# Relationship Among Prevalence, Incidence Rate, and Average Duration of Disease

Prevalence is the proportion of a population that has a condition at a specific time, but the prevalence will be influenced by both the rate at which new cases are occurring and the average duration of the disease. Incidence reflects the rate at which new cases of disease are being added to the population (and becoming prevalent cases). Average duration of disease is also important, because the only way you can stop being a prevalent case is to be cured or to move out of the population or die. For example, about a decade ago the average duration of lung cancer was about six months. Therapy was ineffective and almost all lung cancer cases died. From the time of diagnosis, the average survival was only about six months. So, the prevalence of lung cancer was fairly low. In contrast, diabetes has a long average duration, since it can't be cured, but it can be controlled with medications, so the average duration of diabetes is long, and the prevalence is fairly high.

If the population is initially in a "steady state," meaning that prevalence is fairly constant and incidence and outflow [cure and death] are about equal), then the relationship among these three parameters can be described mathematically as:

P/(1-P) = IR x Avg. Duration,

where P= proportion of the population with the disease and (1-P) is the proportion without it, IR is the incidence rate, and Avg. Duration is the average time that people have the disease (from diagnosis until they are either cured or die). If the frequency of disease is rare (i.e., <10% of the population has it), then the relationship can be expressed as follow:

Prevalence = (Incidence Rate) x (Average Duration of Disease)

• If the average duration of disease remains constant, then preventive measures that reduce the incidence of disease would be expected to result in a decreased prevalence.
• Similarly, if the incidence remained constant, then developing a cure would reduce the average duration of disease, and this would also reduce the prevalence of disease.
• In the late 1990s anti-retroviral therapy was introduced and greatly improved the survival of people with HIV. However, they weren't cured of their disease, meaning that the average duration of disease increased. As a result, the prevalence of HIV increased during this period.

The relationship can be visualized by thinking of inflow and outflow from a reservoir. The fullness of the reservoir can be thought of as analogous to prevalence. Raindrops might represent incidence or the rate at which new cases of a disease are being added to the population, thus becoming prevalent cases. Water also flows out of the reservoir, analogous to removal of prevalent cases by virtue of either dying or being cured of the disease. Imagine that incidence (rainfall) and the rate of cure or death are initially equal; if so, the height of water in the reservoir will remain constant.

• If outflow from the reservoir (rates of cure or death among prevalent cases) remains constant and rainfall (incidence of new disease) increases, then the height of water in the reservoir will rise. Conversely, if incidence (rainfall) declines, then the water level will fall.
• If we start from steady state again, and the rate of rainfall remains constant, but the outflow (rate of cure or rate of death) increases, then the height of the water (prevalence) will fall. Conversely, if incidence is held constant, but outflow falls (e.g., if the lives of prevalent cases are prolonged, but they aren't cured, then the height of the water will rise.

## Calculating Average Duration of Disease

This relationship can also be used to calculate the average duration of disease under steady state circumstances. If Prevalence = (Incidence) X (Average Duration), then it follows that

Average Duration =  (Prevalence) / (Incidence)

Example: Suppose the incidence rate of lung cancer is 46 new cancers per 100,000 P-Y, and the prevalence is 23 per 100,000 population, then

Average Duration of Disease = (23/100,000 persons /  46/100,000 person-years  = 0.5 year

Conclusion: Individuals with lung cancer survived an average of 6 months from the time of diagnosis to death. If the prevalence of a disease has been more or less constant for the past ten years (i.e., new cases have been balanced by cures or deaths of prevalent cases), what would be the effect of a treatment that prolongs the life of people suffering from the disease?

If the prevalence of a disease has been more or less constant for the past ten years (i.e., new cases have been balanced by cures or deaths of prevalent cases), what would be the effect of a new program that reduces the incidence of the disease?

If the prevalence of a disease has been more or less constant for the past ten years (i.e., new cases have been balanced by cures or deaths of prevalent cases), what would be the effect if a large number of healthy people immigrated into the population?