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Incidence (epidemiology)

Incidence (epidemiology) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Incidence (epidemiology) rather than just read about it. In short: In epidemiology, incidence reflects the number of new cases of a given medical condition in a population within a specified period of time. Incidence proportion Incidence proportion (IP), also known as cumulative incidence, is defined as the probability that a particular event, such as occurrence of a particular disease, has occurred in a specified period: Incidence = number of subjects developing disease over a cer…

Incidence (epidemiology) — main illustration
Incidence (epidemiology) — illustration

Key takeaways

  • Incidence (epidemiology) belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Incidence (epidemiology) to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Incidence (epidemiology) from memory before moving on to harder problems.

Reference excerpt

In epidemiology, incidence reflects the number of new cases of a given medical condition in a population within a specified period of time.

Incidence proportion Incidence proportion (IP), also known as cumulative incidence, is defined as the probability that a particular event, such as occurrence of a particular disease, has occurred in a specified period:

Incidence = number of subjects developing disease over a certain period total number of subjects followed over that period {\displaystyle {\text{Incidence}}={\frac {\text{number of subjects developing disease over a certain period}}{\text{total number of subjects followed over that period}}}}

For example, if a population contains 1,000 persons and 28 develop a condition from the time the disease first occurred until two years later, the cumulative incidence is 28 cases per 1,000 persons, i.e. 2.8%.

Incidence rate The incidence rate can be calculated by dividing the number of subjects developing a disease by the total time at risk from all patients:

Incidence rate = number of subjects developing a disease total time at risk for whole population to get the disease {\displaystyle {\text{Incidence rate}}={\frac {\text{number of subjects developing a disease}}{\text{total time at risk for whole population to get the disease}}}}

One of the important advantages of incidence rate is that it doesn't require all subjects to be present for the whole study because it's only interested in the time at risk.

Incidence vs. prevalence

Incidence should not be confused with prevalence, which is the proportion of cases in the population at a given time rather than rate of occurrence of new cases. Thus, incidence conveys information about the risk of contracting the disease, whereas prevalence indicates how widespread the disease is. Prevalence is the proportion of the total number of cases to the total population and is more a measure of the burden of the disease on society with no regard to time at risk or when subjects may have been exposed to a possible risk factor. Prevalence can also be measured with respect to a specific subgroup of a population. Incidence is usually more useful than prevalence in understanding the disease etiology: for example, if the incidence rate of a disease in a population increases, then there is a risk factor that promotes the incidence. For example, consider a disease that takes a long time to cure and was widespread in 2002 but dissipated in 2003. This disease will have both high incidence and high prevalence in 2002, but in 2003 it will have a low incidence yet will continue to have a high prevalence (because it takes a long time to cure, so the fraction of individuals that are affected remains high). In contrast, a disease that has a short duration may have a low prevalence and a high incidence. When the incidence is approximately constant for the duration of the disease, prevalence is approximately the product of disease incidence and average disease duration, so prevalence = incidence × duration. The importance of this equation is in the relation between prevalence and incidence; for example, when the incidence increases, then the prevalence must also increase. Note that this relation does not hold for age-specific prevalence and incidence, where the relation becomes more complicated.

Example Consider the following example. Say you are looking at a sample population of 225 people, and want to determine the incidence rate of developing HIV over a 10-year period:

At the beginning of the study (t=0) you find 25 cases of existing HIV. These people are not counted as they cannot develop HIV a second time. A follow-up at 5 years (t=5 years) finds 20 new cases of HIV. A second follow-up at the end of the study (t=10 years) finds 30 new cases. If you were to measure prevalence you would simply take the total number of cases (25 + 20 + 30 = 75) and divide by your sample population (225). So prevalence would be 75/225 = 0.33 or 33% (by the end of the study). This tells you how widespread HIV is in your sample population, but little about the actual risk of developing HIV for any person over a coming year. To measure incidence rate you must take into account how many years each person contributed to the study, and when they developed HIV because when a subject develops HIV he stops being at risk. When it is not known exactly when a person develops the disease in question, epidemiologists frequently use the actuarial method, and assume it was developed at a half-way point between follow-ups. In this calculation:

At 5 yrs you found 20 new cases, so you assume they developed HIV at 2.5 years, thus contributing (20 * 2.5) = 50 person-years of disease-free life. At 10 years you found 30 new cases. These people did not have HIV at 5 years, but did at 10, so you assume they were infected at 7.5 years, thus contributing (30 * 7.5) = 225 person-years of disease-free life. That is a total of (225 + 50) = 275 person years so far. You also want to account for the 150 people who never had or developed HIV over the 10-year period, (150 * 10) contributing 1500 person-years of disease-free life. That is a total of (1500 + 275) = 1775 person-years of life. Now take the 50 new cases of HIV, and divide by 1775 to get 0.028, or 28 cases of HIV per 1000 population, per year. In other words, if you were to follow 1000 people for one year, you would see 28 new cases of HIV. This is a much more accurate measure of risk than prevalence.

See also Attack rate Attributable risk Rate ratio

References

External links Calculation of standardized incidence rate Archived 2015-01-09 at the Wayback Machine PAMCOMP Person-Years Analysis and Computation Programme for calculating standardized incidence rates (SIRs)

Worked examples

Example 1 — a first encounter with Incidence (epidemiology)

Start with the simplest possible case. Write down what Incidence (epidemiology) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Incidence (epidemiology) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Incidence (epidemiology) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Incidence (epidemiology)

In research
Incidence (epidemiology) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Incidence (epidemiology) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Incidence (epidemiology) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Epidemiology, Hygiene, Medical statistics, so understanding it makes those chapters shorter.
In everyday life
Look for Incidence (epidemiology) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Incidence (epidemiology) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Incidence (epidemiology) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Incidence (epidemiology) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Incidence (epidemiology) in simple terms?

In epidemiology, incidence reflects the number of new cases of a given medical condition in a population within a specified period of time. Incidence proportion Incidence proportion (IP), also known as cumulative incidence, is defined as the probability that a particular event, such as occurrence o…

Why does Incidence (epidemiology) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Incidence (epidemiology)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Incidence (epidemiology).

Tags

  • Epidemiology
  • Hygiene
  • Medical statistics

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