Relative measures of association

Relative measures of association

Let’s return to the example of the association between relative age of school children and diagnosis of ADHD. As previously noted, the study found that children born in December were more likely to receive a diagnosis of ADHD than children born in January. This association was expressed as an absolute risk difference of 1.7% for boys and 1.1% for girls, but the study also described the association using a risk ratio.¹²

Data on exposures and disease (or outcome) from epidemiologic studies is sometimes depicted in a 2 x 2 table as shown in Table 1. Data from the ADHD study showing the diagnosis of ADHD among boys born in January and December are presented in this format in Table 2. In this example, the exposure is having a birth month of December (or being among the youngest in the grade), and the outcome is diagnosis for ADHD.

Table 1. Exposure and disease for entries in a generic 2×2 table

Table 2. Diagnosis of ADHD among boys born in January and December

A risk ratio is a ratio of the risks in the exposed and unexposed groups from a study, and using the notation from Table 1, it can be calculated as: risk ratio (RR) = [a/ (a+b)]/[c/(c+d)]. Applying this formula, the risk ratio is:

RR=[2,874/(2,874+35,126)]/[2,218/(2,218+36,918)], or 1.30.

This may be interpreted as meaning that younger boys in the grade were 30% more likely to receive an ADHD diagnosis than older boys.

Making use of the data from Table 2, we could also calculate another relative measure commonly used in epidemiology, an odds ratio. An odds ratio is the ratio of the odds of developing a disease among the exposed individuals divided by the odds of developing a disease among unexposed individuals.¹ Using the notation from Table 1, an odds ratio (OR) can be calculated as: OR = (a/b)/(c/d), or equivalently OR=ad/bc. Thus, in this case, the odds ratio is:

OR = (2,874/35,126)/(2,218/36,918), or 1.36.

When incidence rates are available for the exposed and unexposed groups, we can calculate an incidence rate ratio (IRR), often referred to as simply a rate ratio, as: IRR=R₁/R₀, where R₁ is the incidence rate in the exposed group and R₀ is the incidence rate in the unexposed group.⁴ For example, if the incidence of type 2 diabetes is 8 cases per 1,000 person-years in the exposed group and 4 cases per 1,000 person-years in the unexposed group, the incidence rate ratio is: IRR= 8/4, or 2.