Abstract
In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model. Potentials for inference about the parameters in proportional vitalities model with possibly time-varying effects are also argued and discussed.
Highlights
The Cox proportional hazards (CPH) model proposed by Cox [1]
In the CPH model, the unique effect of a subject increase in a covariate is multiplicative with respect to the hazard rate
To present the state of scientific development in the context of recent survival models, we consider the works accomplished in the context of the proportional mean residual life (PMRL) model and the additive mean residual life (AMRL) model that are closely related to the proportional vitalities (PVIT) model
Summary
The proportional mean residual life (PMRL) model has been proposed by Oakes and Dasu [2] to model lifetime events. While the former model is more applicable and attractive in the sense of doing computations and calculating likelihood functions based on the available sample data, the latter model gives a survival function that is appeared to be more complicated. Zahedi [16] highlighted the role of this model to be played by a regression model This way, the effect of data in changing the behavior of a baseline mrl function appears in terms of some regression coefficients.
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