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 userselected 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.