A rheumatology clinic reviews records of patients with refractory rheumatoid arthritis tre… — USMLE Step 3

A rheumatology clinic reviews records of patients with refractory rheumatoid arthritis treated with one of two biologic therapies: a tumor necrosis factor-alpha (TNF-alpha) inhibitor or an interleukin-6 (IL-6) receptor antagonist. The primary outcome is the occurrence of disseminated histoplasmosis within the first year of therapy. The review includes $145$ patients who received the TNF-alpha inhibitor and $160$ patients who received the IL-6 receptor antagonist. During the follow-up period, $4$ patients in the TNF-alpha inhibitor group and $0$ patients in the IL-6 receptor antagonist group developed the infection. The investigators wish to determine if the difference in infection risk between the two therapies is statistically significant. Which of the following is the most appropriate statistical test to analyze these data?

A
Chi-square test of independence
B
Mann-Whitney U test
Fisher's exact testAnswer
D
McNemar's test
E
Two-sample Z-test for proportions

Answer

Fisher's exact test

The study evaluates the association between two independent categorical variables (biologic treatment type and occurrence of infection). While the Chi-square test of independence is typically the standard test for a

2 \times 2

contingency table, it fundamentally assumes that the expected frequency in each cell is at least

5

. In this scenario, the overall incidence of the infection is merely

4

out of

305

patients. Consequently, the expected number of infections in the IL-6 antagonist group is approximately

2.1

, which is below the threshold of

5

. Therefore, Fisher's exact test must be utilized. It calculates the exact probability of obtaining the observed data (or more extreme data) rather than relying on an approximation, making it the mathematically robust choice for categorical data with small expected counts.

Step-by-Step Solution

Identify the types of variables being analyzed.

The independent variable is the treatment group (TNF-alpha inhibitor vs. IL-6 receptor antagonist), and the dependent variable is the infection status (developed histoplasmosis vs. did not develop histoplasmosis). Both are nominal categorical variables.

Variable types dictate the family of appropriate statistical tests (e.g., categorical vs. continuous data analysis).

Determine the relationship between the study groups.

The two patient groups are completely independent of one another. They are not matched or paired.

This rules out tests designed for paired categorical data, such as McNemar's test.

Check the statistical assumptions for standard independent categorical tests (like the Chi-square test).

The overall infection rate is

4

events out of

305

total patients. The expected number of infections for the IL-6 group (

160

patients) would be roughly

160 \times (4/305) = 2.1

. This expected cell count is less than

5

The Chi-square test is invalid if any expected cell frequency is less than

5

(or less than

5

>20\%

of cells for larger tables). When this assumption is violated, an exact test must be used.

Select the appropriate alternative test.

Fisher's exact test is selected.

Fisher's exact test is the correct nonparametric equivalent to the Chi-square test for independent categorical variables when expected cell counts are too low.

Key Concept

Fisher's exact test is used to compare the distributions of two categorical variables when the sample sizes or event rates are too small (expected cell counts < 5) to meet the assumptions of the Chi-square test.

Estimated Time:1m 30s

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