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Difficulty: HardMeasures of Disease Frequency

A public health research team is evaluating the longitudinal risk of end-stage renal disease (ESRD) in a community population. They assemble a dynamic cohort of 1,5001,500 adult patients who have recently been diagnosed with severe hypertension but have normal renal function at baseline. The cohort is actively monitored for exactly 1010 years. During this period, the researchers observe the following events and attrition:

- 600600 subjects complete the entire 1010-year study without showing any clinical signs of ESRD.
- 400400 subjects move out of the study region and are lost to follow-up precisely at the end of year 55; all of these individuals were free of ESRD at the time of their departure.
- 300300 subjects are diagnosed with incident ESRD precisely at the end of year 44.
- 200200 subjects die from acute cardiovascular events precisely at the end of year 44, without having developed ESRD prior to death.

Assuming no other losses or events occurred, which of the following is the incidence rate of ESRD in this cohort?

  1. A
    2020 per 1,0001,000 person-years
  2. B
    2525 per 1,0001,000 person-years
  3. 3030 per 1,0001,000 person-yearsAnswer
  4. D
    200200 per 1,0001,000 person-years
  5. E
    250250 per 1,0001,000 person-years

Answer

The correct incidence rate is 3030 per 1,0001,000 person-years.
The incidence rate (incidence density) measures the frequency of new disease cases relative to the exact person-time the population was at risk. The numerator is the 300300 incident cases of ESRD. The denominator is the sum of person-years (PY) contributed by all subjects until they develop the disease, die, are lost to follow-up, or complete the study. The total PY is calculated as follows:

- Completed without disease: 600600 subjects ×10\times 10 years = 6,0006,000 PY
- Lost to follow-up: 400400 subjects ×5\times 5 years = 2,0002,000 PY
- Developed ESRD: 300300 subjects ×4\times 4 years = 1,2001,200 PY
- Died of other causes: 200200 subjects ×4\times 4 years = 800800 PY

The total denominator is 6,000+2,000+1,200+800=10,0006,000 + 2,000 + 1,200 + 800 = 10,000 person-years. The incidence rate is therefore 30010,000\frac{300}{10,000}, which scales to 3030 per 1,0001,000 person-years.

Step-by-Step Solution

1
Identify the total number of new (incident) cases of the disease during the observation period.
There are 300300 incident cases of ESRD.
The numerator for an incidence rate calculation is strictly the count of newly diagnosed disease cases.
2
Calculate the person-years of follow-up for subjects who did not experience an event (those who completed the study or were lost to follow-up).
(600600 subjects ×10\times 10 years) + (400400 subjects ×5\times 5 years) = 6,000+2,000=8,0006,000 + 2,000 = 8,000 person-years.
Subjects contribute 'at-risk' person-time until they reach the end of the study or are censored due to loss to follow-up.
3
Calculate the person-years for subjects who were censored due to disease onset or competing mortality.
(300300 ESRD subjects ×4\times 4 years) + (200200 deceased subjects ×4\times 4 years) = 1,200+800=2,0001,200 + 800 = 2,000 person-years.
Subjects cease to be 'at risk' for the first occurrence of the disease once they either develop the disease or die from a competing risk, and thus stop contributing person-time.
4
Sum all person-years to determine the total denominator, then divide the incident cases by this denominator.
Total denominator = 8,000+2,000=10,0008,000 + 2,000 = 10,000 person-years. Incidence rate = 30010,000\frac{300}{10,000} person-years, which scales to 3030 per 1,0001,000 person-years.
Incidence rate (density) must reflect the exact accumulated person-time observed across the dynamic cohort.

Key Concept

Incidence rate (incidence density) is calculated by dividing the number of incident cases by the total person-time at risk, requiring precise accounting of follow-up duration for both censored individuals and those who develop the outcome.
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Topics

Measures of Disease Frequency

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