A randomized, double-blind, placebo-controlled clinical trial is conducted to evaluate the… — USMLE Step 3

A randomized, double-blind, placebo-controlled clinical trial is conducted to evaluate the efficacy and safety of Agent Z, a novel biologic therapy, in adults with severe plaque psoriasis. The primary efficacy endpoint is the proportion of patients achieving a $75\%$ reduction in the Psoriasis Area and Severity Index (PASI 75) at week 16. The primary safety endpoint is the incidence of serious infections over the same period. The trial enrolls $800$ patients, randomized equally to receive either Agent Z or a placebo.

The trial results at 16 weeks are shown in the table below:

Outcome	Agent Z ( $n = 400$ )	Placebo ( $n = 400$ )	$95\%$ CI of Absolute Difference*
Achieved PASI 75	$240$	$40$	$44.4\%$ to $55.6\%$
Developed serious infection	$12$	$8$	$-1.2\%$ to $3.2\%$

*\*Note: Absolute difference is calculated as the incidence in the Agent Z group minus the incidence in the placebo group.*

Based on these results, which of the following statements most accurately describes the clinical impact of Agent Z compared to placebo?

A
For every $10$ patients treated with Agent Z, $1$ additional patient achieves PASI 75; however, there is insufficient evidence to conclude that Agent Z increases the risk of serious infections.
B
For every $6$ patients treated with Agent Z, $1$ additional patient achieves PASI 75; however, there is insufficient evidence to conclude that Agent Z increases the risk of serious infections.
For every $2$ patients treated with Agent Z, $1$ additional patient achieves PASI 75; however, there is insufficient evidence to conclude that Agent Z increases the risk of serious infections.Answer
D
For every $2$ patients treated with Agent Z, $1$ additional patient achieves PASI 75, and for every $100$ patients treated, $1$ additional serious infection occurs.
E
For every $2$ patients treated with Agent Z, $1$ additional patient achieves PASI 75, and for every $33$ patients treated, $1$ additional serious infection occurs.

Answer

The most accurate statement is that for every 2 patients treated with Agent Z, 1 additional patient achieves PASI 75; however, there is insufficient evidence to conclude that Agent Z increases the risk of serious infections.

The correct answer accurately calculates the Number Needed to Treat (NNT) and correctly identifies that the adverse event data is not statistically significant. First, the Absolute Benefit Increase (ABI) for achieving PASI 75 is calculated as the incidence in the Agent Z group (

\frac{240}{400} = 60\%

) minus the incidence in the placebo group (

\frac{40}{400} = 10\%

), which equals

50\%

(

0.50

). The NNT is the reciprocal of the ABI (

\frac{1}{0.50} = 2

). Second, while there is a numerically higher rate of serious infections in the Agent Z group (

3\%

2\%

), the

95\%

confidence interval for this absolute difference (

-1.2\%

3.2\%

) crosses

0

. An absolute difference CI that crosses

0

indicates that the result is not statistically significant (

p > 0.05

). Therefore, there is insufficient evidence to conclude that Agent Z increases the risk of serious infections, and calculating a Number Needed to Harm (NNH) is epidemiologically inappropriate.

Step-by-Step Solution

Calculate the Absolute Benefit Increase (ABI) for the primary efficacy endpoint.

Agent Z incidence =

\frac{240}{400}

(

60\%

). Placebo incidence =

\frac{40}{400}

(

10\%

). ABI =

60\% - 10\% = 50\%

(

0.50

To determine the absolute clinical benefit attributable to the intervention compared to the control.

Calculate the Number Needed to Treat (NNT).

NNT =

\frac{1}{0.50} = 2

The NNT represents the number of patients who need to receive the experimental treatment to achieve one additional positive outcome. It is always the reciprocal of the absolute difference in efficacy.

Evaluate the statistical significance of the safety outcome (serious infections).

The

95\%

confidence interval for the absolute difference in serious infections ranges from

-1.2\%

3.2\%

. Because this interval includes

0

, the difference is not statistically significant.

If a

95\%

CI for an absolute difference between two groups crosses

0

(the null value for differences), the result is not statistically significant at the

p < 0.05

level.

Synthesize the findings into a clinical conclusion.

The NNT is

2

, and no valid Number Needed to Harm (NNH) can be established.

It is incorrect to report an NNH for an outcome that has not been proven to be statistically different from placebo, as any observed numerical difference is likely due to chance.

Key Concept

Calculating Number Needed to Treat (NNT) from absolute risk differences and interpreting Confidence Intervals to determine statistical significance before calculating Number Needed to Harm (NNH).

Question

Answer

Step-by-Step Solution

Key Concept

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