title: A comparison of methods to adjust for continuous covariates in the analysis of randomised trials.
abstract: BACKGROUND
  Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy.
  
  
  METHODS
  We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets.
  
  
  RESULTS
  Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall.
  
  
  CONCLUSIONS
  For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt.
authors.affiliation: Pragmatic Clinical Trials Unit, Queen Mary University of London, London, UK. b.kahan@qmul.ac.uk.
authors.forename: Brennan C
authors.initials: BC
authors.lastname: Kahan
authors.affiliation: University of Manchester, Manchester, UK.
authors.forename: Helen
authors.initials: H
authors.lastname: Rushton
authors.affiliation: MRC Clinical Trials Unit at UCL, London School of Hygiene and Tropical Medicine, London, UK.|Medical Statistics Department, London School of Hygiene and Tropical Medicine, London, UK.
authors.forename: Tim P
authors.initials: TP
authors.lastname: Morris
authors.affiliation: Medical Statistics Department, London School of Hygiene and Tropical Medicine, London, UK.
authors.forename: Rhian M
authors.initials: RM
authors.lastname: Daniel
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004054:Diethylstilbestrol / Q000008:administration & dosage*; D018572:Disease-Free Survival; D006801:Humans; D016014:Linear Models; D008297:Male; D015233:Models, Statistical; D009361:Neoplasm Invasiveness / Q000473:pathology; D009367:Neoplasm Staging; D016016:Proportional Hazards Models; D011471:Prostatic Neoplasms / Q000188:drug therapy* / Q000401:mortality* / Q000473:pathology; D016032:Randomized Controlled Trials as Topic; D016019:Survival Analysis; D016896:Treatment Outcome
chemical_list: D004054:Diethylstilbestrol
keywords: Continuous variables; Covariate adjustment; Fractional polynomials; Randomised controlled trial; Restricted cubic splines