting distribution. Confidence regions
for the vector of regression parameter are obtained accordingly. Furthermore, an
extensive simulation study is conducted and it shows the proposed method has
better coverage probability. Finally, we use a real data set to illustrate our proposed
method.
2000 AMS Mathematics Subject Classification: Primary: 62N02; Secondary:
62G20.
Keywords and phrases: Confidence region, conditional Kaplan–Meier estimator, link
function, right censoring.