# The relationship between incidence and prevalence rates

### Measures of disease frequency and disease burden | Health Knowledge a) Prevalence b) Incidence c) Calculation of person-time at risk d) Issues in defining the population at risk e) The relationships between incidence and. The mathematical treatment of incidence and prevalence reported elsewhere by the author is extended here to establish an exact implicit equation for the point. The denominator for incidence rates is the population at risk. Formula: The relationship between prevalence & incidence: An illustration.

Person-time at risk Person-time at risk is a measure of the number of persons at risk during the given time-period.

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

In the graph below, different numbers of persons are at risk N-d during the time-period t. The total person-time at risk is represented by the area below the line Y.

Persons who have developed the disease d are no longer considered at risk as they already have the disease. Person-time years at risk for 5 individuals in a hypothetical cohort study between In the above example the incidence rate for disease X is calculated as: Note that for most rare diseases, risks and rates are numerically similar because the number at risk will approximately equal the total population at all times.

Issues in defining the population at risk For any measure of disease frequency, precise definition of the denominator is essential for accuracy and clarity  The population at risk denominator should include all persons at risk of developing the outcome under investigation.

• Lesson 3: Measures of Risk
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• Relationship Among Prevalence, Incidence Rate, and Average Duration of Disease

Therefore, individuals who currently have the disease under study or who are immune e. However, this is not always possible in practice  Note that when individuals not at risk of the disease are included in the denominator population at risk the resultant measure of disease frequency will underestimate the true incidence of disease in the population under investigation 5. The relationship between prevalence and incidence The proportion of the population that has a disease at a point in time prevalence and the rate of occurrence of new disease during a period of time incidence are closely related . The incidence rate r 2. The duration of disease T For example, if the incidence of a disease is low but the duration of disease i.

Mortality, Morbidity and Epidemiology

For example diseases like leprosy or tuberculosis tend to persist for a longer duration, from months to years, hence the prevalence old and new cases would be longer than the incidence. Conversely, if the incidence of a disease is high and the duration of the disease is short, the prevalence will be low relative to the incidence .

For example, acute conditions like diarrhoea have a relatively short duration a few days. A change in the duration of a disease, for example the development of a new treatment which prevents death but does not result in a cure will lead to an increase in prevalence. Fatal diseases or diseases from which a rapid recovery is common have a low prevalence, whereas diseases with a low incidence may have a high prevalence if they are incurable but rarely fatal and have a long duration.

## Incidence and Prevalence

The relationship between incidence and prevalence can be expressed as: In such theoretical circumstances, the point prevalence of disease is approximately equal to the product of the incidence rate and the mean duration of disease i. Other commonly used measures of disease frequency in epidemiology Measures of effect Measures of effect are used in epidemiological studies to assess the strength of an association between a putative risk factor and the subsequent occurrence of disease.

This requires that the incidence of disease in a group of persons exposed to a potential risk factor is compared with the incidence in a group of persons not exposed to the potential risk factor. This comparison can be summarized by calculating either the ratio of measures of disease frequency for the two groups or the difference between the two, and reflects the increase in frequency of disease in one population compared with another, treated as baseline.

These measures are often collectively referred to as measures of relative risk The relative risk is a measure of the strength of an association between an exposure and disease and can be used to assess whether a valid observed association is likely to be causal . The most commonly used measure of effect is the ratio of incidence rates that is: 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. Calculating Average Duration of Disease This relationship can also be used to calculate the average duration of disease under steady state circumstances.

### Concept: Prevalence and Incidence

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. It would increase the prevalence.

It would decrease the prevalence. It would have no effect on prevalence. The effect cannot be predicted from the information given. 