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Paper No. 10-09

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M Akacha, JL Hutton and S Lamb

Modelling Treatment, Age- and Gender-Specific Recovery in Acute Injury Studies

Date: May 2010

Abstract: Background: Acute injury studies often measure physical ability repeatedly over time through scores that have a finite range. This can result in a faster score change at the beginning of the study than towards the end, motivating the investigation of the rate of change. Additionally, the bounds of the score and their dependence on covariates are often of interest. Methods: We argue that transforming bounded data is not satisfactory in some settings. Motivated by the Collaborative Ankle Support Trial (CAST, which investigated different methods of immobilisation for severe ankle sprains, we developed a model under the assumption that the recovery rate at a specific time is proportional to the current score and the remaining score. This model enables a direct interpretation of the covariate effects. We have re-analyzed the CAST data using these improved methods, and explored novel relationships between age, gender and recovery rate. Results: We confirm that using below knee cast is advantageous compared with a tubular bandage in relation with the recovery rate. An age and gender effect on the recovery rate and the maximum achievable score is demonstrated, with older female patients recovering less fast (age-effect: -0.21, 95% confidence interval (CI) [-0.28,-0.14]; gender effect: -0.06, CI [-0.12,-0.004]) and achieving a lower maximum score (age-effect: -8.07, CI [-11.68,-4.01]; gender-effect: -5.34, CI [-8.18, -2.50]) than younger male patients. Conclusions: Our model is able to accurately model repeated measurements on the original scale, while accounting for the bounded nature of a score. We demonstrate that recovery in acute injury trials can differ substantially by age and gender. Older female patients are less likely to recover well from a sprain.

Keywords: Bounded scores, CAST-trial, non-linear mixed models, rate of recovery, repeated measurements