Question

The number of patients required in a clinical trial to treat a specified disease increases as:

• A. the incidence of the disease decreases.
• B. the significance level increases.
• C. the size of the expected treatment effect increased.
• D. the drop-out rate increases.

Hint:

Sample size must be inflated to cover patients lost to follow up, so a higher drop-out rate raises enrolment needs.

Answer 1

The Correct Option is D

This question is about the factors that push up the number of patients a clinical trial must enrol. Let's check each option against how sample size planning actually works.

1. the incidence of the disease decreases: this makes patients harder to find and slows recruitment, but the calculated sample size itself is not raised by a falling incidence, only the time it takes to reach that number.
2. the significance level increases: a more relaxed significance level (more willing to accept a chance finding) actually lets a trial get by with fewer patients, so this does not raise the number needed; a tighter significance level would raise it instead.
3. the size of the expected treatment effect increased: a bigger effect stands out more clearly, so fewer patients are needed to detect it with confidence. This lowers, not raises, sample size.
4. the drop-out rate increases: patients who drop out do not contribute complete data at the end of the trial. To still end up with the number of complete patients the statistics call for, the trial team must enrol more people at the start to absorb this expected loss.

Only the drop-out option genuinely forces the enrolment target upward.

Let's summarize:

• Falling incidence and looser significance affect feasibility or precision, not the core number needed.
• A bigger treatment effect actually needs fewer patients.
• Expected drop-out is added on top of the statistical minimum, so more drop-out means more patients must be recruited.

So the required number of patients rises as the drop-out rate rises.