Introduction to shared frailty Cox models with parametric and non-parametric distributions and their application in medical data

In survival data, it is typical for survival times to be clustered or depend on some unobserved covariates. This can be due to geographical clustering, subjects sharing common genes, specific socioeconomic level, or hereditary and racial characteristics, and other predisposition that cannot be measured and observed directly. Adjusting the effects of these unknown factors on the survival functions is necessary for the independence of survival times and the explanatory variables. The aim of this study is to introduce and compare Cox models with parametric and non-parametric shared frailty on brain stroke survival data. The results showed that non-parametric frailty model has better fitting than parametric distributions (AIC=4686 and BIC=4684), especially when the exact parametric distribution is not known. According to the results of best model, following variables were statistical significant; BMI (HR=0.97, P=0.045); Age (HR=1.04, P<0.001); HDL (HR=1.01, P<0.001); LDL (HR=0.99, P<0.001); Hyperlipidemia (HR=0.72, P<0.014). The nonparametric frailty is desirable, due to potential misspecification of the parametric form and as a method for detecting clusters of groups with similar frailties.