Clinical Trials

❘❙❚■ Chapter 9 | Sample Size and PowerChoosing the power of a trial (Type II error)Consider the reverse situation to the above, that is, in the study on the wholepopulation the new treatment produces a 2% absolute reduction in the mortalityrate and in our RCT we did not find a statistically significant difference. We wouldcall this a false-negative result, or a Type II error. Conventionally, the Type IIerror rate is set at 20%, and this is represented by the constant β. The power ofa study (the ability to find a significant difference if it exists) is 100% – β, which inthis case is 100% – 20% = 80%.The higher we choose to set the power, the more subjects we will need in thestudy. Using a power of 80% (in this case to capture a 2% minimum benefitas significant), there is a one in five chance of failing to detect the difference.This might appear high, but the chance of missing larger effects is smaller.It should be noted that the error rate for a Type I error is set lower than that fora Type II error since in medicine we conventionally have a higher threshold forswitching to a new treatment than for keeping the traditional treatment.Study designThe calculation of the sample size is dependent on the design of the study.A standard parallel arm RCT, with the standard treatment group acting as thecontrol, will require more subjects than a ‘before and after treatment’ type ofstudy in which the subjects act as their own controls. Even with a standard RCT,as in our example, we might choose to have two subjects on the new treatment forevery subject on the standard treatment in order to give us more safetyinformation and experience with the new treatment. If the ratio is higher than 1:1,more subjects will be required. A further component of trial design is whether theoutcome is a categorical event such as death, a continuous variable such ascholesterol level, or the time to the first event, as in a survival analysis. Thefeatures of these outcomes will dramatically influence the sample size. In ourexample, the event of interest is survival (or mortality) at 12 months, a relativelysimple, clear, and meaningful endpoint.To calculate the sample size we can apply the equation shown in Figure 1. In our RCTwe can see that a sample size of 3,842 subjects is required. For any combination ofthe four basic elements (α, β, π 1and δ) there is a corresponding number of patientsper group. Figure 2 shows how the number of patients per treatment group varieswith respect to π 1and δ while α and β remain at 5% and 20%, respectively.The most important observation made from this figure is that the number of patientsrequired per treatment group decreases as the smallest treatment effect to be detectedincreases. For example, for π 1= 50%, as δ changes from 10% through 20%, 30%,and 40%, the sample size decreases from roughly 500 through 100, 50, and 25.84