A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

Abstract

BackgroundAlthough 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.MethodsWe 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.ResultsMethods 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.ConclusionsFor 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.

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“…22 Age was included as a continuous covariate, assuming a linear association with outcome. 23 Missing baseline data for indication for surgery were handled using a missing indicator approach. 24 All-cause mortality within 90 days of surgery was analysed using a mixed-effects parametric survival model with a Weibull survival distribution.…”

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“…Furthermore, linear models require many assumptions including data normality and the absence of multicollinearity, and heteroscedasticity in the data. In addition, linear analysis assumes a constant influence of the independent variable on the outcome [5].…”

“…However, [3]. Reported many pitfalls for this approach such as the loss of information and decrease the power of the model [3][4][5][6][7], while debate over the appropriate cut-off points for normal, overweight and obese further complicate the categorization of BMI.…”

“…Furthermore, linear models require many assumptions including data normality and the absence of multicollinearity, and heteroscedasticity in the data. In addition, linear analysis assumes a constant influence of the independent variable on the outcome [5].Previous research has used quadratic or cubic polynomials (non-linear approach), but the range of curve shapes afforded by low ordered polynomials is restricted [8]. In light of these …”

“…However, [3]. Reported many pitfalls for this approach such as the loss of information and decrease the power of the model [3][4][5][6][7], while debate over the appropriate cut-off points for normal, overweight and obese further complicate the categorization of BMI.A number of studies have used BMI as a continuous variable. However, estimating the association between BMI and a set of covariates using a continuous scale is challenging because the relationship may be nonlinear, and the BMI distribution is often right skewed.…”