Measures of disease frequency

A very common aim of epidemiological investigation is to estimate the frequency of disease in a population. This is of particular importance in the case of surveillance and disease monitoring systems, and is commonly the central aim of many descriptive studies. There are two main measures of disease frequency used by epidemiologists - the prevalence and the incidence of disease, which each measure different aspects of disease. The survival time, which is closely associated with the incidence, is another measure commonly used. Counts of disease are not commonly used in epidemiological studies, although they can be useful when deciding upon resource requirements when implementing disease control strategies.

Counts

Disease counts (i.e. the number of diseased animals at a point in time or over a period of time) provide a useful measure of the number of animals experiencing the disease in question. As such, they are commonly used when disseminating information to the general public, or when deciding upon the resources required to control or manage the disease. However, the figures given in disease counts are not shown in relation to the size of the population of interest (that is, there is no 'denominator'), and so alone do not provide sufficient information for epidemiological investigation or interpretation.

Prevalence

The prevalence (also known as the prevalence risk') of a disease is the proportion of animals in the population of interest which are 'diseased' at any specific point in time, and is calculated by dividing the number of cases of disease by the total size of the population. This may be a single point (in which case, the measure is the point prevalence), or may be over a period (in which case the period prevalence is given). However, it is important to realise that this measure will therefore include both old and new cases of disease, which can be a problem when attempting to investigate risk factors for a disease of long duration (as many of the diseased animals are likely to have had the disease for some time). The prevalence can be viewed at an individual animal level as the 'probability that an animal selected at random from the population will be diseased'. The prevalence of disease is commonly obtained from surveys or cross sectional studies, although in some cases, cohort studies may be appropriate (dependent on how animals were selected).

Incidence

The incidence of disease describes the frequency of new cases of disease amongst previously nondiseased animals, and there are two main methods of measuring it - known as the incidence risk and the incidence rate. The incidence can only be measured from studies which follow animals up over time, such as cohort studies and randomised controlled trials.

Incidence risk

The incidence risk (also known as the cumulative incidence) is the proportion of nondiseased animals which develop disease over a particular period of time, and so only relates to the period of time in question (meaning that this period must always be stated along with the risk estimate). It is calculated as the number of animals which develop disease over the period in question divided by the number of nondiseased animals at the start of the study. This measure assumes that disease does not occur more than once for any individual, that no animals are added to the population over the period of investigation, and that if animals are removed from the population over this period without experiencing disease, that these were lost half way through the study. Animals lost from the study over the study period are accounted for in the calculation of incidence by subtracting half an animal per animal lost from the total number of nondiseased animals at the start of the study. At the individual animal level, the incidence risk can be interpreted as the probability that a nondiseased animal will develop the disease over the period of time in question.

Incidence rate

The incidence rate is a measure of the frequency of disease in relation to both the number of nondiseased animals and the total amount of time for which these animals were followed, meaning that the time period does not need to be provided in order for it to be interpretable. It can also be viewed as the 'instantaneous rate of disease' at any point over the period of investigation (and therefore assumes that this rate is constant over the period). It is calculated by dividing the number of cases of disease over the period of study with the total number of animal-time units which were contributed over this period. These animal-time units are estimated by adding together the total amount of time which each animal was present in the study for (i.e. until animals experienced disease, left the study for other reasons, or the study concluded) for each animal in the study. Examples of animal-time units may be cow-days, or dog-weeks, or horse-years, and so on. As each individual animal contributes its own number of animal-time units, animals which enter the study population during the study period can be included, as can animals which experience more than one episode of disease (in which case, it must be ensured that animals which have experienced disease and are susceptible again contribute animal-time units to the denominator). Unlike the prevalence and the incidence risk, the incidence rate has no interpretation at the individal animal level, only at the population level.

Survival time analysis

Survival analysis (also known as the time-to-event analysis) includes similar concepts to both the incidence risk and the incidence rate, but adopts a different approach to investigation and interpretation. Survival time analysis can be recognised as comprising two different measurements: the survivor function (and survival time) and the hazard function. Of these, the survivor function is most commonly used as a method of data description, with the hazard function being used for comparison of disease experience between groups in the case of analytic studies. As for incidence measurement, these measures are based upon following an initially disease-free population of animals over time, and so require studies such as cohort studies.

Survivor function

The survival function (also known as the cumulative survival probability) describes the proportion of initially disease-free individuals who have not experienced the outcome of interest over time, and so is similar conceptually to the incidence risk. The survival time may be visualised graphically (using a Kaplan-Meier curve, for example) or may be summarised using the survival time. Survival time is measured in units of time and describes the time until animals experience disease. Commonly, the median survival time is presented, which is the time at which 50% of the population have experienced the event (this is the most appropriate measure of the 'average' survival time, as the mean would not be able to account for individuals who have not experienced the outcome by the end of the study). However, if 50% of the individuals have not experienced disease by the end of the study, the median survival time cannot be calculated. Another option is to describe the proportion of individuals who have experienced/not experienced disease at a set point in time, which is the same concept as the incidence risk.

Hazard function

The hazard function describes the pattern of the 'incidence rate' over time (rather than summing an 'average' estimate over the duration of the study, as with the incidence rate itself). Although the hazard function may be described graphically, it is most commonly used in analytic studies, when hazard functions are compared in the form of a hazard ratio (a measure of strength of association).