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

Step 1: Understanding the Question.
We need to know what makes the required sample size (number of patients to enrol) in a clinical trial go UP, not down.

Step 2: Key Formula or Approach.
Sample size for a clinical trial is planned so that, after accounting for patients who will not complete the study, enough patients remain at the end to detect a real treatment effect with the chosen statistical confidence and power. So the planned enrolment number must always be inflated above the bare statistical minimum to cover expected losses during the trial.

Step 3: Detailed Explanation.
Option (A), incidence of the disease falling, makes it harder to recruit patients and slows the trial down, but it does not change the statistically calculated sample size that is needed; it only affects how long recruitment takes.
Option (B), a stricter (smaller) significance level actually needs MORE patients, while a looser (larger) significance level needs FEWER patients; a rising significance level in the usual sense (more tolerance for error) reduces the number needed, so this does not explain an increase.
Option (C), a bigger expected treatment effect is actually easier to detect, so the trial needs FEWER patients to show it clearly; a growing effect size lowers the required sample size, not raises it.
Option (D), a rising drop-out rate means more enrolled patients will be lost to follow up before the trial ends. To still finish with the statistically needed number of complete patients, the trial must enrol extra patients up front to allow for this expected loss. So a higher expected drop-out rate directly raises the number of patients that must be recruited.

Step 4: Final Answer.
The number of patients required goes up as the expected drop-out rate goes up, because extra patients must be enrolled to make up for those who leave the trial early.
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