What considerations guide sample size calculations for a clinical trial with a binary outcome?

• A. Expected event rate in control and treatment groups, desired power, alpha, effect size, and acceptable loss to follow-up
• B. Only the expected event rate matters
• C. Only the effect size matters
• D. Power is fixed and cannot be planned

Answer: (A)

When planning a binary-outcome trial, the sample size you need comes from how likely the outcome is in each group and how precisely you want to test for a difference. You must specify the expected event rates in the control and treatment groups because those proportions determine the variance of the outcome and the size of the difference you’re trying to detect. The bigger the anticipated difference or the more imbalanced the proportions, the smaller the sample needed; smaller differences require more participants.

In addition, you set the desired power (the chance of detecting a true effect) and the alpha level (the chance of a false positive). These choices directly influence how large your trial must be to reliably observe a real difference if one exists. The effect size you aim to detect—whether framed as risk difference, relative risk, or odds ratio—ties the expected rates to the practical impact you want to identify. Finally, accounting for loss to follow-up or noncompliance is essential because any dropouts reduce the number of analyzable subjects, so you inflate the initial sample to maintain the planned power.

So the best answer combines expected event rates in both groups, desired power, alpha, the chosen effect size, and a plan for potential loss to follow-up. The other ideas are incomplete because they omit one or more of these critical components.