Relative and absolute measures of association

In general, there are two types of measures of association: relative and absolute (see online Supplementary material 1). Relative measures of association are estimated by presenting results (eg, risks, odds, rates) as a ratio of two groups. Usually, the two groups represent different categories within the same variable (eg, male vs female within the variable ‘sex’). The aim is to identify the strength of the association between an exposure of interest and injury development expressed in percentage as a higher or lower risk/odds/rate of one group compared with the reference (denominator for the ratio). In sports injury research, commonly used measures in this category are relative risk (or risk ratio), OR, incidence rate ratio and hazard rate ratio. For example, male runners who train more than 40 miles per week have a 2.22 times higher (or 122% increased) injury risk than runners whose mileage is less than 40 miles per week.4

In contrast, absolute measures of association, such as risk differences, incidence rate differences, cumulative risk differences and adverse event rate differences, are produced by subtracting risks or rates from two exposure groups. The aim is to identify how many more injuries are sustained in one group as compared with another group. Such difference is expressed in percentage points (for risks) and in number of athletes per, for example, 1000 hours of training (for rates). For instance, 10% more of all athletes sustain injury in setting A than in setting B means that among 100 athletes, 10 fewer sustain injury in setting B than in setting A.

In a sports science context, relative measures of association are commonly used, whereas absolute measures are rarely used. Specifically, absolute measures of association were used in only 2 of 73 studies that examined risk factors for running-related injuries.5

Consideration regarding relative measures of association

In study 1, the risk of hamstring injury in group A (soccer players playing on artificial turf) is 20% per season (95% CI 18% to 22%), and the risk of hamstring injury in group B (soccer players playing on natural grass) is 10% (95% CI 8% to 12%). Then, a relative measure of association is the relative risk, which is 2 (20%/10%). This is equivalent to a 100% higher risk of hamstring injury among athletes playing on turf than those playing on grass. The absolute measure of association would reveal an absolute risk difference of 10% (20%−10%). This tells us that 10% more players who play on turf would sustain a hamstring injury compared with those who play on grass (eg, 200 injuries in 1000 players on turf and 100 injuries in 1000 players on grass).

In study 2, the risk of hamstring injury in the turf group is 2% per season (95% CI 1% to 3%), and the risk of hamstring injury in the grass group is 1% (95% CI 0.4% to 1.6%). A relative measure of association would reveal a relative risk of 2 (2%/1%). As in study 1, this is equivalent to a 100% higher risk of hamstring injury in the turf group than in the grass group. As the reader will have noted, the absolute measure of association reveals a very big difference compared with study 1, since it indicates that the risk difference is 1% (2%−1%). In other words, 1% more soccer players who play on turf sustain a hamstring injury compared with those playing on grass (eg, 20 injuries in 1000 players on turf and 10 injuries in 1000 players on grass).

By comparing the results from studies 1 and 2, it is clear that the relative risks are similar. A 100% higher risk also sounds alarming and might launch a call for action to combat the hamstring injury problem. However, there is a huge difference in the absolute number of soccer players who sustain a hamstring injury between studies 1 and 2 (10% more vs 1% more football players who played on turf were injured, compared with those who played on grass). These absolute numbers allow the readers to judge if the difference in number of athletes sustaining injuries on turf than grass is clinically relevant: an absolute difference of 10% might be clinically relevant, whereas 1% might not. Assuming a causal relationship, the number of soccer players who need to change surface to avoid one hamstring injury (equivalent to numbers needed to treat) in study 1 is 10 players, whereas 100 players need to change surface to avoid one hamstring injury in study 2. The results from those examples are shown in table 1.

We contend that it is inappropriate to draw conclusions based purely on the relative risk (in this case, 100% higher risk), since that statistic does not consider the absolute number of injuries. The STROBE statement for observational studies and the CONSORT statement for randomised trials recommended that researchers report both relative and absolute measures of association.6 7 Absolute measures of association are recommended in a clinical/public health setting to identify the difference in the proportion of persons sustaining sports-related injuries.