The ‘vicious circle’ of sports injuries: an analysis of 165 athletics (track and field) athletes over a 39-week follow-up using Markov chains

Figures

• 

  Figure 1. Illustration of the Markov chains developed to explore the risk of injuries according to (1) the number of previous injuries (A), and (2) the athletes’ health status (ie, no injury (H), injury with full athletics participation (IF), injury with partial athletics participation (IP), injury with no athletics participation (IN)) (B). For the study objective 1 (A), the transitions from no injuries with participation restriction (No ICPR) state to injuries with participation restriction (ICPR) state (orange arrows) reflect an injury risk, the transitions from No ICPR state to the same No ICPR state (light blue arrows) reflect the availability to athletics practice without ICPR, and the transitions from ICPR state to the same ICPR state (dark blue arrows) reflect the probability to remain in that injury state, and the transitions from ICPR state to no ICPR state reflect the healing process (dotted green arrows). This forms an open-chain Markov process modelling the ‘vicious circle’ of injuries. For study objective 2 (B), the transitions from a less participation-restrictive state to a more participation-restrictive state (orange arrows) reflect an injury risk. The transitions from an…

• 

  Figure 2. Step-by-step example of creating a two-state Markov chain model using fictitious weekly injury data from a group of athletes. (A) The athletes’ raw data of timelines shows the injury status (healthy ‘h’ or injured ‘i’). (B) Transform of the timelines to transitions between injury states (eg, from healthy to injured: h→ i = ‘hi’) of consecutive time points. (C) Each timeline of transitions is summarised in a transition matrix showing how many times each transition was observed (frequency). (D) The individual transition matrices are summed (cell-by-cell), creating the overall transition matrix of frequencies. (E) By dividing each cell of the frequency matrix with the sum of observations in each row (ie, how many transitions shared the same starting state), the probability matrix is created, showing the probability of transitioning to an ending state given a starting state. (F) The Markov chain can be visualised by plotting the states as nodes in a graph, interconnected by arrows indicating the probability of transitioning from the start of the arrow to the end.

• 

  Figure 3. The open-chain Markov process modelling the ‘vicious circle’ of injuries. The transitions from no injuries with participation restriction (No ICPR) state to injuries with participation restriction (ICPR) state (orange arrows) reflect an injury risk. The transitions from the No ICPR state to the same No ICPR state (light blue arrows) reflect the availability of athletics practice without ICPR. The transitions from the ICPR state to the same ICPR state (dark blue arrows) reflect the probability of remaining in that injury state. The transitions from ICPR to no ICPR state reflect the healing process (dashed green arrows). *Statistically significant comparison (ie, the 95% CI of the ratio is entirely above or below 1).

• 

  Figure 4. The closed-chain Markov process modelling the weekly transition between the four injury states with the transition probabilities. The transitions from a less participation-restricting state to a more participation-restricting state (orange arrows) reflect an injury risk. The transitions from an injury state to the same state (blue arrows) reflect the maintenance of the injury consequence on the athletics practice (ie, maintenance of participation restriction), and the transitions from a more participation restriction state to a less participation restriction state reflect a decrease in the injury consequence on athletics practice (dotted green arrows). The thickness of the arrows is proportional to the corresponding probability. The ratios comparing transition probabilities correspond to table 4. *Statistically significant comparison (ie, the 95% CI of the ratio is entirely above or below 1). H, healthy; IF, injury with full participation; IN, injury with no participation; IP, injury with partial participation.