Incidence

Lead Author(s): Jeff Martin, MD

Definition of Incidence

Incidence counts new disease diagnoses during a defined time period.

Incidence vs Prevalence

The difference between incidence and prevalence is a fundamental distinction in epidemiology.

Incident sampling of both cases and controls is preferable to prevalent sampling

The Three Elements in Measures of Disease Incidence

Terminology is not standardized and is used carelessly even by those who know better.

Key to understanding measures is to pay attention to how these 3 elements are used:

• E = number of events = a binary outcome
• N = number of at-risk persons in the population under study
• T = time period during which the events are observed

Even the basic difference between prevalence and incidence is often ignored.

Measures of Incidence

Cumulative Incidence

• The proportion of individuals who experience the event in a defined time period (E/N during some time T) = cumulative incidence

Incidence Rate Using Person-Time

• The number of events divided by the amount of person-time observed or product of persons times time (E/NT) = incidence rate or density (not a proportion)

It is an important to distinguish between the two types of incidence because they are related to different types of analyses. Both are perfectly valid measures of incidence as both include E, N, and T. Both measures of incidence give valid incidence rates. They make some different assumptions and are associated with different analytic techniques, but both are very useful.

Szklo's table below summarizes the assumptions made for both types of analysis.

Denominator for Incidence Varies

The denominator for incidence does not have to be a count of individual persons as one can see in the following table.

Table 2. Different authors terminology of incidence measures (Tapia 1997).

			Incidence measured as
Author	Count of events	Events per time unit	Events per element-time unit	Probability
	E	E/T	E/NT	E/N
Last	Incidence		Person-years incidence rate	Cumulative incidence rate
Freeman		Incidence rate	Incidence density or force of morbidity
Kelsey			Incidence rate	Risk of probability of developing disease; cumulative incidence
Morgenstern		(Instantaneous) rate	"Relative rate"; (relative incidence rate)	Risk (of incidence)
Rothman			Incidence Rate	Cumulative incidence
Selvin			Incidence rate	Incidence proportion
Haberman1 Haberman2		Incidence rate		Incidence rate

As stated above there is a lack of a standard vocabulary for measures of incidence even among epidemiological text books. If you look at the chart above, we have added the E, N, and T to this table in order to show how focusing on those 3 elements can clarify what is being measured despite the differences in terminology among these authors.

Note, however, that when events per person-time unit is being measured, most authors call this a incidence rate (with one of these author calling it an incidence density).

Disease Incidence Key Concept

Numerator is always the number of new events in a time period (E)

Examine the denominator (persons or person-time) to determine the type of incidence measure

Looking at whether the denominator is a number of persons or the product of persons times time will tell you whether you are looking at cumulative incidence or at an incidence rate.

• If you are looking at cumulative incidence, the authors should have given the time at which it was calculated (e.g., 43% at 3 years).

Explicitly Account for E, N, and T

These are examples where either the number of events (E), the number (N) of persons, or the time (T) are not explicitly stated.

References

Freeman, J., & Hutchison, G. B. (1980). Prevalence, incidence and duration. Am J Epidemiol, 112 (5), 707-723.

Haberman, S. (1978a). Mathematical treatment of the incidence and prevalence of disease. Soc Sci Med, 12, 147 – 152.

Haberman, S. (1978b). Probalistic treatment of the incidence and prevalence of disease. Soc Sci Med, 12, 159 – 161.

Kelsey, J., Douglas, T., & Evans, A. (1980). Methods in Observational Epidemiology. New York: Oxford University Press.

Last, J. (1995). A Dictionary of Epidemiology (3rd ed.). New York: Oxford University Press.

Morgenstern, H., Kleinbaum, D. G., & Kupper, L. L. (1980). Department of Epidemiology and Public Health, School of Medicine, Yale University, New Haven, CT. Int J Epidemiol, 9(1), 97-104.

Rothman, K. (1986). Modern Epidemiology. Boston: Little, Brown.

Selvin, S. (1991). Statistical Analysis of Epidemiologic Data. New York: Oxford University Press

Szklo, M., & Nieto, F. (2007). Epidemiology: Beyond the Basics (2nd Edition ed.). Boston: Jones and Bartlett Publishers.

Tapia Granados, J. A. (1997). On the terminology and dimensions of incidence. J Clin Epidemiol, 50 (8), 891-897.

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