Clinical Trials

❘❙❚■ Chapter 19 | Comparison of MeansThe above hypotheses address Question 3 and can be tested using a t-test statistic,as defined in the following equation:where:t =X 1– X 2(7)SE(X 1– X 2)( )SE(X 1– X 2)= [n – 1]S 2 2+ [n1 12– 1]S 2[ 1 + 1 ]n 1+ n 2– 2 n 1n 21/2• X 1, X 2are the sample means of the two treatment groups• S 1, S 2are the sample standard deviations of the two treatment groups• n 1, n 2are the number of patients in each group• SE(X 1– X 2) is the standard error of difference in two sample meansHence, if |t| ≥ t α/2,n1, we can say that there is evidence against the null+n –2 2hypothesis of no treatment difference (H 0: μ 1= μ 2) and state that the treatmentdifference is significant at the α level, where t α/2,n1is the critical t-value+n –2 2of a t-distribution with n 1+ n 2– 2 degrees of freedom. Based on this test,a 100(1 – α)% CI for μ 1– μ 2is given by:(X 1– X 2) ± t α/2,n1 +n 2 –2 × SE(X 1 – X 2 )ExampleWe can again consider the CAL data to illustrate the use of a two-sample t-test.The posttreatment FEV 1concerns two independent samples. Therefore, we canuse the t-test described in equation (7) to test the null hypothesis of no treatmentdifference, as described in (6). Using the summary statistics provided in Table 2,we can calculate the t-value as 2.18. From Table 3, we have t 0.05/2,22= 2.07 and t 0.01/2,22= 2.82. Since t 0.05/2,22< 2.18 < t 0.01/2,22, then 0.05 > P > 0.01, meaning the treatmentdifference between the two posttreatment FEV 1means is significant at the 5%level, but not at the 1% level. The corresponding 95% and 99% CIs for μ 1– μ 2are (19.2, 776.1) (mL) and (–116.7, 912.0) (mL), respectively. Since the 95% CIdoes not contain 0 but the 99% CI does contain 0, we reach the same conclusionas the t-test – ie, the treatment difference in posttreatment FEV 1between the twogroups is statistically significant at the 5% level, but not at the 1% level.For most purposes where the significance level is 5%, the inference here is thatCAL patients on drug A have a better FEV 1value. In some situations, rather thancomparing drug A with placebo, the trial design might compare drug A with a208