Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 1. Practical procedures for hypothesis testing.Step Procedure Illustration with SBP data1 Set up a null hypothesis and H 0: μ = μ 0(= 129), ie, population mean SBP is equal to 129 mm Hgalternative hypothesis that isH a: μ ≠ μ 0, ie, population mean SBP is different from 129 mm Hgof particular interest to study2 Choose a statistical method accordingto data type and distribution, andX – μZ = 0S / √n= 2.24calculate its test statistic fromX = 130 mm Hgthe data collectedS = 10 mm Hgn = 5003 Define a significance level α and α = 0.05 and Z α/2= 1.96its corresponding critical value α = 0.01 and Z α/2= 2.584 Determine the P-value by comparing Since Z = 2.24 > 1.96, P < 0.05the test statistic and the critical value, Since Z = 2.24 < 2.58, P > 0.01or calculate the exact P-value Exact P-value = 0.0255 Make your conclusion according As 0.01 < P < 0.05, there is evidence to reject the null hypothesisto the P-valueof no difference at the 5% level of significance, but there is noevidence to reject the null hypothesis at the 1% level. The P-valueof 0.025 means that the probability of falsely rejecting the nullhypothesis is 1 in 40 if the null hypothesis is trueSBP = systolic blood pressure.probability of committing a Type I error is known as the significance level [1–4].As in Step 3 above, the level of significance is denoted by α. In practice,α represents the consumer’s risk [5], which is often chosen to be 5% (1 in 20).On the other hand, if the null hypothesis is not rejected when it is actually false,then a Type II error (or false-negative result) occurs [1–4]. For example, a Type IIerror is made if the trial result suggests that there is no difference between drug Aand placebo in lowering the cholesterol level when in fact drug A does reduce thetotal cholesterol. The probability of committing a Type II error, denoted by β,is sometimes referred to as the manufacturer’s risk [5]. The power of the test isgiven by 1 – β, representing the probability of correctly rejecting the null hypothesiswhen it is in fact false. It relates to detecting a prespecified difference (seeChapter 8 for more). Type I and II errors are summarized in Table 2.Confidence intervalsThe second strategy for making statistical inference is through the use of CIs.In making inference about a population, we might want to know the likely valueof the unknown population mean (μ). This is estimated from the sample mean(X), and we call X a point estimate of μ.191