mfpa: Extension of mfp using the ACD covariate transformation for enhanced parametric multivariable modeling.

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.