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# Cumulative Incidence - Person-Time

## 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.

Topic revision: r25 - 03 Jun 2009 - 12:15:31 - MaryB?

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