Risk factor

Key takeaways

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

Reference excerpt

In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection. Due to a lack of harmonization across disciplines, determinant, in its more widely accepted scientific meaning, is often used as a synonym. The main difference lies in the realm of practice: medicine (clinical practice) versus public health. As an example from clinical practice, low ingestion of dietary sources of vitamin C is a known risk factor for developing scurvy. Specific to public health policy, a determinant is a health risk that is general, abstract, related to inequalities, and difficult for an individual to control. For example, poverty is known to be a determinant of an individual's standard of health. Risk factors may be used to identify high-risk people.

Correlation vs causation Risk factors or determinants are correlational and not necessarily causal, because correlation does not prove causation. For example, being young cannot be said to cause measles, but young people have a higher rate of measles because they are less likely to have developed immunity during a previous epidemic. Statistical methods are frequently used to assess the strength of an association and to provide supportive evidence for causation, for example in the study of the link between smoking and lung cancer. Statistical analysis along with the biological sciences can strongly suggest that a risk factor is causal. Some prefer the term risk factor to mean causal determinants of increased rates of disease, and for unproven links to be called possible risks, associations, etc. When done thoughtfully and based on research, identification of risk factors can be a strategy for medical screening.

Terms of description Mainly taken from risk factors for breast cancer, risk factors can be described in terms of, for example:

Relative risk, such as "A woman is more than 100 times more likely to develop breast cancer in her 60s than in her 20s." Odds ratio, such as "The odds of developing breast cancer are approximately 2.45 times higher for women with two or more affected first-degree relatives compared to those without a family history." Fraction of incidences occurring in the group having the property of or being exposed to the risk factor, such as "99% of breast cancer cases are diagnosed in women." Increase in incidence in the exposed group, such as "each daily alcoholic beverage increases the incidence of breast cancer by 11 cases per 1000 women." Hazard ratio, such as "an increase in both total and invasive breast cancers in women randomized to receive estrogen and progestin for an average of 5 years, with a hazard ratio of 1.24 compared to controls."

Example At a wedding, 74 people ate the chicken and 22 of them were ill, while of the 35 people who had the fish or vegetarian meal only 2 were ill. Did the chicken make the people ill?

R i s k = number of persons experiencing event (food poisoning) number of persons exposed to risk factor (food) {\displaystyle Risk={\frac {\mbox{number of persons experiencing event (food poisoning)}}{\mbox{number of persons exposed to risk factor (food)}}}}

So the chicken eaters' risk = 22/74 = 0.297 And non-chicken eaters' risk = 2/35 = 0.057. Those who ate the chicken had a risk over five times as high as those who did not, that is, a relative risk of more than five. This suggests that eating chicken was the cause of the illness, but this is not proof. This example of a risk factor is described in terms of the relative risk it confers, which is evaluated by comparing the risk of those exposed to the potential risk factor to those not exposed.

General determinants The probability of an outcome usually depends on an interplay between multiple associated variables. When performing epidemiological studies to evaluate one or more determinants for a specific outcome, the other determinants may act as confounding factors, and need to be controlled for, e.g. by stratification. The potentially confounding determinants varies with what outcome is studied, but the following general confounders are common to most epidemiological associations, and are the determinants most commonly controlled for in epidemiological studies:

Age (0 to 1.5 years for infants, 1.5 to 6 years for young children, etc.) Sex or gender (Male or female) Ethnicity (Based on race) Other less commonly adjusted for possible confounders include:

Social status/income Geographic location Genetic predisposition Gender identity Occupation Overwork Sexual orientation Level of chronic stress Diet Level of physical exercise Alcohol consumption and tobacco smoking Other social determinants of health

Risk marker A risk marker is a variable that is quantitatively associated with a disease or other outcome, but direct alteration of the risk marker does not necessarily alter the risk of the outcome. For example, driving-while-intoxicated (DWI) history is a risk marker for pilots as epidemiologic studies indicate that pilots with a DWI history are significantly more likely than their counterparts without a DWI history to be involved in aviation crashes.

History The term "risk factor" was coined by former Framingham Heart Study director, William B. Kannel in a 1961 article in Annals of Internal Medicine.

See also Health risk assessment Protective factor Risk factor (finance) Social determinants of health

References

Further reading S. P. Case; K. R. Haines (2009). Understanding Youth Offending: Risk Factor Research, Policy and Practice. Willan. 2009. ISBN 9781843923428.

Worked examples

Example 1 — a first encounter with Risk factor

Start with the simplest possible case. Write down what Risk factor 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 Risk factor 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 Risk factor 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 Risk factor

In research: Risk factor 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 Risk factor 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: Risk factor is common in secondary-school and first-year university syllabi. It links to neighbouring topics Medical statistics, Risk factors, so understanding it makes those chapters shorter.
In everyday life: Look for Risk factor 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.

How to study Risk factor in 20 minutes

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

Frequently asked questions

What is Risk factor in simple terms?

In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection. Due to a lack of harmonization across disciplines, determinant, in its more widely accepted scientific meaning, is often used as a synonym.

Why does Risk factor 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 Risk factor?

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 Risk factor.