A - Measure of Association Lesson

Measures of Association

A measure of association quantifies the relationship between exposure and disease among the two groups. Exposure is used to describe exposure to foods, mosquitoes, a partner with a sexually transmissible disease, or a toxic waste dump, but also characteristics of persons such as age, sex, and race; immune status, activities such as jobs or conditions under which they live such as socioeconomic status or access to medical care. Examples of measures of association include risk ratio or relative risk and odds ratio.
A risk ratio (RR), also called relative risk, compares the risk of a health event among one group with the risk among another group. You calculate the risk ratio by dividing the risk (incidence proportion, attack rate) in group 1 by the risk (incidence proportion, attack rate) in group 2. The two groups are usually defined by exposure status (yes/no) to some type of risk factor.

The formula for risk ratio (RR) is:

Relative Risk = $LaTeX: \frac{\frac{A}{A+B}}{\frac{C}{C+D}}=\frac{\frac{3}{3+8}}{\frac{1}{1+8}}=\frac{\frac{3}{11}}{\frac{1}{9}}=\frac{0.27}{0.11}=2.45$ $\frac{\frac{A}{A+B}}{\frac{C}{C+D}}=\frac{\frac{3}{3+8}}{\frac{1}{1+8}}=\frac{\frac{3}{11}}{\frac{1}{9}}=\frac{0.27}{0.11}=2.45$

Since, the relative is risk is greater than 1.0, we can say that there is an increased risk for West Nile Virus among kids who played near the pond. Kids who played near the pond were 2.5 times more likely to contract West Nile Virus

Example Two

In a study of 1000 people, investigators observed who was bitten by a mosquito and who subsequently developed malaria. From the data from 1000 people, here is the 2x2 table and relative risk calculation.

Relative Risk Calculation
	Malaria Yes	Malaria No	Total
Mosquito Bite Yes	200	100	300
Mosquito Bite No	50	150	200
Total	250	250	500

Relative Risk = $LaTeX: \frac{\frac{A}{A+B}}{\frac{C}{C+D}}=\frac{\frac{200}{200+100}}{\frac{50}{50+150}}=\frac{\frac{200}{300}}{\frac{50}{200}}=\frac{0.667}{0.25}=2.67$ $\frac{\frac{A}{A+B}}{\frac{C}{C+D}}=\frac{\frac{200}{200+100}}{\frac{50}{50+150}}=\frac{\frac{200}{300}}{\frac{50}{200}}=\frac{0.667}{0.25}=2.67$

Interpretation: People with mosquito bites had a 2.7 times greater risk of developing malaria than those without mosquito bites.

Football Game Scenario

Odds Ratio

An odds ratio (OR) is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. An odds ratio estimates the probability of disease given exposure to a specific factor by measuring the probability of exposure given the presence of disease. An odds ratio can be calculated from a 2 x 2 table using the following formula:

Odds Ratio = $LaTeX: \frac{\frac{A}{C}}{\frac{B}{D}}=\frac{AD}{BC}$ $\frac{\frac{A}{C}}{\frac{B}{D}}=\frac{AD}{BC}$

Odds Ratio 2X2 Table
	Disease Yes	Disease No
Exposure Yes	A	B
Exposure NO	C	D

Example One

Let's use the same data from the risk ratio example.

At a recent UM football game, a terrorist group flew a crop duster over the stadium and dusted the western side of the stands with anthrax spores. Fortunately, the wind was blowing toward the west. Once cases were discovered, the investigation began. A total of 50 people who sat on the eastern side developed disease and 500 people who sat on the western side developed disease. Of the 50,000 people in attendance, 25,000 were sitting on the western side of the stadium and were considered to have been exposed.

From the given data, here is the 2 x 2 table and odds ratio calculation.

Odds Ratio Calculation
	Anthrax Yes	Anthrax No
West (Exposure Yes)	500	24,500
East (Exposure No)	50	24,950

Odds Ratio = $LaTeX: \frac{500\left(24,500\right)}{24,950\left(50\right)}=\frac{12,475,000}{1,225,000}=10.18$ $\frac{500\left(24,500\right)}{24,950\left(50\right)}=\frac{12,475,000}{1,225,000}=10.18$

Interpretation: The odds of developing anthrax were 10 times higher for those sitting on the western side compared to those sitting on the eastern side of the stadium.

Food Poisoning Activity

Attributable Risk

Assuming a factor is the cause of a disease, attributable risk is the amount of risk that is due to that factor. In other words, it is the amount of risk reduced if the factor is removed. Another way to say this is attributable risk is the difference in risk between exposed and unexposed people.

Example: In this example, non-smokers are expected to develop emphysema at a rate of 10 cases of emphysema per 100,000 people per year. Among smokers, the rate of emphysema is 100 cases of emphysema per 100,000 people per year. This is an excess risk or attributable risk of 90 per 100,000 per year.

Risk of developing emphysema

for non-smokers: 0.0001
for current smokers: 0.001

Attributable Risk = 0.001 - 0.0001 = 0.0009

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