A proportional risk model for time-to-event analysis in randomized controlled trials

Regression models for continuous, binary, nominal, and ordinal outcomes almost completely rely on parametric models, whereas time-to-event outcomes are mainly analyzed by Cox's Proportional Hazards model, an essentially non-parametric method. This is done despite a long list of disadvantages that have been reported for the hazard ratio, and also for the odds ratio, another effect measure sometimes used for time-to-event modelling. In this paper, we propose a parametric proportional risk model for time-to-event outcomes in a two-group situation. Modelling explicitly a risk instead of a hazard or an odds solves the current interpretational and technical problems of the latter two effect measures. The model further allows for computing absolute effect measures like risk differences or numbers needed to treat. As an additional benefit, results from the model can also be communicated on the original time scale, as an accelerated or a prolongated failure time thus facilitating interpretation for a non-technical audience. Parameter estimation by maximum likelihood, while properly accounting for censoring, is straightforward and can be implemented in each statistical package that allows coding and maximizing a univariate likelihood function. We illustrate the model with an example from a randomized controlled trial on efficacy of a new glucose-lowering drug for the treatment of type 2 diabetes mellitus and give the results of a small simulation study.