Ramesh C. Gupta

Random effect models have been widely used in the context of linear models. Besides this, the random effect models have been used in survival analysis and other disciplines.

In this presentation, we shall consider random effect models in the context of survival analysis or, more specifically, in the context of frailty models where the frailty is modeled as an unobservable random effect. A general bivariate frailty model is developed. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. The results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

**Keywords:** Frailty model; Hazard gradient; Bivariate multiplicative model; shared frailty model

**Biography:** Professor Ramesh Gupta has been a faculty member at the University of Maine for over 38 years. His research interests include discrete and continuous distributions, reliability and life testing and survival analysis.