Clinical Trials

❘❙❚■ Chapter 25 | Adjustment for CovariatesWhat are adjusted and unadjusted analyses?To assess the treatment effect in randomized clinical trials, one may or may nottake into account the baseline characteristics of the subjects (or covariates). It isthis inclusion or exclusion of covariates in the analysis that distinguishes adjustedanalyses from unadjusted analyses.In the case of a clinical trial with a carefully conducted randomization, theunadjusted analysis will give an unbiased estimate of the effect of a treatment onan outcome of interest. However, there are situations where adjustment forbaseline covariates will lead to improved estimates in terms of reduced bias andincreased statistical efficiency [1].Example: primary biliary cirrhosis trialWe can illustrate unadjusted and adjusted analyses using the following trial.Primary biliary cirrhosis (PBC) is a chronic but eventually fatal liver disease.A randomized double-blind clinical trial was designed to assess whether the useof azathioprine could increase the survival of patients compared to placebo [2,3].A total of 248 patients were entered into the trial and followed for up to 12 years.The primary endpoint was the time to death from randomization. Clinical andhistological information was recorded at entry to the trial.We will use a subset of the PBC database, containing information on 191 patientswho had entry values for all prognostic variables. Of particular interest to theinvestigators was the biochemical marker bilirubin. Some summary statistics ofbilirubin by treatment group are presented in Table 1, and the overall trial resultsregarding the primary endpoint are summarized in Table 2.Table 1 shows a baseline imbalance across the two treatment arms for bilirubin interms of their average values and spread. Mean and median baseline bilirubin inthe placebo group is 53.75 and 30.90 μmol/L, respectively, much lower than the67.40 and 38.02 μmol/L for patients in the azathioprine group. The range was431.39 μmol/L for the placebo group compared with 529.79 μmol/L for theazathioprine group. Bilirubin is known to be a strong predictor of survival timeand it is expected that this imbalance will have some impact on the observedtreatment effect on the primary endpoint. Due to the higher bilirubin levels in theactive treatment group at baseline, a higher mortality rate may be expected in thisgroup regardless of any treatment effect. In other words, the baseline bilirubinlevel could be a confounding factor in this study (see Chapter 26). We can assess288