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Difficulty: MediumHypothesis Testing and Statistical Power

A multidisciplinary team at an academic medical center is designing a prospective, randomized, double-blind, placebo-controlled trial to evaluate a new targeted biologic therapy for refractory ulcerative colitis. The primary endpoint is the rate of clinical remission at 5252 weeks. The trial is designed with a two-sided alpha level of 0.050.05. A pre-study statistical analysis determines that enrolling 280280 patients per arm will provide a 90%90\% probability of detecting a true absolute difference in clinical remission rates of 15%15\% or greater between the active drug and placebo.

If the actual difference in remission rates between the biologic and placebo is indeed 15%15\%, what is the probability (expressed as a percentage) that the trial will incorrectly fail to demonstrate a statistically significant difference between the two groups?

Answer: 10 %

Answer

10
The scenario describes a study with a statistical power of 90%90\%. Power is defined as the probability of correctly rejecting the null hypothesis when there is a true difference (i.e., avoiding a Type II error). The question asks for the probability of failing to detect a true difference, which is the exact definition of a Type II error (β\beta). Since Power=1−β\text{Power} = 1 - \beta, the Type II error rate is calculated as 1−0.90=0.101 - 0.90 = 0.10, which is 10%10\%.

Step-by-Step Solution

1
Define statistical power in the context of the described study.
The statistical power is given as 90%90\%.
Power is explicitly defined in the stem as the 90%90\% probability of detecting a true absolute difference between the active drug and placebo.
2
Identify what statistical metric the question is asking to find.
The question asks for the probability of incorrectly failing to demonstrate a difference when a true difference exists.
This specific scenario defines a false-negative result, which corresponds to the Type II error rate (β\beta).
3
Calculate the Type II error (β\beta) from the given statistical power.
β=100%−90%=10%\beta = 100\% - 90\% = 10\%.
Statistical power and Type II error are mathematically complementary probabilities (1−β=Power1 - \beta = \text{Power}).

Key Concept

Statistical power (1−β1 - \beta) and Type II error (β\beta) are complementary probabilities. A Type II error occurs when a study incorrectly fails to reject a false null hypothesis.
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Topics

Hypothesis Testing and Statistical Power

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