Estimating uncertainty

CIs convey the uncertainty about a point estimate (in this case, an injury burden rate) and are thus crucial for interpreting results and informing decision-making. Injury burden estimates have typically been modelled using the Poisson distribution.5 Using this approach, the precision around the burden estimate is driven entirely by ‘N’ in Equation 1.5

Equation 1.

However, several different values for ‘N’ in Equation 1 have been used within the literature. Many studies, including the International Olympic Committee consensus statement,3 use the total number of athlete days absence, while others have used the injury burden rate itself6 or the injury count7; each approach produces a different CI width (table 1) and could therefore hugely impact on the interpretation of the burden rate. For example, using the total number of injury days as the ‘N’ value produces a CI that is extremely narrow when the total number of injury days is large, greatly increasing the likelihood of making a type I error. Of these approaches, using the injury count as the ‘N’ value appears most appropriate as it produces a CI width that changes proportionately in line with the sample size (ie, the number of injury events). Yet, there is no consensus on this in the sports medicine literature. Moreover, the appropriateness of assuming a Poisson distribution when modelling injury burden data may be questioned given the extreme positive skew that is often present, and this approach does not account for the multiple sources of random error (ie, from both injury incidence and average injury severity).

Enter bootstrapping

Bootstrapping is a statistical resampling technique that involves sampling with replacement from an original dataset (at least 1000 iterations are recommended), with confidence limits derived from percentiles of the sampled values.8 Bootstrapping enables the estimation of the sampling distribution of a statistic without making assumptions about the underlying population distribution. As such, it appears a promising solution for producing robust CIs around an injury burden estimate. Bootstrapping is now readily available for descriptive statistics in statistical programmes such as SPSS and R (see online supplemental materials for worked examples). Note, a burden value is required for each injury record in the dataset, which may be obtained by dividing each injury severity value by the athlete’s exposure time (and then multiplying by 1000 to express as days absence per 1000 athlete-hours); where individual exposure time is not available, the total/team exposure time should be divided by the total injury count. As shown in table 1, the bootstrapping method changes proportionately in line with the sample size and produces the most conservative CI width. By avoiding the need to make assumptions about the distribution from which the data were obtained, we believe the bootstrapped CIs are the most trustworthy estimates of the precision around the burden estimate.

The ‘Delta Method’ is another viable solution for obtaining a valid SE that accounts for both sources of uncertainty when calculating a burden value.8 Further considerations are needed when modelling injury burden as an outcome variable in regression models (eg, the use of a negative binomial distribution and/or bootstrapping approaches to account for clustering),5 but this is beyond the scope of the current editorial.

Moving forward with confidence

The uncertainty associated with output measures from injury surveillance studies should always be presented and used to guide decisions (eg, whether a meaningful change has occurred between seasons). Although a full methodological review of the proposed methods is warranted, bootstrapping appears to provide a robust and appropriate estimate of uncertainty for burden rate estimates, and this key methodological point should be considered by sports injury researchers.