The Cox regression model with a shared frailty for clustered data and its application in medical data

Abstract

چکیده انگلیسی Background: nowadays, survival analysis is widely used in various sciences, especially medicine, and its purpose is to measure the time to event or censorship in the survival data. Semi-parametric Cox regression or parametric survival regression is used to model the risk factors of patients’ survival. There are some unknown and unobserved effecting factors on patients’ survival time that not been measured for a variety of reasons. Frailty models account for the effect of these unobserved factors. The frailty component can be considered a multiplicative effect in survival models. Objectives: This study aimed to Introduction and to evaluate Cox models with parametric and non-parametric shared frailty and comparison to parametric survival models with shared frailty with their application in brain stroke survival. Material and methods: In this study, 1036 Patients with first-ever stroke, were recruited with convenience sampling in Emam Reza and Razi hospitals of Tabriz city. The follow-up period was two years. Cox model with shared frailty and parametric survival models were used for the analysis of data. The shared frailty models were used to study the quality of health care providers (in the format of the hospital) and the effect of demographic and clinical factors such as the history of hypertension, diabetes, heart disease, etc. on the survival of patients. Frailty models modify the effect of unknown factors in the survival models, express within-cluster dependence through a shared unobservable random effect, two hospitals were considered two different clusters, It was assumed that the patients who admitted to each hospital received the same services. To compare the survival models and choose the best model, the goodness of fit criterion (such as AIC and BIC) were used. Statistical analysis was done by Stata version 16 (College Station, TX: Stata Corp LLC; 2019) and R-3.4. Software. Result: According to the AIC and BIC goodness of fit criterion, the log-logistic distribution with gamma frailty had the best fit for our data (AIC=2647.34 BIC=2519.46). Among the semiparametric Cox models, the model with a nonparametric frailty term will fit well (AIC=4488.29, BIC=4488.00). According to the results of best model: significant variables were: NIHSS Score (TR=0.03; CI=0.01-0.07), age (TR=0.95; Cl=0.93-0.98), type-stroke (TR=0.42; Cl=0.23-0.75). Conclusions: sometimes, the frailty models are appropriate and significant in the multicenter studies. These models is caused high accuracy in the estimate of the survival time and effects of other demographic and clinical variables. Keywords: Brain stroke, health care provider, multicenter studies, non-parametric approach, parametric survival models, semi-parametric Cox model, survival analysis, sh ared frailty