Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 2. Summary statistics for one-sample statistical inference by treatment for the myocardial infarction trial.StatisticsActive drugTreatmentPlaceboNull hypothesis (π 0= 8.00%) H 0: π 1= π 0H 0: π 2= π 0Proportion of death (number of patients) 5.38% (2045) 8.16% (2022)Standard error 0.50% 0.61%Z-statistic –5.25 0.26P-value P < 0.001 P = 0.79295% CI (4.40%, 6.36%) (6.97%, 9.35%)that the population proportion of MI patients who died (π 2) in the placebo groupis statistically significantly different from 8% (π 0) at the 5% significance level.The detailed summary results for one-sample inference based on the Table 1 dataare presented in Table 2 for the active treatment and placebo groups, respectively.The statistical inference for one sample can also be made by calculating a CI.Based on equation (2), a 100 (1 – α) % CI for the population proportion in theactive treatment group (π 1) can be obtained as:p 1± Z α/2SE(p 1)Thus the 95% CI is:5.38% ± 1.96 × 0.50% = 4.40% to 6.36%Based on the 95% CIs, we can reach the same conclusion as the Z-test. The 95%CI (4.40%, 6.36%) does not contain 8% in the active drug group, and we thereforeconclude that it is significantly lower than 8%. For the placebo group, the 95% CIincludes 8% (6.97%, 9.35%), so we therefore conclude that the proportion of MIpatients who died is not significantly different from 8%, as revealed in the Z-test.In this example, death has been used as the outcome. However, the significancetesting and CI used in this example can apply to any binary outcome, such aswhether or not a patient shows improvement after treatment, whether or notthere is recurrence of disease, whether or not the patient has an admission tohospital, and so on.221