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❘❙❚■ Chapter 25 | Adjustment for CovariatesTable 3. Comparison of unadjusted and adjusted hazard ratios of death from the Cox proportional hazardsmodel (primary biliary cirrhosis trial).Covariate Hazard ratio P-value 95% CIUnadjusted analysisTreatment (A vs P) 0.86 0.455 0.57, 1.28Adjusted analysisTreatment (A vs P) 0.65 0.044 0.43, 0.99Log bilirubin 2.80
<strong>Clinical</strong> <strong>Trials</strong>: A Practical Guide ■❚❙❘data in the PBC trial, and particularly holds true in analysis of covariance(ANCOVA) models, where a continuous outcome is regressed on treatment groupindicator and some continuous explanatory variables (covariates) [5].A sensitivity analysis shows that, unless a baseline covariate is uncorrelated withthe outcome, the unadjusted analysis might not yield the correct P-values underthe null hypothesis of no treatment effect [5]. Therefore, adjustment for a baselinecovariate is recommended if the covariate is correlated to the outcome (eg, acorrelation coefficient >0.50 as suggested by Pocock et al) [5]. Interestingly,if the baseline covariate is strongly correlated with the outcome, there is still anadvantage in adjusting for a baseline covariate even if this is perfectly balancedacross the treatment arms [5].A second reason for adjusting for prognostic covariates is the increase in precisionof the estimated treatment effect [4,5]. This, however, only applies to linearregression models. Thus, from a study design perspective, there could beconsiderable gains (in terms of increased power and reduction in the sample sizerequired) from collecting data on highly prognostic variables at baseline and thenincluding them in any analysis. In particular, one could take baselinemeasurements of the outcome of interest, as these are likely to be stronglycorrelated with the values of the outcome at the endpoint.Slightly different considerations apply to non-normal outcomes modeled using,for example, logistic or Cox regression models. In particular, adjustment fora baseline prognostic variable will not increase precision; rather, in general,an increase in standard errors will be observed [6,7]. However, in the PCB trial,the standard error for the treatment effect was reduced after adjusting forlog bilirubin. A summary of the advantages and disadvantages of an adjustedanalysis is displayed in Table 4.What are the main methods of covariate adjustment analysis?If imbalances are found for some baseline characteristics that are predictors ofoutcome variables, then covariate adjustment analysis can be performed toestimate adjusted treatment effects. As mentioned earlier, for highly prognosticcovariates, the adjusted analysis might be preferable even in the absence ofimbalance, especially for a continuous outcome. Adjustment is often performedthrough the application of multivariate regression methods, by including therelevant baseline variables as extra predictors.291
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❘❙❚■ ContributorsStephen L
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Clinical Trials: A Practical Guide
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■■❚❙❘Chapter 1RandomizedC
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■■❚❙❘Part IIIBasics ofSta
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■■❚❙❘Chapter 19Comparison
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■■❚❙❘Chapter 20Comparison
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■■❚❙❘Chapter 33Trial Prof
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■■❚❙❘GlossaryGlossary453
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■■❚❙❘IndexIndex467
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