Specificity, sensitivity, and prevalence in the design of randomized trials: a univariate analysis

The number of cases needed to conduct a randomized trial is related to the sensitivity and specificity of a measurement indicative of a condition, to the prevalence of the condition, to the expected benefit of therapy (or other basis for change), and to the statistical precision desired. Sample size calculations frequently ignore sensitivity and specificity (at least qualitatively) probably because no simple formula is provided in the literature. Such a formula is included here. As an example, the number of patients required for a randomized clinical trial was calculated for a clinical outcome (nonfatal myocardial infarction or coronary artery disease death) used to detect atherosclerotic heart disease and is compared to the sample sizes required for each of three noninvasive diagnostic studies (exercise ECG ST depression, exercise LVEF reduction, and thallium myocardial imaging) performed for the detection of atherosclerotic heart disease. We calculated that the sample size should be much smaller when these diagnostic studies are employed compared to the clinical outcome, thereby offering the potential for reduced cost and complexity of a randomized clinical trial.