Power and sample size — MCQs

A health system implements a new sepsis protocol across 20 hospitals. A researcher plans to evaluate effectiveness using a stepped-wedge cluster randomized design where hospitals sequentially adopt the protocol every 3 months. She calculates sample size based on individual patient outcomes (mortality) needing 2,000 patients total. The biostatistician identifies a critical error. Evaluate what modification is needed.

A 41-year-old research fellow designs a non-inferiority trial comparing oral to IV antibiotics for osteomyelitis. She sets the non-inferiority margin at 10% (cure rate difference), expects 85% cure in both groups, and calculates 300 patients per arm for 80% power with α=0.025 (one-sided). Her mentor suggests this underestimates required sample size. Evaluate the mentor's concern.

A pharmaceutical company tests a new antidepressant in 500 patients (250 per arm) and finds a 2-point improvement on a 52-point depression scale compared to placebo (p=0.04). The study was originally powered to detect a 4-point difference. The company seeks FDA approval citing statistical significance. Analyze the regulatory and scientific implications.

A meta-analysis of 5 previous trials testing a surgical technique shows a pooled effect size of 15% complication reduction (from 20% to 17%, p=0.30, I²=0%). An investigator wants to design a definitive trial. She calculates that 1,200 patients per arm would provide 80% power to detect this 3% absolute difference. Analyze whether this sample size is justified.

A 52-year-old oncologist designs a trial comparing chemotherapy regimens for pancreatic cancer. She plans 60 patients per arm for 80% power to detect a 3-month improvement in median survival (from 9 to 12 months) with α=0.05. After IRB approval, a competing trial publishes results showing the control regimen actually achieves 11-month median survival. Apply the appropriate modification to the study.