A multicenter research network evaluates the risk of developing secondary acute myeloid le… — USMLE Step 3

A multicenter research network evaluates the risk of developing secondary acute myeloid leukemia (sAML) in a cohort of $440$ patients who previously received targeted chemotherapy for a solid tumor. All patients are enrolled on the day they complete their initial chemotherapy and are confirmed to be free of hematologic malignancies. The study is planned for a $5$ -year follow-up period.

During the observation period, the following events occur:
- $40$ patients are diagnosed with sAML at exactly $3$ years of follow-up.
- $40$ patients move out of the country and are lost to follow-up at exactly $2$ years.
- The remaining patients remain free of leukemia and complete the full $5$ -year observation period.

Based on these data, what is the incidence rate of sAML in this cohort, expressed as cases per $1,000$ person-years?

Answer: 20 cases per 1,000 person-years

Answer

The correct calculation accounts for the dynamic nature of the cohort. Person-time at risk must be strictly calculated based on the exact time each patient was observed while disease-free. By separately multiplying each subgroup's patient count by their respective years under observation (

40 \times 3

for cases,

40 \times 2

for drop-outs, and

360 \times 5

for those completing the study), we determine the true denominator of

2,000

person-years. Dividing the

40

incident cases by

2,000

yields an incidence rate of

20

cases per

1,000

person-years.

Step-by-Step Solution

Calculate person-years for patients diagnosed with sAML

40

patients

\times

3

years =

120

person-years

Patients stop contributing at-risk person-time once they develop the disease of interest.

Calculate person-years for patients lost to follow-up

40

patients

\times

2

years =

80

person-years

Patients stop contributing at-risk person-time when they leave the study and can no longer be observed.

Calculate person-years for the remaining patients

360

patients

\times

5

years =

1,800

person-years

The patients who did not develop the disease and were not lost to follow-up (

440 - 40 - 40 = 360

) contribute the full planned duration of the study.

Sum total person-years

120 + 80 + 1,800 = 2,000

person-years

The incidence rate denominator requires the total accumulated person-time for the entire cohort.

Calculate the incidence rate

40

cases

\div

2,000

person-years =

0.02

cases per person-year

Incidence rate is defined as new cases divided by total person-time at risk.

Convert to the requested unit (per 1,000 person-years)

0.02 \times 1,000 = 20

The question specifically asks for the rate expressed per

1,000

person-years.

Key Concept

Incidence rate calculations require an accurate accounting of the denominator (person-time at risk), meaning patients must be censored at the time they develop the disease, die, or are lost to follow-up.

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