# Cumulative Incidence - Person-Time

*Lead Author(s):* Jeff Martin, MD
## Definition of Cumulative Incidence

The **proportion** of individuals who experience the event in a defined time period **(E/N during some time T) = cumulative incidence**
**OR**
**E(vent)/N(umber) during some time T(ime) = cumulative incidence**
## Time Period for Cumulative Incidence

If the measure is a proportion of persons, it is unitless since it has to vary between 0 and 1. In other words it is a probability.
- But because it is unitless, the time element T has to be explicitly added; for example, the proportion of persons diagnosed during a one-year period. This is a common error in the literature. The time period for cumulative incidence is often missing.

## Cumulative Incidence Measure

Perhaps **most intuitive measure of incidence** since it is just proportion of those observed who got the disease
- Proportion = probability =
**risk**

- Basis for
**Survival Analysis**

Two primary methods for calculating cumulative incidence:
Of the two methods for calculating cumulative incidence, the life table method is older but is now seldom used except in actuarial tables of life expectancy and a few similar settings with large numbers of persons. The Kaplan-Meier method is very similar and has become the usual method for estimating cumulative incidence.
## Calculating Cumulative Incidence

**With complete follow-up cumulative incidence is just number of events (E) divided by the number of persons (N) = E/N**
The simplest situation in which to calculate cumulative incidence is if all of the persons are followed for the same length of time.
- In that case the cumulative incidence is simply the total number of events divided by the total number of persons.
*All individuals are included in the denominator,*
- In long term cohort studies this never happens, but in the time limited outbreak investigations typical of a CDC investigation of gastroenteritis, it may well happen.
- Although technically one still needs to attach a time period to the analysis (at one week, or some such), an outbreak of gastrointestinal illness is usually understood to be a matter of a few days, so even that element will probably be omitted.

**Outbreak investigations, such as of gastrointestinal illness, typically calculate ***attack rates* with complete follow-up on a *cohort* of persons who were exposed at the beginning of the epidemic. An example can be found in the GI illness in Livington County.
Unfortunately, the term *attack rate* has traditionally been used to describe the proportion of persons who develop illness.
- As we have been arguing, this is an incorrect use of
*rate*, since the denominator is just the number of persons investigated.
- Another example of how terminology in the literature can be confusing.

## Clinical Trial Denominator

Counting all individuals in the denominator can also be found in a clinical trial, which you will recall is formally a type of cohort study.
- A very well run clinical trial of a non-fatal condition with relatively short follow-up time might achieve the same amount of follow-up time on everyone enrolled if everyone were enrolled on the same day (as in the gastroenteritis example everyone was exposed on the same day).
- But it is a rare study that enrolls everyone on one day, yet nearly all studies stop on a given day, resulting in some difference in follow-up time even if no one was lost or dropped out.

## Specifying Time Period for Cumulative Incidence

Calculating cumulative incidence with different follow-up times, assumes the probability of the outcome is not changing during the study period = **no temporal/secular trends affecting the outcome.**
**Cumulative incidence cannot be interpreted without specifying the time period.**
- The cumulative incidence of death for the whole U.S. population at 1 year is about 0.8% but at 100 years it is greater than 99.9%.

## Temporal Trends

**Temporal trends**, such as improved survival, can lead to changes in cumulative incidence as seen in the Australian children's cancer study and the SEER cancer monitoring program.
**The longer the follow-up period of an analysis**, the greater the threat that changes in the underlying incidence rate of the outcome may be causing an estimate of cumulative incidence to be invalid.
Changes in treatment are a common way in which survival analysis may be biased by the assumption of no temporal trends.
There are other changes that can produce **temporal trend bias** as well, such as:
- changes in living habits,
- epidemics,
- environmental hazards that apply only during specific periods,
- etc.