title: Interaction of treatment with a continuous variable: simulation study of power for several methods of analysis.
abstract: In a large simulation study reported in a companion paper, we investigated the significance levels of 21 methods for investigating interactions between binary treatment and a continuous covariate in a randomised controlled trial. Several of the methods were shown to have inflated type 1 errors. In the present paper, we report the second part of the simulation study in which we investigated the power of the interaction procedures for two sample sizes and with two distributions of the covariate (well and badly behaved). We studied several methods involving categorisation and others in which the covariate was kept continuous, including fractional polynomials and splines. We believe that the results provide sufficient evidence to recommend the multivariable fractional polynomial interaction procedure as a suitable approach to investigate interactions of treatment with a continuous variable. If subject-matter knowledge gives good arguments for a non-monotone treatment effect function, we propose to use a second-degree fractional polynomial approach, but otherwise a first-degree fractional polynomial (FP1) function with added flexibility (FLEX3) is the method of choice. The FP1 class includes the linear function, and the selected functions are simple, understandable, and transferable. Furthermore, software is available. We caution that investigation of interactions in one dataset can only be interpreted in a hypothesis-generating sense and needs validation in new data.
authors.affiliation: MRC Clinical Trials Unit, University College London, London, WC2B 6NH, U.K.
authors.forename: Patrick
authors.initials: P
authors.lastname: Royston
authors.forename: Willi
authors.initials: W
authors.lastname: Sauerbrei
mesh_terms: D000328:Adult; D000368:Aged; D000465:Algorithms; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D015987:Effect Modifier, Epidemiologic; D005910:Glioma / Q000188:drug therapy / Q000401:mortality; D006801:Humans; D017567:Karnofsky Performance Status; D008875:Middle Aged; D015233:Models, Statistical; D011379:Prognosis; D016032:Randomized Controlled Trials as Topic; D012044:Regression Analysis; D018401:Sample Size; D016019:Survival Analysis
keywords: categorisation; continuous covariate; fractional polynomials; interaction; randomised controlled trials