Cumulative Incidence

Cumulative incidence is the proportion of an initially disease-free population that develops a condition over a specified period. Also called the incidence proportion or risk, it is calculated as the number of new cases divided by the number of people at risk at the start of follow-up, yielding a dimensionless value between 0 and 1 that directly estimates the probability of developing the condition.

Definition

Cumulative incidence is the proportion of a defined at-risk, initially disease-free population that develops the condition during a specified period, computed as new cases divided by the number of people at risk at the start of the interval.

Scope

This entry covers cumulative incidence as one of the two forms of incidence: its definition as a proportion, its interpretation as average risk over a defined interval, the assumption of complete follow-up that it relies on, and how it differs from incidence density. It is methodological and does not provide clinical guidance.

Key concepts

• Incidence proportion
• Risk as a probability
• Population at risk at baseline
• Fixed reference period
• Dimensionless value between 0 and 1
• Sensitivity to loss to follow-up

Mechanisms

Cumulative incidence takes the number who newly develop the condition over a period and divides it by the number at risk when the period began. Because the denominator is a count of people rather than person-time, the result is a proportion that estimates the average probability, or risk, that an at-risk individual develops the condition over that fixed interval. Its validity rests on knowing the outcome status of everyone in the starting group for the whole period; when people are lost to follow-up or are removed by competing events, the simple proportion becomes biased, and survival or actuarial methods are used to estimate cumulative incidence in the presence of incomplete follow-up. Cumulative incidence is always tied to a stated length of time, since longer observation allows more cases to accumulate.

Clinical relevance

Cumulative incidence is the measure that expresses risk over a defined horizon and is the frequency measure behind risk differences and risk ratios, so it is central to appraising evidence about how likely an outcome is over time. It describes average population risk and is not a prediction for, or instruction about, any individual patient.

Epidemiology

Cumulative incidence is the natural risk measure in cohort studies and randomised trials with a defined follow-up period, and in outbreak investigations, where the attack rate is a cumulative incidence over the outbreak. It is most straightforward when follow-up is complete and short; with long follow-up or substantial dropout, time-to-event methods are preferred to recover an unbiased estimate.

History

The distinction between incidence as a proportion (risk) and incidence as a rate emerged as twentieth-century epidemiology formalised the role of the denominator and of follow-up time. Standard textbooks and dictionaries codified cumulative incidence as the probability interpretation of incidence, and the link to survival-analytic estimation under incomplete follow-up was made explicit in the methodological literature.

Debates

How should incomplete follow-up be handled?

The simple proportion assumes every person is observed for the full period; when people are lost to follow-up or experience competing events, this assumption fails, and survival or competing-risks methods are needed to estimate cumulative incidence without bias.

Seminal works

• grimes-cohort-2002
• rothman-2008
• porta-2014

Frequently asked questions

Is cumulative incidence the same as risk?

Yes. Cumulative incidence, also called the incidence proportion, estimates the average probability that an at-risk person develops the condition over a specified period, which is what is meant by risk over that interval.

How does cumulative incidence differ from incidence density?

Cumulative incidence divides new cases by the number of people at risk and is a dimensionless proportion tied to a fixed period; incidence density divides new cases by accumulated person-time and is a rate with units of inverse time.