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Zorluk: ZorHypothesis Testing and Statistical Power

A pharmaceutical company is developing a novel Janus kinase (JAK) inhibitor for the treatment of severe, refractory rheumatoid arthritis. Regulatory guidelines stipulate that the manufacturer must conduct two independent, pivotal Phase III randomized controlled trials demonstrating efficacy. The research team designs Trial X with a statistical power of 80% and Trial Y with a statistical power of 90% to detect the predefined minimum clinically important difference. Both trials use a two-sided alpha level of 0.05.

Assuming the new JAK inhibitor is genuinely effective at or above the minimum clinically important difference, what is the probability (expressed as a percentage) that BOTH trials will fail to yield statistically significant results?

Cevap: 2 %

Cevap

2
Statistical power (1−β1 - \beta) is the probability of correctly rejecting the null hypothesis when a true effect exists. A Type II error (β\beta) occurs when a study fails to detect a true effect, resulting in a false negative. The probability of Trial X failing is its Type II error rate: βX=1−0.80=0.20\beta_X = 1 - 0.80 = 0.20. The probability of Trial Y failing is βY=1−0.90=0.10\beta_Y = 1 - 0.90 = 0.10. Because the two pivotal trials are designed to be independent, the joint probability of both trials simultaneously failing to detect the true effect is the product of their individual Type II error rates: 0.20×0.10=0.020.20 \times 0.10 = 0.02. Expressed as a percentage, this is 2%.

Adım Adım Çözüm

1
Define statistical power and Type II error
Power = 1−β1 - \beta, so β\beta (Type II error rate) = 1−Power1 - \text{Power}
To find the probability of a trial failing to detect a true effect, we must calculate its Type II error rate.
2
Calculate Type II error for each trial
Trial X β=1−0.80=0.20\beta = 1 - 0.80 = 0.20; Trial Y β=1−0.90=0.10\beta = 1 - 0.90 = 0.10
Each trial has an independent probability of failing to achieve statistical significance despite a true underlying effect.
3
Calculate joint probability
Joint probability = 0.20×0.10=0.020.20 \times 0.10 = 0.02
The probability of multiple independent events all occurring is the product of their individual probabilities.
4
Convert to percentage
0.02×100=2%0.02 \times 100 = 2\%
The question specifically asks for the probability expressed as a percentage.

Anahtar Kavram

The probability of failing to detect a true difference in a study is the Type II error rate (β\beta), calculated as 1−Power1 - \text{Power}. The probability of independent trials both making a Type II error is the product of their individual β\beta values.
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Hypothesis Testing and Statistical Power

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