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Relative Risk and

Odds Ratios

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Table of Contents

Relative Risk and Odds Ratios ........................................................................................... 1

What is RELATIVE RISK?............................................................................................ 1

What are ODDS RATIOS?............................................................................................. 1

Calculating Relative Risk ................................................................................................... 1Calculating Relative Risk ............................................................................................... 1

Relative Risk: A Rule of Thumb .................................................................................... 2Summary......................................................................................................................... 2

Calculating Odds Ratios ..................................................................................................... 2

Calculating Odds Ratios ................................................................................................. 2

Important Considerations.................................................................................................... 3List .................................................................................................................................. 3

Attributable Risk................................................................................................................. 5

What is Attributable Risk?.............................................................................................. 5Calculating Attributable Risk ......................................................................................... 5

Glossary .............................................................................................................................. 6References........................................................................................................................... 7

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Relative Risk and Odds Ratios

What is RELATIVE RISK?

In the population under investigation, relative risk refers to a ratiobetween members of the population expressing the trait of interest

(e.g. cancer), with distinction made between whether or not those

members had previously been exposed to a related risk.

What are ODDS RATIOS?

Odds ratios refer to a ratio between members within a population

expressing a trait or not, relative to their exposure to a related risk(i.e.has trait(exposed)/has trait(not exposed) x lacks trait (exposed)/lacks trait (notexposed)).

Calculating Relative Risk

Calculating Relative Risk

Relative risk is often calculated for the following types of

epidemiological studies:

- Cohort studies

- Disease register studies

- Randomized control trials

The following table will be of use in calculating relative risk:

Rate of incidence for members with risk factor present = a/a+b

Rate of incidence for members lacking risk factor = c/c+d

Relative risk = rate with risk = (a/a+b)

rate without risk (c/c+d)

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Relative Risk: A Rule of Thumb

Generally, when comparing an experimental group to a control group:

- A relative risk of 1 indicates a lack of difference between the two

groups in terms of risk.

- A relative risk less than 1 indicates the trait has a lesser likelihood of

being expressed in the experimental group than in the control group.

- A relative risk greater than 1 indicates the trait has a greater

likelihood of being expressed in the experimental group than in the

control group.

Summary In calculations of relative risk, researchers should weigh additional

considerations aside from the initial association, making the required

modifications. For example, age and sex standardizations may be

required, but these are beyond the scope of this tutorial.

Having made the needed changes, a researcher can view the relative

risk as a reasonable guage of the strength of an association.

Calculating Odds Ratios

Calculating Odds Ratios

Refer to the chart above. From this chart, the odds of exposure to a

risk factor for the group with a disease is a / c and the odds of

exposure to the risk factor for the group without the disease is b / d.

Similar to relative risk, the odds ratio for exposure is equal to a/c

divided by b/d.

Similar to the odds ratio for exposure, the odds ratio for disease is

equal to a/b divided by c/d, where a/b represents the odds for diseasein those exposed to the risk and c/d represents the odds for disease in

those not exposed to the risk factors.

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So, we have found the following two formulas:

Exposure Odds Ratio: Disease Odds Ratio:

In terms of computation, it is typically simpler to multiply than to

divide, leading us to rearrange the odds ratios in finding the cross-

product ratio.

Exposure Odds Ratio: Disease Odds Ratio:

Cross-Product Ratio:

Note that the cross-product ratio is exactly the same for exposure and

disease!

Important Considerations

List

1) Mistaken Estimations of Relative Risk

As was touched on previously, we may run into problems when

calculating disease incidence in a population to find relative risk. For

instance, numerous experimenters have committed the error of

gathering data from large populations and comparing the resulting

incidence rates and relative risk to those of small populations. This

may cause issues by falsely attributing cases of disease and risks of

disease to smaller populations. These and other considerations must

be factored in before calculating and interpreting relative risk.

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2) Cases Where Relative Risk Lacks Usefulness

Incidence data is needed to calculate relative risk, which we know

from the definition of relative risk (i.e. it is the ratio of two incidence

rates). For instance, relative risk cannot be calculated for case-control

studies, as they provide no incidence data. Unfortunately, relative risk

can be calculated for some case-control studies, but this is beyond the

scope of this module.

Relative risk also lacks usefulness in the event that non-occurrence of

disease is of equal interest to occurrence of disease. As we have seen

previously, the odds ratio gives a symmetrical result, while the

relative risk does not.

3) Cases Where the Odds Ratio is Useful

- the prevalence rate ratio when the prevalence of exposure is low.

Note, prevalence refers to a sum of instances of particular traits within

a population at a certain moment in time.

- Relative risk in a cohort study where the incidence of disease in the

control group is low, generally viewed as those less than 10-20%,

which is a common occurrence.

- the relative risk in a case-control study where exposure in the control

group is equivalent to the population from which the instances are

drawn.

4) Take Care in Interpreting the Odds Ratio

If there is a significant difference between the levels of exposure and

rates of incidence, the odds ratios are not equivalent across time,

population, or location. For instance, studies from Timmins will likely

differ from studies conducted in Collingwood, due to the fact that thelevel of exposure in the control group is not equivalent. This holds

even when the relative risks are equivalent, as per our previous

discussions.

Note, epidemiologists often misinterpret the odds ratio, so take care in

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accepting the results of studies which report it. Many will incorrectly

consider the odds ratio as a fair measure of risk.

Attributable Risk

What is Attributable Risk?

Attributable risk refers to the number of instances which would not

have been observed had a certain risk factor not been present.

In other words, attributable risk refers to the proportion of the

incidence of disease in individuals having had risk exposure that can

be ascribed to that risk factor.

Calculating Attributable Risk

Taking the total number of instances, subtract the number of cases that

would have happened regardless of whether the risk factor had been

present. The remaining instances represent those that can be

accounted for by the risk factor. This value is typically written as a

percentage.

So, attributable risk is the surplus risk in the exposure group, written

as a fraction of total risk.

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Glossary

Relative Risk (RR): In the population under investigation,

relative risk refers to a ratio betweenmembers of the population expressing the

trait of interest (e.g. cancer), with distinction

made between whether or not those

members had previously been exposed

to a related risk.

Odds Ratio (OR): Odds ratios refer to a ratio betweenmembers within a population expressing a

trait or not, relative to their exposure to a

related risk.

Attributable Risk (AR): Attributable risk refers to the number ofinstances which would not have been

observed had a certain risk factor not been

present.

Incidence: is a measure of the risk of developing somenew condition within a specified period of

time, often loosely expressed as the numberof new instances within a specific time

period.

Prevalence: prevalence refers to a sum of instances ofparticular traits within a population at a

certain moment in time, which can be

expressed as the total number of instances in

the population, divided by the total number

of individuals in the population.

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References

Bhopal, R. 2002. Concepts of Epidemiology. Oxford: Oxford University

Press.