Multilevel survival models to investigate survival durations of patients requiring aortic valve replacement

Abstract

Traditional survival models are based on the assumption that the population under investigation is fairly homogenous and that a few observed covariates can explain the data very well. However, in real survival data sets there is often considerably unobserved heterogeneity which cannot be simply explained by a few covariates. Survival data having a multilevel structure is often encountered across a range of disciplines, including epidemiology, public health, education, electronics, sociology and engineering. Such data can be used to estimate the survival duration of electronic devices in several environmental conditions, assess the safety of medical devices and therapies on patients with different frailties, estimate the life expectancy of humans in different regions, and evaluate the profitability of financial schemes in different economic conditions, amongst other applications.

This paper presents the theoretical framework of multilevel mixed effects survival models to address the frailty (unobserved heterogeneity) that may exist in the data. It is common to assume a proportional hazards structure that is conditional on frailty, which is basically a proportional hazards model with mixed effects. These models will be used to analyze the survival durations of patients following aortic valve replacement surgery and will incorporate both fixed and random group-level effects. To accommodate the nesting structure of the model, the patients (level-1 units) will be nested by their diabetes condition (level-2 units). Using the facilities of STATA, these models will be fitted using both the frequentist and Bayesian approaches by assuming an Exponential or a Weibull survival distribution. For the Bayesian approach, normal priors and inverse-gamma hyperpriors will be assumed.