The multivariate shared truncated normal frailty model with application to medical data

Abstract

Abstract A new multivariate shared frailty model based on the truncated normal distribution is proposed. For the basal distribution of failure times, we assume a parametric approach through the Weibull and piecewise exponential distributions and also a nonparametric approach. Similar to the traditional gamma frailty model, the Laplace transform, the hazard and survival functions of our proposal have a simple and closed form. In addition, the n-th derivative of the Laplace transform can be expressed recursively. Parameter estimation is performed by a classical approach through the EM algorithm. A simulation study is presented to demonstrate the consistency of the estimators in finite samples. Finally, two applications to medical data modelling the recurrence of infection in renal patients and patients with fibrosarcoma are presented to demonstrate the effectiveness of the model compared to other classical approaches in the literature. The computational implementation of the model is available in the extrafrail package of R.

Keywords

• Frailty models
• Cox model
• Kendall’s $$\tau$$
• Extrafrail package
• EM algorithm
• Kidney Disease