Burke K, MacKenzie G
Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
CREST, Ensai, Rennes, France.
Biometrics. 2017 Jun;73(2):678-686. doi: 10.1111/biom.12625. Epub 2016 Nov 28.
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.
协变量通过单个感兴趣的分布参数进入参数模型是标准做法，例如，许多标准生存模型中的尺度参数。事实上，著名的比例风险模型就是这种类型。在本文中，我们讨论一种更通用的方法，即协变量通过多个分布参数同时进入模型（例如，尺度和形状参数）。我们将这种做法称为“多参数回归”（MPR）建模，并探讨其在生存分析背景下的应用。我们发现多参数回归会产生更灵活的模型，能够更深入地洞察潜在的数据生成过程。为了说明这一概念，我们考虑双参数威布尔模型，它会导致随时间变化的风险比，从而放宽了典型的比例风险假设，并激发了一种新的比例性检验。针对此类多参数回归模型引入了一种新颖的变量选择策略。它考虑了两个或多个线性预测变量中估计回归系数之间产生的相关性——这一特征在类似背景下尚未被其他作者考虑。所讨论的方法已在R语言的mpr包中实现。
