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Difficulty: HardStatistical Inference and Hypothesis Testing

Investigators are designing a prospective, randomized controlled trial to evaluate the efficacy of a novel continuous positive airway pressure (CPAP) mask in reducing daytime somnolence among patients with moderate obstructive sleep apnea. The primary outcome is the mean change in the Epworth Sleepiness Scale (ESS) score after 88 weeks of use, compared to the standard CPAP mask. A pilot study of 3030 patients (1515 per group) reveals a mean ESS reduction of 4.24.2 points (standard deviation: 2.12.1) in the novel mask group and 2.82.8 points (standard deviation: 2.42.4) in the standard mask group. An unpaired t-test yields a p-value of 0.100.10. The 95%95\% confidence interval for the difference in means is [−0.3,3.1][-0.3, 3.1]. Based on these preliminary results, the research team decides to halt the development of the novel mask, concluding that it does not provide a superior clinical benefit. Which of the following is the most accurate critique of the investigators' statistical conclusion?

  1. A
    The findings are definitive because a confidence interval containing zero mathematically proves the null hypothesis is true.
  2. The study likely lacked sufficient statistical power, risking a Type II error due to the small sample size.Answer
  3. C
    A retrospective cohort design is required to accurately calculate statistical significance for longitudinal changes.
  4. D
    The lack of statistical significance demonstrates that an unmeasured confounding variable is masking the true therapeutic effect.
  5. E
    The low prevalence of severe somnolence in the sample population decreased the positive predictive value of the hypothesis test.

Answer

The study likely lacked sufficient statistical power, risking a Type II error due to the small sample size.
The correct answer accurately identifies that a small pilot study (n=30n=30) evaluating a continuous variable (ESS score) will naturally have low statistical power. The study observed a clinically notable difference (1.41.4 point reduction), but the wide confidence interval crossing zero and p=0.10p = 0.10 indicate insufficient evidence to reject the null hypothesis. Halting development solely on this basis ignores the high probability of a Type II error (failing to detect a true difference due to inadequate sample size).

Step-by-Step Solution

1
Analyze the statistical outputs provided in the stem.
The difference in means is 1.41.4. The p-value is 0.100.10, and the 95%95\% CI is [−0.3,3.1][-0.3, 3.1].
Understanding the clinical outcome versus the statistical significance threshold (typically α=0.05\alpha = 0.05) is required to interpret the results.
2
Evaluate the sample size and its mathematical relationship to the statistical findings.
The sample size is very small (n=30n=30, with 1515 per group). Small sample sizes produce large standard errors, resulting in wide confidence intervals that are more likely to cross zero.
Statistical power is heavily dependent on sample size. A small sample size directly limits a study's ability to detect a true difference.
3
Identify the logical flaw in the investigators' conclusion.
The investigators concluded the mask has NO benefit because p>0.05p > 0.05. However, failing to reject the null hypothesis in an underpowered study suggests a high risk of a Type II error (β\beta).
Concluding that an intervention is ineffective simply because a severely underpowered pilot study did not reach statistical significance is a fundamental misinterpretation of hypothesis testing.

Key Concept

Statistical power and Type II error
Estimated Time:1m 30s
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Topics

Statistical Inference and Hypothesis Testing

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