Relative Risk and
Odds Ratios
Table of Contents
Relative Risk and Odds Ratios ........................................................................................... 1
What is RELATIVE RISK?............................................................................................ 1
What are ODDS RATIOS?............................................................................................. 1
Calculating Relative Risk ................................................................................................... 1
Calculating Relative Risk ............................................................................................... 1
Relative Risk: A Rule of Thumb .................................................................................... 2
Summary ......................................................................................................................... 2
Calculating Odds Ratios ..................................................................................................... 2
Calculating Odds Ratios ................................................................................................. 2
Important Considerations.................................................................................................... 3
List .................................................................................................................................. 3
Attributable Risk................................................................................................................. 5
What is Attributable Risk?.............................................................................................. 5
Calculating Attributable Risk ......................................................................................... 5
Glossary .............................................................................................................................. 6
References........................................................................................................................... 7
Relative Risk and Odds Ratios
What is RELATIVE RISK?
●
In the population under investigation, relative risk refers to a ratio
between 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 (not
exposed)).
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
=
rate without risk
1
(a/a+b)
(c/c+d)
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 disease
in 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 crossproduct 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 the
level 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 between
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.
Odds Ratio (OR):
Odds ratios refer to a ratio between
members 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 of
instances which would not have been
observed had a certain risk factor not been
present.
Incidence:
is a measure of the risk of developing some
new condition within a specified period of
time, often loosely expressed as the number
of new instances within a specific time
period.
Prevalence:
prevalence refers to a sum of instances of
particular 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.
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