# Epidemiology & Biostatistics

Key concepts in epidemiology and biostatistics for APRNs

## Risk

Risk is an important concept in planning of health care services and health education programs. As advanced practice nurses, we need to understand the concept of risk so that we can tailor our care to individuals. A risk factor is a behavior, environmental exposure, or inherent human characteristic that is associated with an important health condition.  In other words, a risk factor is a condition that is associated with an increased probability of a health-related state or event. Risk statistics are an excellent example of how epidemiology informs clinical practice.

When the risk of diseases and injuries is known, health care professionals can plan programs to help prevent the disease, or to diagnose the disease early and implement appropriate treatment to minimize long term sequelae of the disease.

Information about risk enables health care providers to target screening. For example, routine screening for breast cancer is focused on women rather than men, because women are at much great risk than men. And, screening for breast cancer is targeted towards women at the greatest risk – older women, women with a significant family of the disease, and women who have an increased genetic risk for the disease. Thus, screening can be offered to the people who are most likely to develop the disease.

There are many ways to describe risk but we are going to focus on three common risk statistics: attributable risk, relative risk, and odds ratios, which are described below. A section follows these types of risk that explains confidence intervals, which must be considered when interpreting relative risk and odds ratios.

## Attributable Risk

Attributable Risk (AR), also known as the Attributable Proportion or Attributable Fraction, is a measure of the portion of disease attributable to the exposure. This ratio calculates the number of cases that would be eliminated if the exposure were also eliminated. For example, if smoking was eliminated, how many deaths from bronchial cancer can be averted? AR is a measure of statistical association, not causation.

Formula:  AR = (RR-1)  ∕  RR

How to Interpret:  The formula for AR results in a decimal that is interpreted as a percentage. So, for an AR of 0.26 we could say that approximately 26% or ¼ of the time the disease occurrence is due to the exposure.

When to Use:  When there is a need to measure the excess risk associated with the risk factor. May be used to determine potential impact of prevention or health promotion if exposure prevalence is reduced.

## Relative Risk

Relative Risk (RR), also called Risk Ratio, is a measure of association between the risk of disease in the exposed group versus risk of disease in the unexposed group. Relative risk can only be calculated from prospective studies and can only be calculated from incidence rates.

Formula:  RR = Risk of disease in exposed group  ∕  Risk of disease in the unexposed group

How to Interpret:  risk = chance of the outcome of interest  ∕  all possible outcomes.

• RR = 1: Incidence of disease in the exposed group is equal to the incidence in the non-exposed group (no additional risk due to the exposure)
• RR > 1: Incidence of disease in the exposed group is greater than the risk in the non-exposed group (the exposed group had increased risk of disease)
• RR < 1: Incidence of disease in the exposed group is lower than the risk in the non-exposed group (the unexposed group had increased risk of disease.  Or, the exposure was protective)

When to Use:  Relative Risk is used to measure strength of association of a causal link between a risk factor and an outcome. Relative risk can only be calculated from prospective studies and can only be calculated from incidence rates. It is usually preferable to an odds ratio.

## Odds Ratio

Odds Ratio (OR) is a measure used to determine the likelihood of an exposure in a group with disease compared to likelihood of exposure in a group without disease.

Formula:  OR = Odds of exposure in the disease group   ∕   Odds of exposure in the group without disease

How to Interpret: odds = chance of the outcome of interest  ∕  chance of not having outcome of interest)

• OR = 1: Incidence of exposure in the diseased group is equal to the incidence of exposure in the non-exposed group (no additional exposure in the diseased group)
• OR > 1: Incidence of exposure in the diseased group is greater than the incidence of exposure in the group without disease (the diseased group had increased exposure)
• OR < 1: Incidence of exposure in the diseased group is lower than the incidence of exposure in the group without disease (the group without disease group had increased risk of exposure.  Or, the exposure was protective)

When to Use:  Odds ratios are used in case-control and other retrospective studies when RR cannot be calculated.

## Confidence Intervals

Confidence Intervals are in place because although our sample gives us information, we realize that sampling has limitations. Confidence intervals provide a way to account for sampling error. When we have an alpha of 0.05 the results tell us that we are 95% confident that if we were able to study the entire population the results would fall between the range offered by the confidence intervals. Here is an example:  Let’s say we find a mean of 20 in our study sample. The calculated confidence interval is 14-27.  This could be written as 20(14-27). This means that there is a 95% chance the mean of the overall population will fall somewhere between 14 to 27. There is a 5% chance the overall population mean will fall outside of the 14-27 range. This is another way of describing probability.

In the literature when OR and RR are offered, they often come with confidence intervals. Here is an example: OR of 5.3 (3.3-6.7). This means that in our sample we saw an odds ratio of 5.3 but we are 95% confident that if we could measure the entire population the OR would fall between 3.3 and 6.7. This is an important concept to remember.

For OR and RR if the confidence interval contains 1 the OR is not considered valid. Why?  Because if the overall population’s RR or OR could contain 1 it means that potentially there is no difference, even if the calculated risk in the study was statistically significant. Here is an example of a RR that is not valid: RR of 5.3 (0.54-9.6). Although the study sample had a relative risk of 5.3, in our population, the risk could be lower  (RR < 1), higher (RR > 1), or no risk at all (RR = 0)!

The table below shows comparisons of risk calculations.

## Comparison of Risk Calculations

Statistic Definition and Formula Interpretation Use
Odds Ratio

The odds of exposure in the disease group divided by the odds of exposure in the group without disease.

OR =
Odds of exposure in the disease group   ∕   Odds of exposure in the group without disease

Note: Odds are ratios between outcomes

OR = 1 means no risk
OR > 1 increased risk
OR < 1 decreased risk

Used in case control studies because RR cannot be calculated; when incidence or prevalence of the outcome is small but significant

Relative Risk

Relative risk is a measure of association between the exposure to a particular factor and the risk of a particular disease or other health outcome.

RR =
Risk of disease in exposed group   ∕   Risk of disease in unexposed group

Note: Probability is the ratio between an outcome and all possible outcomes.

Same as OR;
RR = 1 means no risk
RR > increased risk
RR < 1 decreased risk

Used to measure strength of association or a causal link between a risk factor and an outcome.
Relative risk can only be calculated from prospective studies and can only be calculated from incidence rates.
Usually preferable to an odds ratio.

Attributable Risk
(Sometimes called risk difference, attributable proportion, or attributable fraction)

The portion of disease attributable to the exposure.

AR =
(RR-1)  ∕  RR
Then convert to a percentage by multiplying result by 100 (move the decimal point to the right two places).

An AR of 0.26 means that approximately 26% or ¼ of the time the disease occurrence is due to the exposure

A measure of statistical association.
Measures excess risk associated with a particular risk factor.
May be used to determine potential impact of prevention or health promotion if exposure prevalence is reduced.