Identifying risk factors of aortic valve replacement using survival frailty models

Authors: Liberato Camilleri, Lawrence Grech, Alexander Manché

Corresponding: Liberato Camilleri (

Keywords: Survival models, Shared and unshared frailty, Gamma and Inverse Gaussian distributions, Aortic valve replacement

Doi: 10.7423/XJENZA.2022.1.03

Traditional survival modeling techniques, including the Kaplan Meier estimator, Cox regression and parametric survival models assume a fairly homogeneous population, where variation in survival durations can be explained by a small number of observed explanatory variables. However, in the presence of heterogeneity, frailty models are more appropriate to model survival data by introducing random effects that account for the variability generated from unobserved covariates. This paper presents two types of frailty models. The unshared frailty model assumes that different individuals have distinct frailties, while the shared frailty model assumes that the population can be divided into clusters, where members in the same cluster share the same frailty. Due to their nice mathematical properties, the Gamma and the Inverse Gaussian distributions are the most popular choices for the frailty distribution.

These survival models are fitted to a data set using the facilities of STATA. The participants are patients who underwent an aortic valve replacement procedure at a Maltese hospital between 2003 and 2019. The dependent variable is the duration till death or till censored and the eleven predictors provide information about the patients’ health condition; surgery operative procedures; and duration of convalesce period. Moreover, in shared frailty models the patients are clustered by their diabetic condition since it is known that diabetic patients are more at risk of dying following aortic surgery.

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