PUBH5010 · Epidemiology Methods And Uses
Measures of Frequency
Before you can compare two groups you have to count disease correctly, and the first question is always which denominator are you dividing by? A ratio divides two unrelated quantities; a proportion is a ratio whose numerator is part of its denominator (so it runs 0–1); a rate divides events by the person-time at risk and carries units of 1/time. The two headline measures are prevalence — the proportion of a population that has the disease at a point (point prevalence) or over an interval (period prevalence) — and incidence, which counts new cases: cumulative incidence (new cases ÷ people at risk at the start, a risk, 0–1) and the incidence rate (new cases ÷ total person-time, a rate). The trap that costs marks is using the wrong denominator: prevalence needs the whole population, cumulative incidence needs only those at risk and disease-free at baseline, and the incidence rate needs person-time, which you must sometimes build up from individual follow-up. Prevalence ≈ incidence × average duration ties the two together — anything that lengthens survival without curing raises prevalence even if incidence is flat.
What this chapter covers
- 01Ratio vs proportion vs rate, and the units each carries
- 02Point prevalence and period prevalence
- 03Cumulative incidence (a risk) and the at-risk denominator
- 04The incidence rate and the person-time denominator
- 05Computing person-time from individual follow-up
- 06Prevalence ≈ incidence × duration, and what it implies
- 07Choosing the right frequency measure for the question
Worked example: cumulative incidence vs incidence rate from follow-up
- +1(a) Cumulative incidence. New cases over people at risk at the start: CI = 40/500 = 0.08 (8% over one year). It is a proportion, dimensionless, bounded 0–1.
- +2(b) Build the person-time. The 460 non-cases each contribute 1.0 year = 460 py; the 40 cases each contribute about 0.5 year = 20 py. Total = 480 person-years.
- +1Incidence rate. IR = 40 / 480 = 0.083 per person-year (about 83 per 1,000 py). It is a rate, with units of 1/time.
- +1(c) Why they differ. The cumulative incidence uses everyone's start as the denominator; the incidence rate credits only the time people were actually at risk, which is less for those who became cases. Removing their post-event time shrinks the denominator, so the rate is slightly higher than the risk.
Key terms
- Prevalence
- The proportion of a defined population that has the disease at a given time — point prevalence at an instant, period prevalence over an interval. It measures existing burden, depends on both how many get the disease and how long they have it, and is the natural output of a cross-sectional study.
- Cumulative incidence
- New cases arising over a period divided by the number of disease-free people at risk at the start — a risk, a proportion bounded 0–1. It requires a closed at-risk group followed for the whole period and assumes negligible loss to follow-up.
- Incidence rate
- New cases divided by the total person-time at risk, with units of 1/time (e.g. per person-year). It handles people entering, leaving and being followed for different lengths of time, by crediting each only for the time they were actually at risk.
- Person-time
- The sum of the time each individual is followed while at risk of the outcome — the denominator of an incidence rate. A person followed for 2 years contributes 2 person-years; someone who develops the outcome or is lost contributes only the time up to that point.
- Prevalence ≈ incidence × duration
- In a steady state, prevalence is roughly the incidence rate multiplied by the average duration of disease. It explains why a treatment that extends survival without curing raises prevalence even when incidence is unchanged, and why prevalence is a poor measure of risk.
Measures of Frequency FAQ
What's the difference between prevalence and incidence?
Prevalence counts all existing cases (old and new) at a point in time, as a proportion of the population — it measures the burden of disease. Incidence counts only new cases over a period — it measures the risk or rate of getting the disease. A long-lasting disease can have high prevalence but low incidence; a quickly-fatal or quickly-cured one can have high incidence but low prevalence.
When do I use a rate instead of a risk?
Use a risk (cumulative incidence) when you have a fixed group followed for the same period with little loss to follow-up. Use an incidence rate when follow-up varies between people — some enter late, some are lost, some develop the outcome partway through — because the rate's person-time denominator credits each person only for the time they were actually at risk.
How do I compute person-time?
Add up the time each person is followed while still at risk. Someone followed the whole 2-year study contributes 2 person-years; someone who develops the outcome or drops out after 8 months contributes 8/12 of a year. The total is the denominator of the incidence rate; the number of new cases is the numerator.
Why does prevalence rise when treatment improves survival?
Because prevalence ≈ incidence × duration. A treatment that lets people live longer with the disease (without curing it) increases the average duration, so even with the same incidence, more people are alive with the disease at any moment — prevalence goes up. This is why prevalence should not be read as a measure of risk.
Exam move
Treat "which denominator?" as the first question of every frequency item: prevalence divides by the whole population, cumulative incidence by those at risk and disease-free at baseline, and the incidence rate by person-time. Practise building person-time from individual follow-up lines, because that is where marks are lost. Keep the units straight — proportions are dimensionless 0–1, rates carry 1/time — and remember prevalence ≈ incidence × duration for the conceptual questions about why prevalence can move without incidence moving.
