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**OR**

**E(vent)/N(umber) during some time T(ime) = cumulative incidence**

- 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.

- Proportion = probability =
**risk**

- Basis for
**Survival Analysis**

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.

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.

**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%.

**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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