A pharmaceutical company sponsors a phase III, randomized, double-blind clinical trial to … — USMLE Step 3

A pharmaceutical company sponsors a phase III, randomized, double-blind clinical trial to compare a newly developed oral targeted therapy against standard methotrexate for the treatment of moderate-to-severe rheumatoid arthritis. The study protocol pre-specifies an alpha level of $0.05$ and a power of $80\%$ to detect a $15\%$ absolute difference in the rate of clinical remission at $24$ weeks. Based on these parameters, the required sample size is calculated to be $800$ patients. Due to strict inclusion criteria and recruitment challenges, the enrollment period is closed early after only $400$ patients have been randomized.

At the $24$ -week follow-up, the clinical remission rate is $45\%$ in the new therapy group and $33\%$ in the methotrexate group. The statistical analysis yields a p-value of $0.09$ . The investigators publish their findings, concluding that the new oral therapy is not superior to standard methotrexate.

Which of the following is the most accurate statistical critique of this trial's conclusion?

The trial was inadequately powered, resulting in a high risk of a Type II error despite the observed clinical difference.Answer
B
The non-significant p-value indicates that an incorrect inferential statistical test was utilized for this type of dependent variable.
C
The results indicate that the treatment effect was masked by confounding rather than an effect modifier.
D
The small sample size primarily decreased the positive predictive value of the clinical remission outcome.
E
The investigators' conclusion is flawed because it relies on anchoring bias toward the initial $800$ -patient target.

Answer

The trial was inadequately powered, resulting in a high risk of a Type II error despite the observed clinical difference.

Statistical power (

1 - \beta

) is the probability of correctly rejecting the null hypothesis when a true difference exists. Power is heavily dependent on sample size. In this scenario, the trial was designed to enroll

800

patients to achieve

80\%

power. Because only

400

patients were randomized, the trial's power was substantially reduced. The investigators observed a large absolute difference of

12\%

between the groups, but the p-value was

0.09

(which is

> 0.05

). When a study fails to reach statistical significance primarily due to an inadequate sample size, it is considered underpowered and is at a high risk for a Type II error (represented by

\beta

). A Type II error occurs when investigators incorrectly accept the null hypothesis, missing a true effect.

Step-by-Step Solution

Identify the original trial design parameters.

The trial was powered at

80\%

to detect a

15\%

difference with a planned sample size of

800

patients.

Understanding the baseline statistical assumptions is necessary to evaluate the final outcome.

Evaluate the impact of the recruitment shortfall.

Only

400

patients were enrolled, which is half of the required sample size.

Sample size is directly proportional to statistical power; a significant reduction in enrollment drastically reduces the power of the study.

Interpret the final results in the context of the reduced power.

An absolute difference of

12\%

was observed, but the p-value was

0.09

(greater than the

0.05

threshold).

Because the study was underpowered, it failed to reject the null hypothesis despite a potentially clinically meaningful difference, which defines a high risk for a Type II error.

Key Concept

Sample size is a primary determinant of statistical power; an under-enrolled study has a high risk of a Type II error (failing to reject a false null hypothesis).

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Answer

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Key Concept

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