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Difficulty: HardStatistical Inference and Hypothesis Testing

A research group conducts a randomized, double-blind, placebo-controlled trial to evaluate the efficacy of a novel biologic agent for patients with severe, treatment-resistant rheumatoid arthritis. The study's primary endpoint is the proportion of patients achieving clinical remission at 66 months. During the trial design phase, the researchers determine that 500500 patients are required to achieve 80%80\% power to detect a 10%10\% absolute difference in remission rates, with an α\alpha level of 0.050.05. The trial ultimately enrolls 500500 patients; however, due to unforeseen logistical challenges during the study period, 35%35\% of the enrolled participants are lost to follow-up and excluded from the final primary analysis. The final results show a 9%9\% absolute higher remission rate in the treatment group compared to the placebo group, with a pp-value of 0.070.07 and a 95%95\% confidence interval for the difference ranging from −1%-1\% to +19%+19\%. Which of the following best explains why the trial failed to demonstrate a statistically significant benefit for the novel biologic agent?

  1. Reduced statistical power due to a smaller-than-anticipated final sample sizeAnswer
  2. B
    Increased risk of a Type I error due to the high rate of participant attrition
  3. C
    Failure to adjust for confounding variables during the initial randomization process
  4. D
    The presence of effect modification masking the true therapeutic benefit
  5. E
    Decreased negative predictive value of the primary clinical endpoint assessment

Answer

Reduced statistical power due to a smaller-than-anticipated final sample size
The correct answer identifies that the failure to reach statistical significance is most likely due to reduced statistical power resulting from participant attrition. Power is the probability of correctly rejecting a false null hypothesis (i.e., detecting a true difference). The power of a study is heavily dependent on the sample size. The investigators calculated that 500 patients were needed to achieve 80% power. However, a 35% loss to follow-up significantly reduced the final sample size. This smaller sample size increased the standard error, which widened the 95% confidence interval (causing it to cross zero, from -1% to +19%) and resulted in a non-significant p-value (0.07 > 0.05). When a study is underpowered, it has a high risk of a Type II error (failing to detect a true difference that actually exists).

Step-by-Step Solution

1
Analyze the initial trial design parameters.
The trial was designed for 80% power with 500 patients to detect a 10% difference at an alpha level of 0.05.
Establishing the baseline power calculation helps identify what changed during execution.
2
Identify deviations from the trial design.
There was a 35% loss to follow-up, leaving approximately 325 patients for the final analysis.
Participant attrition directly impacts the effective sample size.
3
Determine the statistical consequence of the deviation.
A smaller sample size increases the standard error and widens the confidence interval (ranging from -1% to +19%, crossing 0).
Power is directly proportional to sample size; reducing the sample size increases the risk of a Type II error (failing to detect a true difference).

Key Concept

Statistical power and sample size in clinical trials
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Topics

Statistical Inference and Hypothesis Testing

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