title: Multi-parameter regression survival modeling: An alternative to proportional hazards.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
authors.forename: K
authors.initials: K
authors.lastname: Burke
authors.affiliation: CREST, Ensai, Rennes, France.
authors.forename: G
authors.initials: G
authors.lastname: MacKenzie
mesh_terms: D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D016019:Survival Analysis
keywords: Converging hazards; Crossing hazards; Diverging hazards; Multi-parameter regression; Non-proportional hazards; Survival analysis; Time-dependent effects; Variable selection