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Difficulty: MediumStatistical Inference and Hypothesis Testing

Health administrators at a large regional healthcare network evaluate a newly implemented electronic sepsis-alert algorithm. They compare the 30-day mortality rates of patients treated before and after the system's deployment. In a preliminary sample of 8080 patients, mortality was 15%15\% in the pre-intervention group and 12%12\% in the post-intervention group (p=0.24p = 0.24). The administrators conclude the algorithm is ineffective and discontinue its use.

One year later, a national multicenter trial evaluates the exact same algorithm across 4040 hospitals, enrolling 5,0005,000 patients. This trial demonstrates a statistically significant reduction in mortality from 16%16\% to 11%11\% (p<0.01p < 0.01). Assuming both evaluations were methodologically sound in their execution, which of the following best explains the discrepancy between the regional hospital's internal review and the national trial?

  1. Low statistical power leading to failure to reject the null hypothesisAnswer
  2. B
    The occurrence of a Type I error in the regional hospital's internal review
  3. C
    Unrecognized confounding by disease severity masking the true association
  4. D
    Differences in positive predictive value caused by baseline sepsis prevalence
  5. E
    Bias introduced by the use of an inappropriate retrospective study design

Answer

Low statistical power leading to failure to reject the null hypothesis
The correct answer identifies that the regional hospital's study was underpowered. Statistical power (1−beta1 - \\beta) is the probability of correctly rejecting a false null hypothesis (i.e., successfully detecting a true difference). Power is heavily dependent on sample size. Because the regional hospital only evaluated 8080 patients, the study lacked the statistical power to detect the true difference in mortality. This resulted in a non-significant pp-value (0.240.24), representing a Type II error (a false negative finding). The national trial, with 5,0005,000 patients, had adequate power to detect the true benefit of the algorithm.

Step-by-Step Solution

1
Analyze the results of the regional hospital's internal review.
The study showed a numerical difference in mortality (15%15\% vs 12%12\%) but the pp-value (0.240.24) was greater than the standard alpha level of 0.050.05.
This establishes that the initial study failed to reject the null hypothesis, concluding there was no statistically significant difference.
2
Analyze the results of the national multicenter trial.
The larger trial showed a similar magnitude of difference (16%16\% vs 11%11\%) but achieved high statistical significance (p<0.01p < 0.01).
This confirms that the algorithm is actually effective (assuming the national trial represents the true effect).
3
Compare the study parameters to identify the cause of the discrepancy.
The primary difference is the sample size (n=80n = 80 vs n=5,000n = 5,000).
Sample size is the main determinant of statistical power. A small sample size leads to low power, increasing the risk of a Type II error (failing to detect a true difference).

Key Concept

Statistical power and Type II errors in hypothesis testing
Estimated Time:1m 0s
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Topics

Statistical Inference and Hypothesis Testing

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