Frailty models that yield proportional hazards

Proportional hazards is commonly assumed in survival analysis. This assumption appears to be mainly a mathematical convenience, made in order to interpret Cox models in a simple manner. There remains the questions of whether this assumption is actually true to reality in a sufficient number of cases, and whether the assumption relates to other ways of modelling survival data. We shall look at the latter issue, in pointing out that certain frailty models may yield proportional hazards in a natural way. We consider frailty distributions determined by Levy processes. In our framework, the hazard ratio may be interpreted as the ratio between the squared coefficients of variation of the frailty distributions. (C) 2002 Elsevier Science B.V. All rights reserved.