Confidence intervals for injury surveillance data using negative binomial regression

Purpose: It is common in injury surveillance to calculate injury rates and their confidence intervals. However, standard statistical methods assume that rates follow a Poisson distribution, which is often not true in injury surveillance data, and thus the confidence intervals produced using standard methods are too narrow. This presentation discusses an alternative method based on negative binomial regression. Methods: We analyzed data from 15 collegiate sports collected by the National Collegiate Athletic Association's Injury Surveillance System (ISS) over 15 years (1988-89 to 2002-03). We compared confidence intervals computed from the ISS data using three methods: 1) standard formula (no model), 2) Poisson regression, and 3) the NB1 negative binomial regression model. Results: We used the game-to-practice rate ratio to compare the three methods (it is well-established that there is a higher rate of injury in games relative to practices in most sports). The game-to-practice rate ratios produced using standard formula and Poisson regression were identical (RR=6.65; 95%CI: 6.58, 6.73; CLR: 1.02). This confidence interval is too narrow, because the NCAA injury rates have a higher variance than predicted by the Poisson distribution (so-called “over-dispersion”). The game-to-practice rate ratio produced using NB1 negative binomial regression was 6.65 (95%CI: 6.41, 6.91; CLR: 1.08). NB1 negative binomial regression provides a more realistic (i.e. wider) confidence interval than standard statistical methods. Conclusion: NB1 negative binomial regression outperforms standard statistical methods. Users of injury surveillance data should be aware that confidence intervals for injury rates may be too narrow if computed using standard statistical methods.