Researchers at an academic medical center investigate the use of a novel microbiome restor… — USMLE Step 3

Researchers at an academic medical center investigate the use of a novel microbiome restorative therapy to prevent recurrent *Clostridioides difficile* infection (CDI). The study enrolls adults who have recently completed standard antibiotic therapy for a first episode of CDI. Participants are randomly assigned in a 1:1 ratio to receive either the novel therapy or a visually matched placebo.

Over a 6-month follow-up period, the following data are recorded:

Group	Total Patients	Recurrent CDI Events
Placebo	400	80
Novel therapy	400	32

Based on the study results, what is the number needed to treat (NNT) to prevent one additional episode of recurrent CDI? (Provide your answer as a whole number, applying standard epidemiological rounding principles).

Answer: 9 patients

Answer

To find the number needed to treat (NNT), first calculate the absolute risk reduction (ARR). The risk of recurrent CDI in the placebo group (CER) is

80/400 = 0.20

. The risk in the treatment group (EER) is

32/400 = 0.08

. The ARR is the difference between these two rates:

0.20 - 0.08 = 0.12

. The NNT is the reciprocal of the ARR:

1 / 0.12 = 8.33

. In biostatistics, the NNT must always be rounded up to the next whole number (ceiling function) to provide a conservative estimate. Therefore,

8.33

rounds up to

9

Step-by-Step Solution

Calculate the Control Event Rate (CER).

CER =

80 / 400 = 0.20

(

20\%

This establishes the baseline risk of the outcome (recurrent CDI) without the new intervention.

Calculate the Experimental Event Rate (EER).

EER =

32 / 400 = 0.08

(

8\%

This establishes the risk of the outcome when using the novel therapy.

Calculate the Absolute Risk Reduction (ARR).

ARR = CER - EER =

0.20 - 0.08 = 0.12

(

12\%

ARR represents the actual difference in risk between the two groups, showing how much the intervention reduces the absolute risk of the event.

Calculate the Number Needed to Treat (NNT).

NNT =

1 / \text{ARR} = 1 / 0.12 = 8.33

NNT is the reciprocal of the Absolute Risk Reduction. It indicates the theoretical number of patients that need to be treated to prevent one bad outcome.

Apply conservative rounding rules for NNT.

Round

8.33

up to

9

Because treating

8

patients would only prevent

8 \times 0.12 = 0.96

events (less than one full event), you must treat the

9^{\text{th}}

patient to guarantee the prevention of at least one event. NNT is always rounded up to the nearest whole number (ceiling function) to avoid overstating clinical benefit.

Key Concept

Number Needed to Treat (NNT) calculation and conservative rounding principles

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