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Difficulty: MediumHypothesis Testing and Statistical Power

A cardiovascular research consortium is designing a randomized, placebo-controlled trial to evaluate a novel PCSK9 inhibitor for the prevention of major adverse cardiovascular events (MACE) in patients with stable coronary artery disease. The investigators initially calculate that enrolling 4,5004,500 patients followed for an average of 44 years will provide 80%80\% statistical power to detect a 20%20\% relative risk reduction in MACE, assuming a two-sided α\alpha of 0.050.05. The sample size calculation is based on an expected placebo event rate of 4%4\% per year. However, just before enrollment begins, a large epidemiological registry publishes data showing that due to widespread adoption of high-intensity statin therapy, the actual background rate of MACE in this specific population has decreased to 2%2\% per year. If the investigators proceed with the originally planned sample size and follow-up duration, which of the following is the most likely consequence for the trial?

  1. Increased probability of committing a Type II errorAnswer
  2. B
    Increased probability of committing a Type I error
  3. C
    Narrowing of the 95%95\% confidence interval around the effect estimate
  4. D
    Decreased Number Needed to Treat (NNT) to prevent one event
  5. E
    Increased statistical power to detect the 20%20\% relative risk reduction

Answer

The trial will have an increased probability of committing a Type II error because the lower baseline event rate will result in fewer total endpoints, reducing the study's statistical power.
Statistical power is the probability of correctly rejecting the null hypothesis when a true effect exists (1−β1 - \beta). In event-driven trials, power is primarily determined by the total number of clinical endpoints that occur during the study. If the baseline incidence of the event is significantly lower than expected (2%2\% instead of 4%4\%), fewer total events will accrue over the same follow-up period. This reduction in events decreases the precision of the study (widening confidence intervals), thereby decreasing the statistical power. Because power is defined as 1−β1 - \beta, a decrease in power directly corresponds to an increase in β\beta, which is the probability of committing a Type II error (failing to detect a true difference).

Step-by-Step Solution

1
Analyze the change in the study population's baseline parameters.
The expected baseline event rate decreased from 4%4\% per year to 2%2\% per year.
Identifying altered baseline metrics is the first step in determining how a trial's mechanics will be affected.
2
Determine the effect of this change on the total accrued events.
With a fixed sample size (4,5004,500) and follow-up duration (44 years), a halving of the event rate yields significantly fewer total MACE endpoints.
In time-to-event or binary outcome trials, statistical power is driven primarily by the number of events, not just the number of enrolled patients.
3
Identify the impact on statistical precision and power.
Fewer events lead to wider confidence intervals and decreased statistical power.
Less data (fewer events) means the study has less ability to confidently distinguish a true treatment effect from random variation.
4
Relate the change in statistical power to the specific error types.
Decreased statistical power (1−β1-\beta) directly corresponds to an increased β\beta, which is the Type II error rate.
Type II error is the probability of failing to detect a true difference; as power drops, this risk inherently rises.

Key Concept

In clinical trials, statistical power (1−β1-\beta) depends on the total number of accrued events. A lower-than-expected baseline event rate yields fewer events, which decreases power and increases the probability of committing a Type II error (β\beta).
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Topics

Hypothesis Testing and Statistical Power

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