2. Person-Time and Incidence Rate: When Counting People Fails
After this lesson you can
- Explain why late entry, loss to follow-up and competing events break a closed-cohort risk
- Add up person-time by hand, stopping each clock at the case, the loss or the end of follow-up
- Compute an incidence rate with its units and read it as a speed rather than a percent
- Compare risk and rate and choose the right one for a question
- Use prevalence is approximately incidence rate times duration, and state its two assumptions
- Predict how a treatment that prolongs survival without cure changes prevalence
The second counting lesson. It shows why a closed-cohort risk breaks down when people enter late, are lost, or have competing events, and replaces people with person-time as the denominator. It then contrasts the incidence rate with risk and links prevalence to the incidence rate and the average duration of a condition.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- Why can't I just compute a risk when people come and go?
Show answer
Risk divides new cases by the people at risk at the start, which assumes a closed cohort where nobody enters or leaves. In an open population people enter late, are lost to follow-up, or have a competing event such as death from another cause. Counting people at the start, at the end, or on average all mishandle that unequal follow-up, so the honest denominator is time at risk.
- How do I add up person-time?
Show answer
Start each person's clock when they enter observation and stop it at the first of: becoming a case, being lost, a competing event, or the end of the study. Add the observed time across everyone. In the five-person example, the contributions are 5, 4, 3, 3 and 1 person-years, for a total of 16.
- How is an incidence rate different from a risk?
Show answer
Risk is new cases over people at risk at the start; it has no units, lies between 0 and 1, and reads as a probability. The incidence rate is new cases over person-time at risk; it has units of one over time, has no upper bound, and reads as a speed. Risk needs a closed cohort; the rate does not.
- Can a rate of 50 per 1,000 person-years be read as 5 percent of people per year?
Show answer
Not in general. 1,000 person-years is not 1,000 people, so there is no group for the percent to be a percent of. The translation to a risk holds only when follow-up is short and nearly complete and the outcome is uncommon.
- How do prevalence, incidence and duration relate?
Show answer
Prevalence is approximately the incidence rate times the average duration of the condition. This simple product rests on two assumptions: a steady state, where inflow equals outflow, and an uncommon disease. In Oakhaven, 2 per 100 person-years times 3 years gives a prevalence of about 6 percent.
Practice quiz
- Question 1Five people contribute 5, 4, 3, 3 and 1 person-years, and two become cases. What is the incidence rate?
- Question 2Ten people followed for up to five years contribute 30 person-years, and three become cases. What is the rate?
- Question 3Which denominator does an incidence rate use?
- Question 4The incidence rate is 2 per 100 person-years, the average duration is 3 years, the population is in steady state and the disease is uncommon. Prevalence is about:
- Question 5A new treatment prevents death but does not cure. Over time, prevalence will:
- Question 6In the five-person set, Person B becomes a case at year four of a five-year study. How much person-time does Person B contribute?
- Question 7In the Oakhaven factory, exposed workers have 60 cases in 2,000 person-years and unexposed workers have 30 cases in 2,000 person-years. What is the rate ratio?
- Question 8Which statement about a rate is correct?
- Question 9A lethal acute disease with many new cases but a very short duration will usually show:
- Question 10Ten people are followed for up to five years. Why is "10 people times 5 years = 50 person-years" wrong when only 30 person-years were observed?
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Principles of Epidemiology is education in epidemiologic reasoning, not clinical, screening, or policy guidance. Every example is set in the fictional Oakhaven Health District, and every number is invented for teaching.