Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsComparing proportions between two groupsThe primary objective of the MI trial is to directly compare the proportion of MIpatients who died on the active drug with that of patients on placebo, within thetime period of the trial follow-up (30 days). The efficacy of the active drug, againstthe control, can be examined by testing the null hypothesis that the proportions ofdeaths in both populations are equal:H 0: π 1= π 2vs (3)H a: π 1≠π 2This section will describe three methods for testing the above hypotheses: thechi-squared (χ 2 ) test, Fisher’s exact test, and the Z-test [2,3].Chi-squared (χ 2 ) testThe most common approach for comparing two proportions is the chi-squaredtest. The chi-squared test involves comparing the observed numbers in each of thefour categories in the contingency table with the numbers expected if there was nodifference in proportions between the active drug and placebo groups.Overall, 275 / 4067 (6.76%) patients died during the trial. If the active drug andplacebo were equally effective, one would expect the same proportion of deaths ineach of the two groups: that is, 275 / 4067 × 2045 = 138.3 in the drug group and275 / 4067 × 2022 = 136.7 in the placebo group. Similarly, 3792 / 4067 × 2045 =1906.7 patients in the active drug group and 3792 / 4067 × 2022 = 1885.3 patientsin the placebo group would be expected to survive to 30 days after randomization.The expected numbers are shown in Table 3. They add up to the same row andcolumn totals as the observed numbers. The chi-squared value used to assess thedifference in the proportions under the null hypothesis (3) can be expressed as:where:(O –χ 2 E)2= ΣE(4)• O represents the observed numbers in each cell of the 2 × 2 table• E represents the expected numbers in each cell of the 2 × 2 tableas shown in Table 3.222