University of Warwick. Centre for Research in Statistical Methodology
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
