Interval estimation of random effects in proportional hazards models with frailties.
Semi-parametric frailty models are widely used to analyze clustered survival data. In this article, we propose the use of the hierarchical likelihood interval for individual frailties. We study the relationship between hierarchical likelihood, empirical Bayesian, and fully Bayesian intervals for frailties. We show that our proposed interval can be interpreted as a frequentist confidence interval and Bayesian credible interval under a uniform prior. We also propose an adjustment of the proposed interval to avoid null intervals. Simulation studies show that the proposed interval preserves the nominal confidence level. The procedure is illustrated using data from a multicenter lung cancer clinical trial.
Department of Asset Management, Daegu Haany University, Gyeongsan, South Korea idha@dhu.ac.kr.
Il Do
ID
Ha
Division of Biostatistics and Bioinformatics, Department of Family and Preventive Medicine, University of California, San Diego, CA, USA.
Florin
F
Vaida
Department of Statistics, Seoul National University, Seoul, South Korea.
Youngjo
Y
Lee
D001499:Bayes Theorem; D002986:Clinical Trials as Topic; D016001:Confidence Intervals; D006801:Humans; D016013:Likelihood Functions; D008175:Lung Neoplasms / Q000188:drug therapy; D015337:Multicenter Studies as Topic; D016016:Proportional Hazards Models
Empirical bayes; Survival analysis; hierarchical likelihood; interval estimator; random effects