# UCL Discovery

## A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials.

Royston, P; Sauerbrei, W; (2004) A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Stat Med , 23 (16) pp. 2509-2525. 10.1002/sim.1815.

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## Abstract

We consider modelling interaction between a categoric covariate T and a continuous covariate Z in a regression model. Here T represents the two treatment arms in a parallel-group clinical trial and Z is a prognostic factor which may influence response to treatment (known as a predictive factor). Generalization to more than two treatments is straightforward. The usual approach to analysis is to categorize Z into groups according to cutpoint(s) and to analyse the interaction in a model with main effects and multiplicative terms. The cutpoint approach raises several well-known and difficult issues for the analyst. We propose an alternative approach based on fractional polynomial (FP) modelling of Z in all patients and at each level of T. Other prognostic variables can also be incorporated by first constructing a multivariable adjustment model which may contain binary covariates and FP transformations of continuous covariates other than Z. The main step involves FP modelling of Z and testing equality of regression coefficients between treatment groups in an interaction model adjusted for other covariates. Extensive experience suggests that a two-term fractional polynomial (FP2) function may describe the effect of a prognostic factor on a survival outcome quite well. In a controlled trial, this FP2 function describes the prognostic effect averaged over the treatment groups. We refit this function in each treatment group to see if there are substantial differences between groups. Allowing different parameter values for the chosen FP2 function is flexible enough to detect such differences. Within the same algorithm we can also deal with the conceptually different cases of a predefined hypothesis of interaction or searching for interactions. We demonstrate the ability of the approach to detect and display treatment/covariate interactions in two examples from controlled trials in cancer.

Type: Article A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. England 10.1002/sim.1815 Age Factors, Aged, Aged, 80 and over, Antineoplastic Agents, Hormonal, Antineoplastic Agents, Phytogenic, Breast Neoplasms, Diethylstilbestrol, Disease-Free Survival, Female, Humans, Male, Middle Aged, Models, Statistical, Multivariate Analysis, Predictive Value of Tests, Prostatic Neoplasms, Randomized Controlled Trials as Topic, Tamoxifen UCL > School of Life and Medical SciencesUCL > School of Life and Medical Sciences > Faculty of Population Health SciencesUCL > School of Life and Medical Sciences > Faculty of Population Health Sciences > MRC Clinical Trials Unit at UCL http://discovery.ucl.ac.uk/id/eprint/43734