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Difficulty: MediumHypothesis Testing and Statistical Power

An academic surgical collaborative is finalizing the protocol for a randomized controlled trial comparing a new robot-assisted technique to traditional laparoscopic cholecystectomy for patients with symptomatic cholelithiasis. The primary outcome is the rate of major biliary complications within 30 days post-operation. The trial is initially powered at 80%80\% to detect a 3%3\% absolute reduction in complications, using a preset significance level (α\alpha) of 0.050.05. During the scientific review board meeting, a reviewer raises concerns about the potential for adopting an inferior, more expensive technique based on a false-positive finding. To address this concern, the principal investigator amends the protocol to use a stricter significance level of 0.010.01 instead of 0.050.05. Assuming the planned sample size and the anticipated absolute risk reduction remain unchanged, which of the following is the most likely statistical consequence of this protocol amendment?

  1. The probability of failing to reject the null hypothesis when it is actually false will increase.Answer
  2. B
    The statistical power of the study to detect the 3%3\% absolute reduction will increase.
  3. C
    The probability of falsely concluding that the robot-assisted technique is superior will increase.
  4. D
    The positive predictive value of a statistically significant finding will decrease.
  5. E
    The trial will become more susceptible to confounding bias due to the stricter significance threshold.

Answer

The probability of failing to reject the null hypothesis when it is actually false will increase.
In hypothesis testing, there is an inverse relationship between the probability of a Type I error (α\alpha) and a Type II error (β\beta) when the sample size and effect size are held constant. A Type I error occurs when a true null hypothesis is incorrectly rejected (false positive). A Type II error occurs when a false null hypothesis is not rejected (false negative). By decreasing the significance level from 0.050.05 to 0.010.01, the investigators are making the criteria for rejecting the null hypothesis stricter. While this successfully lowers the probability of a Type I error, it makes it more difficult to reject the null hypothesis overall, thereby increasing the probability of a Type II error (β\beta). Consequently, the statistical power of the study, defined as 1−β1 - \beta, will decrease.

Step-by-Step Solution

1
Identify the protocol change made by the investigator.
The significance level (α\alpha) was decreased from 0.050.05 to 0.010.01.
To determine the downstream statistical effects, the exact modification to the trial design must first be established.
2
Determine the impact of decreasing α\alpha on the criteria for statistical significance.
A smaller α\alpha means stricter criteria are required to reject the null hypothesis.
α\alpha represents the maximum acceptable probability of a Type I error (rejecting a true null hypothesis).
3
Evaluate the inverse relationship between Type I (α\alpha) and Type II (β\beta) errors.
Making it harder to reject the null hypothesis decreases Type I errors but increases the likelihood of failing to reject a false null hypothesis (Type II error).
When sample size and effect size are held constant, α\alpha and β\beta are inversely related. An increase in β\beta means a decrease in statistical power (1−β1 - \beta).

Key Concept

The inverse relationship between Type I error (α\alpha) and Type II error (β\beta) for a fixed sample size and effect size.
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Topics

Hypothesis Testing and Statistical Power

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