BMJ 2014;349:g6150 doi: 10.1136/bmj.g6150 (Published 10 October 2014)
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Endgames
ENDGAMES STATISTICAL QUESTION
Poisson regression Philip Sedgwick reader in medical statistics and medical education Institute for Medical and Biomedical Education, St George’s, University of London, London, UK
Researchers investigated whether a neuromuscular training programme was effective in preventing non-contact leg injuries in female floorball players. The programme was designed to enhance players’ motor skills and body control, as well as to activate and prepare their neuromuscular system for sports specific manoeuvres. A cluster randomised controlled study design was used. Participants were 457 players (mean age 24 years), recruited from 28 top level female floorball teams in Finland. Teams were allocated to treatment using cluster random allocation with 14 teams allocated to the intervention (256 players) and 14 to the control (201 players). Teams in the control group were asked to do their usual training during the study period. Clubs were followed up for one league season (six months).1
The primary outcome was the occurrence of acute non-contact injuries of the legs during training or play. In total, 32 327 scheduled hours of training and play were recorded for the intervention group (mean number per player 126.3 hours (standard deviation 32.5)), compared with 25 019 hours for the control group (124.5 (30.8)). Over the season, 20 acute non-contact leg injuries were reported for the intervention group, compared with 52 injuries for the control group. Some players may have experienced more than one injury. The injury incidence rate per 1000 hours of training and play was 0.65 (95% confidence interval 0.37 to 1.13) in the intervention group and 2.08 (1.58 to 2.72) in the control group. The unadjusted injury incidence rate ratio for the intervention compared with the control was 0.31 (0.17 to 0.58). Poisson regression was used to adjust the injury incidence rate ratio for potential confounding (including age, body mass index, floorball experience, playing position, number of orthopaedic operations, and league). The adjusted injury incidence rate ratio was 0.34 (0.20 to 0.57). Which of the following statements, if any, are true? a) The players were not equally as likely to experience acute non-contact leg injuries because they differed in the number of hours of training and play
b) The outcome variable for the Poisson regression was the number of acute non-contact leg injuries during the season
c) It can be concluded that the training programme significantly reduced the risk of acute non-contact leg injuries in female floorball players d) Treatment was independently associated with the occurrence of acute non-contact leg injuries
Answers
Statements a, b, c, and d are all true.
The aim of the trial was to investigate whether the neuromuscular training programme was effective in preventing non-contact leg injuries in female floorball players. The players in the control group undertook their usual training. The primary outcome was the occurrence of acute non-contact leg injuries during the study period of six months. It would not have been appropriate to compare treatment groups in the total number of acute non-contact leg injuries that occurred during the season because the scheduled number of hours of training and play differed between these groups. During the season, 32 327 hours of training and play were reported for the intervention group, compared with 25 019 hours for the control group. The intervention group might have been expected to experience more injuries because it reported more hours of training and play. The difference between the treatment groups in the total number of hours of training and play was partly due to the difference in the number of players. Furthermore, there was a wide variation between players in the number of hours of training and play, as indicated by the standard deviations of number of hours for the treatment groups. The more hours that players trained and played the more acute non-contact leg injuries they might experience (a is true). Therefore, when comparing treatment groups in the number of acute non-contact leg injuries it was important to account for differences between players and treatment groups in exposure—that is, differences in the number of hours of training and play. To account for differences in the number of hours of training and play between treatment groups, the number of acute non-contact leg injuries was presented as an incidence rate. The incidence rate was the total number of injuries experienced during the study period divided by the total number of hours of training and play. The researchers reported that 20 acute
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BMJ 2014;349:g6150 doi: 10.1136/bmj.g6150 (Published 10 October 2014)
Page 2 of 2
ENDGAMES
non-contact leg injuries were reported during 32 327 scheduled hours of training and play for the intervention group, compared with 52 injuries during 25 019 hours of training and play in the control group. Therefore, the incidence rate in the intervention group was 0.00065 and 0.00208 in the control group. Because the rate in each group was small, for convenience it was presented as the number of injuries per 1000 hours of training and play. Hence, the injury incidence rate per 1000 hours was 0.65 (95% confidence interval 0.37 to 1.13) in the intervention group compared with 2.08 (1.58 to 2.72) in the control group.
The injury incidence rate ratio, sometimes referred to as the relative rate, was 0.31 (0.17 to 0.58). Described in a previous question,2 it provides a relative measure of the effect of the intervention compared with control and was derived as the incidence rate for the intervention group divided by the incidence rate for the control group. It is interpreted in a similar manner to a relative risk. The injury incidence rate ratio was 0.31, and therefore the intervention group experienced a 69% reduction in the risk of acute non-contact leg injuries relative to control. The reduction in risk was significant at the 5% level of significance because the 95% confidence interval for the incidence rate ratio did not include unity (1.0). A rate ratio equal to unity would indicate that the incidence rate was the same in both treatment groups. As described in a previous question, when the 95% confidence interval for a ratio excludes unity, the ratio is significantly different from unity.3
The injury incidence rate ratio presented above was not adjusted for confounding—that is, it was not adjusted for any potential differences between treatment groups in the rate of acute non-contact leg injuries that may have been due to differences in, for example, age. The injury incidence rate ratio comparing the intervention group with the control group was adjusted for potential confounding using Poisson regression. Poisson regression models the rate of an event occurring when the length of exposure or follow-up differs between the participants. Poisson regression is similar to other regression methods described in previous questions.4-6 Referred to as multivariable analysis, it investigates the association between a dependent variable (sometimes referred to as an outcome variable) and one or more predictor variable(s) simultaneously. The dependent variable for Poisson regression is a count, in contrast to simple linear regression and multiple regression analyses, where the outcome is continuous. In the above study the outcome variable was the number of acute non-contact leg injuries during the season (b is true). The predictor variables, sometimes referred to as explanatory variables, can be any mixture of continuous, binary, or categorical variables. In the above study these variables were treatment group (intervention v control) plus
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potential confounding variables including age, body mass index, floorball experience, playing position, number of orthopaedic operations, and league. The number of hours of training and play was included to indicate the length of exposure to training and play. The application of Poisson regression assumed that the number of acute non-contact leg injuries during the study period had a Poisson distribution. It was therefore assumed that leg injuries occurred infrequently (were a rare event), randomly (independently of each other), and at a constant rate.
The Poisson regression model provided the incidence rate ratio of acute non-contact leg injuries for each of the explanatory variables, adjusted for all other variables included in the regression analysis. The adjusted injury incidence rate ratio for the treatment group (intervention group v control group) was 0.34 (0.20 to 0.57). Therefore, after adjustment for confounding it was estimated that the intervention group experienced a significantly lower rate of acute non-contact leg injuries, with a 66% reduction in risk compared with the control group. The reduction in risk was significant at the 5% level of significance because the 95% confidence interval for the adjusted incidence rate ratio did not include unity (1.0). Therefore, it can be concluded that the training programme significantly reduced the risk of acute non-contact leg injuries in female floorball players (c is true). Because the effect of the intervention compared with the control was significant after adjustment for potential confounding, the treatment group is said to be independently associated with the occurrence of acute non-contact leg injuries (d is true). The difference in size between the unadjusted and adjusted incidence rate ratios was small, which suggests that the extent of confounding was minimal. The effects of the potential confounding variables were not of interest in themselves, but rather the overall effect of potential confounding. Therefore, the injury incidence rate ratios were not presented for the other explanatory variables. Competing interests: None declared. 1 2 3 4 5 6
Pasanen K, Parkkari J, Pasanen M, Hiilloskorpi H, Mäkinen T, Järvinen M, et al. Neuromuscular training and the risk of leg injuries in female floorball players: cluster randomised controlled study. BMJ 2008;337:a295. Sedgwick P. Incidence rate ratio. BMJ 2010;341:c4804. Sedgwick P. Confidence intervals and statistical significance: rules of thumb. BMJ 2012;345:e4960. Sedgwick P. Simple linear regression. BMJ 2013;346:f2340. Sedgwick P. Multiple regression. BMJ 2013;347:f4373. Sedgwick P. Logistic regression. BMJ 2013;347:f4488.
Cite this as: BMJ 2014;349:g6150 © BMJ Publishing Group Ltd 2014
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