Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsIntroductionCategorical data are common in clinical research, arising when outcomes arecategorized into one of two or more mutually exclusive groups. The first step fora categorical data analysis is to produce a frequency table of each outcome,and calculate relevant proportions or percentages of patients with each outcomewithin each treatment group. The second step is to compare these proportionsusing significance tests and confidence intervals (CIs). In this chapter, we describethe methods for such comparisons and illustrate these with examples.Example: myocardial infarction trialLet us assume that a multicenter, randomized, placebo-controlled clinical trial isconducted to determine whether a new drug, compared to placebo, reduces all-causemortality in 4,067 patients following myocardial infarction (MI), who otherwisereceive optimal treatment. The primary endpoint is the occurrence of death fromany cause at 30 days following randomization. This generates a binary variable (diedor survived), which is often summarized as the proportion of patients who have died.The numbers of patients who died or survived at 30 days in each of the twotreatment groups form a 2 × 2 contingency table, as shown in Table 1. This alsoshows the notations representing the number of patients in each group inbrackets. For example, we use the letters a and b to denote the number of patientswho died, c and d to denote the number of patients who survived, and n 1and n 2todenote the number of patients randomized in the active drug and placebo groups,respectively. The total number of patients is n (= n 1+ n 2).Following the above notations, the proportion of deaths in the active drug andplacebo groups are denoted by p 1= a / n 1and p 2= b / n 2, respectively. FromTable 1, we can see that the proportion of deaths was lower in the active drug group(p 1= [110 / 2045] × 100 = 5.38%) than in the placebo group (p 2= [165 / 2022]× 100 = 8.16%). Overall, 6.76% (p = [{a + b} / n] × 100 = [{110 + 165} / {2045+ 2022}] × 100) of MI patients died within the first 30 days after randomization.In this chapter, the proportion and percentage are interchangeably used in thetext, but distinguished in the formulas.Although the observed difference in mortality from the above data is in favor ofthe active drug treatment, we are not certain whether this is a real drug effect orcaused by random error, confounding, or bias (see also Chapters 1, 18, and 19) [1].Assuming the study has no systematic bias or confounding, we can use significancetesting or CI methods to assess whether chance variation could reasonably explain218