A hospital quality improvement committee is designing a prospective intervention study to … — USMLE Step 3

A hospital quality improvement committee is designing a prospective intervention study to reduce catheter-associated urinary tract infections (CAUTIs) in the intensive care unit. They plan to compare a new silver-alloy catheter to the standard silicone catheter. A priori power analysis determines that 108 patients per intervention group are required to achieve a statistical power of $80\%$ ( $\beta = 0.20$ ) at a significance level of $\alpha = 0.05$ to detect a clinically meaningful reduction in CAUTI incidence. Based on prior hospital initiatives, the committee anticipates a $20\%$ loss of analyzable data due to early patient transfers or incomplete electronic health records.

To ensure the study maintains the desired $80\%$ power, what is the minimum total number of patients the committee must initially enroll across both groups combined?

Answer: 270 patients

Answer

270

Statistical power heavily relies on the final number of subjects analyzed at the conclusion of a study. If an a priori power calculation determines that 108 patients are required per group, and a

20\%

dropout rate is expected, enrolling exactly 108 patients would result in only

\approx 86

analyzable patients per arm. This severely diminishes the study's power and substantially increases the risk of a Type II error (failing to detect a true difference). To ensure the final analyzed sample meets the target for robust statistical power, the initial enrollment per group must account for this loss using the formula:

N_{enrolled} = \frac{N_{needed}}{1 - \text{attrition rate}}

. For this study,

N_{enrolled} = \frac{108}{1 - 0.20} = \frac{108}{0.80} = 135

patients per group. Because the trial compares two groups (a new silver-alloy catheter and a standard silicone catheter), the total minimum enrollment required across both arms combined is

135 \times 2 = 270

patients.

Step-by-Step Solution

Identify the target final sample size and anticipated attrition rate.

Target = 108 patients per group; Attrition = 20% (0.20).

These specific variables are required to accurately adjust the initial enrollment target upward.

Calculate the required initial enrollment per group.

108 / (1 - 0.20) = 135 patients per group.

Dividing the required final size by the proportion of patients expected to complete the study ensures that, after attrition, the group still contains 108 patients.

Calculate the total required enrollment across the entire study.

135 patients/group * 2 groups = 270 patients.

The study compares two separate groups (silver-alloy vs. standard catheter). Therefore, the calculated per-group enrollment must be multiplied by 2.

Key Concept

To maintain statistical power despite anticipated patient dropout or data loss, the initial enrollment target per study arm must be calculated as: Required Sample Size / (1 - Attrition Rate).

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