Multi-parameter regression survival modeling: An alternative to proportional hazards

It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known proportional hazards model is of this kind. In this article, we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously (e.g., scale and shape parameters). We refer to this practice as “multi-parameter regression” (MPR) modeling and explore its use in a survival analysis context. We find that multi-parameter regression leads to more flexible models which can offer greater insight into the underlying data generating process. To illustrate the concept, we consider the two-parameter Weibull model which leads to time-dependent hazard ratios, thus relaxing the typical proportional hazards assumption and motivating a new test of proportionality. A novel variable selection strategy is introduced for such multi-parameter regression models. It accounts for the correlation arising between the estimated regression coefficients in two or more linear predictors—a feature which has not been considered by other authors in similar settings. The methods discussed have been implemented in the mpr package in R.