Hazard Rate

The hazard rate is a measure used to quantify the relative frequency of disease occurrence in a population [Page 458]and plays an important role in descriptive and etiologic investigations. The definition of hazard rate is given as the instantaneous change in the occurrence of new cases per unit change of time at a particular time point, relative to the size of the disease-free population at that particular point in time. It is a theoretical limit of the rate as the time interval goes to zero and could seldom be obtained in reality. Instead, an average rate for a given period is usually estimated and used in epidemiology, analogous to the use of speed as an estimate of average velocity. This average rate is called the incidence rate, force of morbidity or mortality, or incidence density.

Typically, the incidence rate is estimated from studies that involve the follow-up of a population, such as cohort studies. The estimate of incidence rate takes into account both the number of new cases and the size and follow-up time of population:

The denominator is the sum of each individual's follow-up time until the occurrence of disease or until the end of the study. Therefore, the above calculation accounts for the situation that different individuals were observed for different lengths of time. As a hypothetical example, suppose that eight healthy 60-yearold women without coronary heart disease (CHD) were followed up to study the incidence rate of CHD. One of them developed CHD after 1 year of followup, two of them developed CHD after 3 years of follow-up, one of them was lost to follow-up without developing CHD after 4 years, and the last four did not develop CHD after 5 years at the end of the study. Thentherearethreenewcaseswithinthe5-yearstudy period and total person-time of observation = (1 × 1) +(2 × 3) + 4 + (4 × 5) = 31 person-years and the incidence rate = 3/31 person-years = 0.097/personyears. For most chronic diseases, especially incurable conditions, such as diabetes and multiple sclerosis, the deathrate, hazard rate, and incidence rate often include only the first occurrence of new cases. For recurring disease such as cancer or heart disease, both first and subsequent occurrence could be of great interest.

The numerical value of hazard rate and incidence rate has a low bound of zero but has no upper bound. Their interpretability depends on the selection of the time unit. The above incidence rate of 0.097/person-years could be expressed as 0.008/person-months, or 97/1,000 person-years. It is thus essential in presenting incidence rates with appropriate time units. For clarity, the numerator is often expressed as a power of 10. Incidence rate should not be confused with prevalence, which is defined as the number of individuals with a certain disease in a population at a specified time divided by the population size at that time.