A clinical research organization is finalizing the methodology for a randomized, placebo-controlled trial evaluating a novel pharmacologic agent for generalized anxiety disorder. The investigators stipulate that they are willing to accept a 5% risk of concluding the agent is effective when it is truly no different from placebo. Furthermore, formal sample size calculations reveal a 0.14 probability of concluding that the drug has no effect when it actually provides a clinically meaningful benefit to patients.
Based on these parameters, what is the planned statistical power of this trial, expressed as a percentage?
Answer: 86 %
Answer
The planned statistical power of the trial is 86%.
Statistical power is defined mathematically as , where is the probability of committing a Type II error (failing to detect a true difference). In this scenario, the probability of concluding there is no effect when the drug actually provides a benefit is given as 0.14. Therefore, the statistical power is , which equates to 86%. The 5% risk mentioned in the stem represents the Type I error rate (), which is used to set the significance threshold but is not directly subtracted to calculate power.
Step-by-Step Solution
Key Concept
Statistical power is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true, calculated as (where is the Type II error rate).
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