Frailty models for pneumonia to death with a left-censored covariate.
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.
Department of Epidemiology & Biostatistics, Case Western Reserve University, Cleveland, OH, U.S.A.
Abdus
A
Sattar
School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada.
Sanjoy K
SK
Sinha
Department of Quantitative Health Sciences, Cleveland Clinic Foundation, Cleveland, OH, U.S.A.
Xiao-Feng
XF
Wang
Department of Statistics, Iowa State University, Ames, IA, U.S.A.
Yehua
Y
Li
D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D015982:Bias; D017714:Community-Acquired Infections; D003198:Computer Simulation; D005260:Female; D005819:Genetic Markers; D006801:Humans; D016753:Interleukin-10 / Q000097:blood*; D057230:Limit of Detection; D008297:Male; D008875:Middle Aged; D011014:Pneumonia / Q000150:complications / Q000175:diagnosis / Q000401:mortality*; D011379:Prognosis; D016016:Proportional Hazards Models; D018805:Sepsis / Q000175:diagnosis* / Q000209:etiology* / Q000401:mortality; D018709:Statistics, Nonparametric; D016019:Survival Analysis; D055815:Young Adult
D005819:Genetic Markers; D016753:Interleukin-10
censored covariate; frailty models; likelihood method; limit of detection; nonparametric smoothing