Clinical Trials

❘❙❚■ Chapter 20 | Comparison of ProportionsWe can perform a Z-test to test this hypothesis. Under the null hypothesis,a Z-statistic approximation can be generated as follows:Z =SE(p 1) =p 1– π 0SE(p 1)p 1(1 – p 1)n 1(2)where SE(p 1) stands for the standard error of p 1.At a prespecified level of significance α, we have evidence against the nullhypothesis in equation (1) and conclude that the proportion of MI patients whodied in the test drug group is statistically significantly different from 8% if:|Z| ≥ Z α/2where Z α/2is the critical value from the standard normal distribution.The exact P-value in the Z-test is the probability that Z ≤ – Z α/2or Z ≥ Z α/2.This can be determined by calculating the area under the curve in two-sidedsymmetric tails from a standard normal distribution table.Using the data in Table 1:p 1= 5.38%SE(p 1) =5.38 / 100 × (1 –5.38 / 100) = 0.005 or 0.50%2045Z = 5.38% – 8% = –5.240.50%As a result, since the absolute value of observed Z is >Z 0.05/2= 1.96, the P-value is