In a recent article, Royston (2015, Stata Journal 15: 275-291) introduced the approximate cumulative distribution (acd) transformation of a continuous covariate x as a route toward modeling a sigmoid relationship between x and an outcome variable. In this article, we extend the approach to multivariable modeling by modifying the standard Stata program mfp. The result is a new program, mfpa, that has all the features of mfp plus the ability to fit a new model for user-selected covariates that we call fp1(p1, p2). The fp1(p1, p2) model comprises the best-fitting combination of a dimension-one fractional polynomial (fp1) function of x and an fp1 function of acd (x). We describe a new model-selection algorithm called function-selection procedure with acd transformation, which uses significance testing to attempt to simplify an fp1(p1, p2) model to a submodel, an fp1 or linear model in x or in acd (x). The function-selection procedure with acd transformation is related in concept to the fsp (fp function-selection procedure), which is an integral part of mfp and which is used to simplify a dimension-two (fp2) function. We describe the mfpa command and give univariable and multivariable examples with real data to demonstrate its use.

中文翻译：

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mfpa：使用 ACD 协变量变换扩展 mfp 以增强参数多变量建模。

在最近的一篇文章中，Royston (2015, Stata Journal 15: 275-291) 介绍了连续协变量 x 的近似累积分布 (acd) 变换作为对 x 和结果变量之间的 sigmoid 关系进行建模的途径。在本文中，我们通过修改标准的 Stata 程序 mfp 将方法扩展到多变量建模。结果是一个新程序 mfpa，它具有 mfp 的所有功能以及为用户选择的协变量拟合新模型的能力，我们称之为 fp1(p1,p2)。fp1(p1, p2) 模型包括 x 的一维分数多项式 (fp1) 函数和 acd (x) 的 fp1 函数的最佳拟合组合。我们描述了一种新的模型选择算法，称为带有 acd 变换的函数选择过程，它使用显着性检验来尝试简化 fp1(p1, p2) 模型到子模型、fp1 或 x 或 acd (x) 中的线性模型。带有 acd 变换的函数选择过程在概念上与 fsp（fp 函数选择过程）有关，fsp 是 mfp 的一个组成部分，用于简化二维 (fp2) 函数。我们描述了 mfpa 命令，并给出了带有真实数据的单变量和多变量示例来演示它的使用。