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Difficulty: Very hardMeasures of Disease Frequency

An occupational health department initiates a 55-year prospective cohort study on January 1 to determine the incidence rate of a newly recognized interstitial lung disease among factory employees exposed to a specific chemical aerosol. Initially, 1,0001,000 healthy, disease-free employees are enrolled.

Participant follow-up data is recorded at the end of each year. The events are as follows:
- End of Year 1: 100100 employees relocate and are lost to follow-up.
- End of Year 2: 150150 employees transition to a different industry and are censored from the study.
- End of Year 3: 5050 employees are diagnosed with the interstitial lung disease.
- End of Year 4: 5050 employees are diagnosed with the interstitial lung disease.
- End of Year 5: The study concludes. All remaining employees complete the full 55-year follow-up without developing the disease.

Assuming that individuals diagnosed with the disease are no longer considered at risk and do not contribute further person-time, what is the incidence rate of the interstitial lung disease in this cohort, expressed per 1,0001,000 person-years?

  1. A
    2020
  2. B
    2424
  3. 2525Answer
  4. D
    2727
  5. E
    100100

Answer

The correct incidence rate is 2525 per 1,0001,000 person-years.
The correct option is 2525. Incidence rate (or incidence density) is the number of new cases divided by the total person-time at risk. In this dynamic cohort, the population at risk decreases at the end of each year. During Year 1, 1,0001,000 people are at risk (1,0001,000 PY). After 100100 leave, 900900 are at risk during Year 2 (900900 PY). After 150150 leave, 750750 are at risk during Year 3 (750750 PY). The 5050 who develop the disease in Year 3 stop contributing person-time, leaving 700700 at risk during Year 4 (700700 PY). After another 5050 develop the disease, 650650 complete Year 5 (650650 PY). Total person-time = 1,000+900+750+700+650=4,0001,000 + 900 + 750 + 700 + 650 = 4,000 PY. With 100100 total cases, the rate is 100/4,000100 / 4,000 PY, which scales to 2525 per 1,0001,000 person-years.

Step-by-Step Solution

1
Calculate the person-years (PY) contributed by participants during each year of the study.
Year 1: 1,000 PY. Year 2: 900 PY. Year 3: 750 PY. Year 4: 700 PY. Year 5: 650 PY.
The at-risk population changes at the end of each year due to dropouts and incident cases. Those who leave or get the disease at the end of the year contribute a full year of time before being removed.
2
Sum the total person-years across the 5-year period.
1,000+900+750+700+650=4,0001,000 + 900 + 750 + 700 + 650 = 4,000 total person-years.
Incidence rate requires the total sum of observation time for all individuals while they were at risk.
3
Determine the total number of incident cases.
5050 (Year 3) + 5050 (Year 4) = 100100 total cases.
The numerator for incidence rate is the total number of new cases developed during the observation period.
4
Calculate the incidence rate per 1,000 person-years.
(100100 cases / 4,0004,000 PY) * 1,0001,000 = 2525 per 1,0001,000 person-years.
Dividing total cases by total person-time yields the rate, which is then scaled to the requested denominator of 1,000.

Key Concept

Incidence rate calculations in dynamic cohorts require determining the exact person-time at risk, meaning individuals must be removed from the denominator once they develop the disease or are lost to follow-up.
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Topics

Measures of Disease Frequency

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