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Frailty models for pneumonia to death with a left‐censored covariate
Author(s) -
Sattar Abdus,
Sinha Sanjoy K.,
Wang XiaoFeng,
Li Yehua
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6466
Subject(s) - covariate , estimator , statistics , mathematics , inference , nonparametric statistics , proportional hazards model , multiplicative function , hazard ratio , confidence interval , mean squared error , computer science , econometrics , artificial intelligence , mathematical analysis
Frailty models are multiplicative hazard models for studying association between survival time and important clinical covariates. When some values of a clinical covariate are unobserved but known to be below a threshold called the limit of detection (LOD), naive approaches ignoring this problem, such as replacing the undetected value by the LOD or half of the LOD, often produce biased parameter estimate with larger mean squared error of the estimate. To address the LOD problem in a frailty model, we propose a flexible smooth nonparametric density estimator along with Simpson's numerical integration technique. This is an extension of an existing method in the likelihood framework for the estimation and inference of the model parameters. The proposed new method shows the estimators are asymptotically unbiased and gives smaller mean squared error of the estimates. Compared with the existing method, the proposed new method does not require distributional assumptions for the underlying covariates. Simulation studies were conducted to evaluate the performance of the new method in realistic scenarios. We illustrate the use of the proposed method with a data set from Genetic and Inflammatory Markers of Sepsis study in which interlekuin‐10 was subject to LOD. Copyright © 2015 John Wiley & Sons, Ltd.