A general internist is reviewing the medical literature to update the clinic's management … — USMLE Step 3

A general internist is reviewing the medical literature to update the clinic's management protocol for diabetic peripheral neuropathy. The physician reads a newly published randomized, placebo-controlled trial evaluating a novel oral analgesic. The study enrolled a total of $30$ patients ( $15$ in the treatment arm and $15$ in the placebo arm). The results demonstrate that patients receiving the novel analgesic experienced a mean reduction in pain scores of $4.5$ points on a $10$ -point visual analog scale, whereas the placebo group experienced a $1.2$ -point reduction. The reported p-value for this difference is $0.11$ . Based solely on this p-value, the physician decides not to incorporate the new medication into practice, concluding that the drug has been definitively proven to be no better than placebo. Which of the following best describes the primary statistical error in the physician's reasoning?

Failing to recognize that the small sample size resulted in low statistical power and a high risk of a false-negative finding.Answer
B
Assuming the non-significant result implies the presence of effect modification rather than uncontrolled confounding variables.
C
Incorrectly concluding that the investigators used an inappropriate categorical statistical test for continuous pain score data.
D
Overlooking the fact that the positive predictive value of the trial's conclusion depends heavily on the baseline prevalence of neuropathy.
E
Exhibiting anchoring bias by fixating on an isolated statistical threshold rather than evaluating the clinical magnitude of the effect.

Answer

The physician failed to recognize that the small sample size resulted in low statistical power, leading to a high risk of a Type II error (a false-negative finding).

Statistical power is the probability of correctly rejecting the null hypothesis when a true difference exists (calculated as

1 - \beta

). Power is heavily dependent on sample size. In this scenario, the study has a very small sample size (

n=30

total), making it highly likely that it is underpowered to detect a statistically significant difference, even though a large, clinically meaningful effect was observed (

4.5

1.2

point reduction). When an underpowered study yields a non-significant p-value (

p=0.11

), it simply indicates a failure to reject the null hypothesis; it does not prove that the null hypothesis is true. By concluding the drug is definitively ineffective based on this result, the physician is falling victim to a potential Type II error (a false negative).

Step-by-Step Solution

Analyze the reported results of the trial.

There is a large clinical difference between the groups (a

4.5

-point reduction versus a

1.2

-point reduction), but the p-value is

0.11

, which is not statistically significant at the standard alpha of

0.05

To identify a discrepancy between the clinical magnitude of the effect and the statistical significance.

Evaluate the study design parameters.

The sample size is extremely small, with only

15

patients per group.

Sample size is the primary determinant of a study's statistical power.

Correlate the sample size with the statistical outcome.

A small sample size directly leads to low statistical power (typically

1 - \beta

Low power means the study lacks the ability to reliably detect a true difference, leading to a high risk of failing to reject a false null hypothesis (Type II error).

Critique the physician's conclusion.

The physician concluded the drug is 'definitively proven to be no better than placebo'.

A non-significant p-value in an underpowered study means 'absence of evidence', not 'evidence of absence'. The physician is committing a Type II error in their interpretation.

Key Concept

Hypothesis Testing and Statistical Power

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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