Epidemiologic Measures

Core Concepts

The four building blocks: counts, ratios, proportions, and rates

A count is the raw number of events (e.g., 40 new cases). A ratio is one number divided by another, where the two need not be related (e.g., male-to-female cases, 2:1). A proportion is a ratio in which the numerator is included in the denominator — the fraction of a population that has the characteristic (e.g., 40 cases out of 2,000 people = 0.02 or 2%); proportions range from 0 to 1. A rate adds time to the denominator: cases per population per unit of time, such as "12 new cases per 1,000 people per year." Rates are the only measure that lets you compare disease occurrence between populations of different sizes or over different time spans.

Prevalence: the pool of existing disease

Prevalence counts existing cases in a defined population at a given time.

• Point prevalence = (number of existing cases at a moment) ÷ (population at that moment).
• Period prevalence = cases existing at any time during a window ÷ average population over the window.

Prevalence describes the burden of disease — how much exists now — guiding staffing, services, and resources. It is a snapshot, not a flow: it rises when new cases appear or when people live longer with the condition (improved survival). For stable situations, prevalence ≈ incidence × average duration of disease, so a chronic condition can have high prevalence but low incidence, and vice versa.

Incidence: the flow of new cases

Incidence counts new cases over a period of time — the rate at which people become ill. Two versions:

• Cumulative incidence (risk) = (number of new cases during the period) ÷ (number of people at risk at the start). It is a proportion with no units of time in the denominator, and it assumes everyone was followed for the full period. Person-time is the sum of time each person was observed and at risk (e.g., 1,000 person-years could be 1,000 people followed one year or 500 followed two). Because it accounts for people entering, leaving, or dying during follow-up, the incidence rate is the more precise measure used in most surveillance reporting.

Incidence is the measure of risk — the probability that a person in the population will develop the condition — and it is the foundation of etiologic (cause-seeking) research.

Measures of association: comparing exposed and unexposed

To ask "does exposure matter?", compare the occurrence of disease between exposed and unexposed groups.

• Risk ratio / relative risk (RR) = risk in the exposed ÷ risk in the unexposed (from cohort studies or trials). RR = 1 means no association; RR > 1 means higher risk in the exposed group; RR < 1 means lower risk (protective).
• Odds ratio (OR) = odds of exposure in cases ÷ odds of exposure in controls (from case-control studies, calculated as ad/bc from a 2×2 table). When the outcome is rare, the OR closely approximates the RR; when the outcome is common, the OR overstates the RR and should be interpreted with care.
• Risk difference / attributable risk (AR) = risk in exposed − risk in unexposed. This is the excess risk that can be attributed to the exposure — arguably the most useful number for public health, because it states how many cases per population would be prevented if the exposure were removed (assuming the association is causal).

Measures of impact: how much does the exposure matter to the population?

• Attributable risk percent (ARP) = (risk exposed − risk unexposed) ÷ risk exposed × 100 — the proportion of cases among the exposed attributable to the exposure.
• Population attributable fraction (PAF) additionally accounts for how common the exposure is: a large RR applied to a rare exposure affects few people, while a modest RR applied to a common exposure can drive most of a population's cases. PAF tells decision-makers where intervention will yield the greatest community benefit.

Rates in practice: attack rates and mortality measures

During outbreaks, the attack rate — (number of people who became ill) ÷ (number exposed) over the outbreak period — measures how widely an exposure spread; the secondary attack rate counts new cases among contacts of known cases and reflects person-to-person transmission. Among mortality measures, the case-fatality ratio (deaths among those with the disease) is a proportion, not a rate, and describes severity, while crude mortality rates describe deaths per population per time. Because crude rates mix populations of different age structures, standardized (adjusted) rates apply a common age structure so comparisons reflect real risk differences rather than age differences. What matters here is knowing which measure answers which question; exact formulas are found in current epidemiology references.

Common Confusions