Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘However, the graphical method to assess proportionality is still a subjectiveapproach and does not provide a statistical test for assessing the proportionalassumption for a group of covariates. The proportionality can be formally assessedusing a chi-squared test with the two hazard functions proportional in the nullhypothesis, ie:H 0: h 1 (t) = γh 2(t)where γ is a constant [1,2].If nonproportionality is found in an analysis, the proportional hazards model (1)is no longer suitable and more complex modeling may be necessary, for exampleby incorporating some sort of interaction between treatment and time into themodel [1,2].Interpretation of regression resultsTable 5 displays the extracted results from the Cox proportional model analysis ofprimary endpoint in the CHARM (Candesartan in Heart failure Assessment ofReduction in Morbidity and mortality) trial [6]. In this trial, the primary endpointwas the time to first occurrence of cardiovascular death or hospitalization dueto chronic heart failure (CHF). Table 5 gives the coefficient estimate (b k) andassociated statistics. The column labeled hazard ratio is e b k.For a binary (dummy) variable with values of 1 and 0, the hazard ratio can beinterpreted as the ratio of the estimated hazard for those with a value of 1 to theestimated hazard for those with a value of 0 (controlling for other covariates).For example, the estimated hazard ratio for the variable ‘female’ is 0.83. Thismeans that the hazard of having a cardiovascular death or CHF hospitalizationfor females is estimated to be 83% (95% confidence interval [CI] 76%, 91%)of the hazard for males (controlling for other covariates).For a quantitative covariate, a more helpful statistic is obtained by subtracting 1from the hazard ratio and multiplying by 100. This gives the estimated percentchange in the hazard for each 1-unit increase in the covariate. For the variable‘age’ in Table 5, the hazard ratio is 1.04, yielding (1.04 – 1) × 100 = 4. Therefore,for each 1-year increase in the age of the patient at randomization, the hazard ofhaving a primary endpoint goes up by an estimated 4% (95% CI 3%, 5%).For a categorical covariate, the hazard ratio can be interpreted as the ratioof hazard for those in a group compared with that of the reference group.For example, the covariate ‘diabetes’ has three categories:247