This article discusses the concept of ‘association’ in biostatistics. Measures of association assume categorical or continuous level of data. The article also discusses in detail three kinds of risks and odd ratio. Attributable risk is also known as excess risk which is calculated when individuals or subjects in a research are assembled on exposure status. Population attributable risk is also discussed which indicates reduction in an incidence which may be observed in case the whole population were completely unexposed.

statistics attribution risk odds ratio

Image: “Statistics” by geralt. License: CC0 1.0


Association

Association in statistics refers to a wide variety of co-efficients which are required to measure the statistical strength of different variables. There are many statistical distinctions associated with understanding of association between statistical measures. The statistical measures are different from statistical significance. Measures of association assume categorical or continuous level of data. The categorical data include nominal or cordial data level. Whereas the casual direction followed by the measure of association is based on symmetrical or asymmetrical direction.

When we say, “smoking is associated with lung cancer”, what exactly do we mean by “associated”?

Attributable Risk

This is a kind of risk which relates to difference in rate of a condition of an exposed population to unexposed population.

This risk is also known as excess risk which is calculated when individuals or subjects in a research are assembled on exposure status. The evaluators count the occurrence of disease. The level of exposure and frequency of disease is further divided into sub groups. One of such sub group is exposed and the other one is unexposed.

Exposure ↓ / Outcome → Yes No Totals
Yes a b
No c d
Totals N

Formula for Exposed group

Attributable risk = (Ie – Io) / Ie

In above formula, Ie denotes to incidence in exposed and Io denotes to incidence in unexposed. In order to find out the percentage of attributable risk, the difference between Ie and Io is further divided by Ie.

Attributable Risk and Odds Ratio

“Attributable Risk” by Lecturio

Example
The population of 200 individuals is observed over a period of 10 years comprising of 100 smokers and 100 nonsmokers. The observation aimed at finding out the impact of smoking on lung cancer to find out who dies earlier from lung cancer in the following 10 years.

Smoker ↓ / Lung Cancer → Yes No Totals
Yes 75 25  100
No 10 90  100
Totals  85  115 N

The statistics proved that 86.7 % smokers were exposed to lung cancer.

Attributable Risk Example

“Attributable Risk of Lung Cancer” by Lecturio

The study later revealed that out of a total of 100 smokers, 76.5 % would have been prevented in case they had quit smoking earlier.

Attributable Risk Example 2

“Attributable Risk – possible Prevention” by Lecturio

Population attributable risk (PAR)

This risk indicates reduction in an incidence which may be observed in case the whole population was completely unexposed. The unexposed factor of population is compared with actual or exposed pattern in order to find out population attributable risk.

Example

To find out the expected percentage of people who will live more than 60 years of average life expectancy in case they quit smoking in early 30’s.

It is usually expressed as a fraction of all exposed data from a whole population. It is the percentage of elimination of a disease or incident in case exposure is eliminated. PAR is calculated by eliminating incidence in the total population including both exposed and unexposed to the incidence in unexposed.

Odds Ratio (OR)

In case incidence rate can not be computed accurately, odd ratio can be used to find out the desired results. Several case studies which involve case control can not measure incidence accurately; for that purpose relative risk is required to be measured for accurate evaluation of results. Relative risk can be used for measurement of odd ratio in case the disease is rare to occur in a patient. It refers to how strong the association of a disease in a patient is linked with association of causation factor in the same patient.

Exposure ↓ / Outcome → Yes No Totals
Yes a b
No c d
Totals N
Odds Ratio undiseased

“Odds Ratio – undiseased” by Lecturio

Odds Ratio diseased

“Odds Ratio – diseased” by Lecturio

Example

This ratio is used to calculate the association of property A in a patient, i.e., high blood pressure to the property B, i.e., high level of alcoholic consumption. These two properties are interlinked.

Relative Risk (RR)

It refers to the probability of occurrence of an event, i.e., development of a disease in exposed group to the probability of occurrence of another event in an unexposed group. Relative risk has two importance features, i.e.,

  1. comparison between two exposures and
  2. proper denominator representing the exposure.

The formula used to calculate relative risk is given as follows

RR = Prevent when exposed / Prevent when not exposed

Example

If probability of development of lungs cancer in smokers is 20 % it may be 2 % in case of nonsmokers.

This situation can be expressed as follows

Smoker ↓ / Lung cancer → Yes No Totals
Yes 20 80  100
No 1 99  100
N

Putting the values in below formula

Relative Risk

RR-unexposed

“Relative Risk among the unexposed” by Lecturio

That is:

RR = (20/ (20 + 80)) / (1 / (1 + 99))

RR = 20

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