Clinical Trials

❘❙❚■ Chapter 19 | Comparison of MeansTable 3 displays some selected critical values for t-distributions with differentdegrees of freedom. This table contains the significance levels for one- andtwo-tailed (sided) t-tests (a tail is either end of a t-distribution curve) (seereferences [3] and [4] for more about one- and two-sided tests). For the alternativehypothesis currently under examination, we use a two-sided test because the truepopulation mean could be larger or smaller than the hypothesized mean FEV 1.The corresponding 100(1 – α)% CI for a population mean (μ) can be calculatedfrom the following equation:X ± t α/2,n–1× SE(X) (3)ExampleThe t-test can be illustrated using the CAL trial data. Suppose, from the literature,the mean FEV 1for patients with CAL is 2000 mL (= μ 0). Hence, it might be ofclinical interest to know whether the mean FEV 1for the CAL patient populationtreated with test drug A is different from 2000 mL.From Table 2, we have X = 2482.8, S = 437.2, and n = 12 for FEV 1posttreatment. Placing those values in equation (2), we have:atSE(X) = 437.2 / √12 = 126.2t = 2482 – 2000 = 3.83126.2From Table 3, we can see that the critical t-values corresponding to 11 degrees offreedom are t 0.01/2,11= 3.11 and t 0.001/2,11= 4.44 for α = 0.01 and 0.001, respectively.Since t 0.01/2,11< 3.83 < t 0.001/2,11, then 0.001 < P-value < 0.01. Therefore, we concludethat the data provide evidence that the population mean for FEV 1after activetreatment A is (statistically) significantly different from 2000 mL at the 5%significance level. The corresponding 95% CI, as calculated from equation (3),is (2205.1, 2760.6), suggesting that we estimate that the true posttreatment FEV 1mean for patients in group A is 95% likely to fall between 2205.1 and 2760.6 mL.Similarly, we can perform t-tests (H 0: μ = 2000) for FEV 1and estimate the 95%CIs for the population mean of FEV 1for patients in group A at baseline, and forpatients in group B at baseline and posttreatment. These corresponding resultsare presented in Table 4. The results show that there is insufficient evidence tosuggest that population means for the three outcomes are significantly differentfrom 2000 mL.202