Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Figure 1. Calculating the sample size. The following formula can be used to calculate the sample sizethat is required in each arm of the example randomized controlled trial.n =[ z (α / 2) √2π (1 – π) + z (β) √π 1(1 – π 1) + π 2(1 – π 2) ] 2δ 2α = the Type I error rateβ = the Type II error rateπ 1= the expected event rate in the control groupπ 2= the expected event rate in the treatment groupπ = (π 1+ π 2) / 2δ = π 1– π 2z (α / 2) = constant from the standard normal distribution depending on the value of αz (β) = constant from the normal distribution depending on the value of βFor this example:α = 5% = 0.05β = 20% = 0.20π 1= 12% = 0.12π 2= 10% = 0.10π = (π 1+ π 2) / 2 = (12% +10%) / 2 = 11% = 0.11δ = π 1– π 2= 12% – 10% = 2% = 0.02z (α / 2) = 1.96z (β) = 0.842n =[ 1.96 √2 x 0.11 (1 – 0.11) + 0.842 √0.12 (1 – 0.12) + 0.10 (1 – 0.10) ] 20.02 2 = 3,842Therefore for our RCT, a sample size of 3,842 subjects is required for each group.Taking subject dropout into accountDuring any clinical study, subjects might leave the study due to a variety ofreasons, such as loss to follow-up, noncompliance with treatment, or moving awaygeographically. The sample size should therefore be increased to allow for this.If our RCT has a likely dropout rate of 20% (a ratio of 0.20) within the first yearof the trial, the sample size per group should be adjusted accordingly, ie,3,842 / (1 – 0.20) = 4,803. Our RCT therefore requires a total of 9,606 subjects, or4,803 subjects in each treatment group.Are negative trials due to small sample sizes?A negative clinical trial is a trial in which the observed differences between thenew and standard treatments are not large enough to satisfy a specifiedsignificance level (Type I error threshold), so the results are declared to be notstatistically significant [2]. With the benefit of hindsight, analyses of negativeclinical trials have shown that the assumptions chosen by investigators often lead85