## Event Rates

In the example given in the “Incidence and Prevalence” section that illustrates prevalence growth, we stated that the death rate was 20% per year. This is one way of describing the rate of an event such as death. It states that 20% of all patients prevalent during one year died during that year. In fact, expressing the event rate in this way does not provide much information. It does not tell us anything about how long the patients survived before death. If all the deaths occurred in patients who had been on treatment less than 6 months, then that would have a different meaning than if the deaths occurred in those patients who had been on treatment for several years.

### Events per Period Risk

To get around this problem another way of reporting events is used: event rate per period at risk. For this calculation and to express, for example, death rate per years at risk, the number of days that each prevalent patient is at risk is summed and divided by 365. If a patient is incident on February 1st and dies on March 31st the period risk is (28+30) days which is (58/365 = 0.16) of one year risk. A patient who enters treatment on or before January 1st and is alive on December 31st contributes (365/365 = 1) year of risk during that year.  The number of deaths during the year is then expressed as the rate for the total number of contributed patient years. Similarly, death rate may be expressed per 100 years or per 1000 years; the choice of denominator depends on what makes sensible reporting. More stable and consistent data may be obtained if the risk period and rate is extended to a longer period (e.g., 2 or 3 years). Any other event such as hospitalization, rate of infection, etc. can be similarly described.

Event rates reported in this way may be further categorized by demographic or diagnostic characteristic of a patient subset – e.g., death rate in diabetic patients or death rate in males. Event rates between groups can then be compared – e.g., whether male death rate exceeds female death rate. Moreover, such rates can be compared using appropriate statistical methods to determine whether a detected difference is significant (a variety of more or less complex statistical methods are available for such measurement; in essence, they bear some similarity to the Chi-square test described earlier).

#### References:

Greenberg RS, Daniels SR, Flanders WD, Eley JW, Boring JR. Chapter 4. Medical Surveillance. In: Greenberg RS, Daniels SR, Flanders WD, Eley JW, Boring JR, eds. Medical Epidemiology. 4th ed. New York: McGraw-Hill; 2005.

Dawson B, Trapp RG. Chapter 3. Summarizing Data & Presenting Data in Tables & Graphs. In: Dawson B, Trapp RG, eds. Basic & Clinical Biostatistics. 4th ed. New York: McGraw-Hill; 2004.

Lashner BA, Kirsner JB. Chapter 12. Describing Patterns of Disease and Disability in Populations. In: Lang TA, Secic M, eds. How to Report Statistics in Medicine. 2nd ed. Philadelphia: American College of Physicians; 2006.

P/N 101855-01 Rev B 02/2021