Questions: Person-Time Calculations and Follow-Up Study Design

Question 1

In a 10-year cohort study, participant A develops the outcome at year 7. Participant B is lost to follow-up after 3 years without experiencing the outcome. How much person-time does each contribute?

• A. A contributes 7 person-years; B contributes 0 (censored participants are excluded)
• B. A contributes 10 person-years; B contributes 10 person-years (both enrolled for the full study)
• C. A contributes 7 person-years; B contributes 3 person-years (each contributes until follow-up ends)
• D. A contributes 7 person-years; B contributes 10 person-years (B assumed event-free for full study)

Answer: (C)

A contributes time until the outcome event — 7 years. B contributes time until censoring — 3 years. Censored participants are NOT excluded (option 0 is wrong); their follow-up time correctly contributes to the denominator. They are NOT assigned the full study duration (options 1 and 3) because we don't know what happened after loss to follow-up. Each participant contributes exactly the time they were actually observed — this is the fundamental accounting principle of person-time analysis.

Question 2

A cohort study records 25 new cases among 500 participants. After accounting for losses to follow-up, the total person-time is 2,200 person-years rather than the maximum possible 2,500. What is the correct incidence rate?

• A. 5 cases per 100 participants (25/500)
• B. 11.4 cases per 1,000 person-years (25/2,200 × 1,000)
• C. 10 cases per 1,000 person-years (25/2,500 × 1,000)
• D. 5% incidence (25/500 = 0.05)

Answer: (B)

The incidence rate uses the actual observed person-time denominator: 25 ÷ 2,200 = 0.01136 per person-year = 11.4 per 1,000 person-years. Using 2,500 person-years (option 2) would underestimate the rate by pretending censored participants contributed time they didn't. Options 0 and 3 calculate cumulative incidence (a proportion), not an incidence rate — they ignore unequal follow-up duration entirely and cannot be directly compared across studies with different designs.

Question 3

A participant who leaves a cohort study early (lost to follow-up) should be excluded from the analysis to prevent bias.

• T. True
• F. False

Answer: False

Excluding censored participants would both waste valid data and introduce bias. Their observed follow-up time correctly contributes to the person-time denominator up to the point of censoring. Person-time analysis was specifically designed to handle incomplete follow-up: each participant contributes what was actually observed. Systematic exclusion of censored participants would remove those who may differ from completers in important ways, potentially biasing incidence estimates more than proper censoring handling does.

Question 4

The incidence rate calculated using person-time is comparable across studies with very different follow-up durations, because it accounts for how long each person was actually observed.

• T. True
• F. False

Answer: True

This is the key advantage of person-time analysis. Whether participants are followed for 1 year or 8 years, their contributions to the denominator are proportional to actual observation time. The resulting incidence rate (cases per person-year) is a rate — an intensity of event occurrence per unit of time — that is directly comparable across studies with different designs, enrollment windows, and follow-up durations. Simple cumulative incidence (a proportion) cannot do this because it depends on the length of the observation period.

Question 5

What is 'non-informative censoring,' and why is it an important assumption underlying person-time analysis?

Model answer: Non-informative censoring means the reason a participant's follow-up ended does not predict whether they would have experienced the outcome. Under this assumption, censored participants are representative of those who remained under observation — their unobserved future is similar to the observed future of those who stayed. If censoring is informative (e.g., sick participants are more likely to drop out), the incidence rate will be biased because censored individuals are not exchangeable with those still under observation.

This is why high loss to follow-up threatens validity in cohort studies — not because censoring itself is wrong, but because informative censoring violates the exchangeability assumption. Investigators minimize this threat by tracking participants aggressively, investigating reasons for dropout, and using sensitivity analyses to test how much informative censoring could plausibly change their conclusions.