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Edited by: Robert James Aughey, Victoria University, Australia

Reviewed by: Pascal Edouard, Centre Hospitalier Universitaire de Saint-Étienne, France; James Michael Smoliga, High Point University, United States

This article was submitted to Exercise Physiology, a section of the journal Frontiers in Physiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Injuries are a common occurrence in team sports and can have significant financial, physical and psychological consequences for athletes and their sporting organizations. As such, an abundance of research has attempted to identify factors associated with the risk of injury, which is important when developing injury prevention and risk mitigation strategies. There are a number of methods that can be used to identify injury risk factors. However, difficulty in understanding the nuances between different statistical approaches can lead to incorrect inferences and decisions being made from data. Accordingly, this narrative review aims to (1) outline commonly implemented methods for determining injury risk, (2) highlight the differences between association and prediction as it relates to injury and (3) describe advances in statistical modeling and the current evidence relating to predicting injuries in sport. Based on the points that are discussed throughout this narrative review, both researchers and practitioners alike need to carefully consider the different types of variables that are examined in relation to injury risk and how the analyses pertaining to these different variables are interpreted. There are a number of other important considerations when modeling the risk of injury, such as the method of data transformation, model validation and performance assessment. With these technical considerations in mind, researchers and practitioners should consider shifting their perspective of injury etiology from one of reductionism to one of complexity. Concurrently, research implementing reductionist approaches should be used to inform and implement complex approaches to identifying injury risk. However, the ability to capture large injury numbers is a current limitation of sports injury research and there has been a call to make data available to researchers, so that analyses and results can be replicated and verified. Collaborative efforts such as this will help prevent incorrect inferences being made from spurious data and will assist in developing interventions that are underpinned by sound scientific rationale. Such efforts will be a step in the right direction of improving the ability to identify injury risk, which in turn will help improve risk mitigation and ultimately the prevention of injuries.

Injuries are a common occurrence in team sports such as Australian football (

In the context of injuries, association can help us understand why an injury occurs (

There is also always a level of uncertainty when it comes to injuries. Acute injuries occur following an inciting event and this event may be extrinsic, such as contact with another player, or intrinsic, such as jumping or changing directions (

Methods that are used to determine injury risk factors typically involve classifying athletes as sustaining an injury or remaining injury free, based on the presence or absence of a variable of interest (or injury risk factor). This is referred to as binary classification. There are four possible outcomes in binary classification:

True positive (TP) = the variable of interest was present and the athlete was injured.

False positive (FP) = the variable of interest was present but the athlete avoided injury.

True negative (TN) = the variable of interest was absent and the athlete avoided injury.

False negative (FN) = the variable of interest was absent but the athlete was injured.

These outcomes can be expressed in a contingency table (

A contingency table which can be used to express the outcomes of binary classification.

A contingency table expressing the outcomes of a mock dataset. The frequency distribution of athletes that have or have not sustained a previous injury is displayed against the frequency distribution of athletes that did or did not sustain a prospective injury.

Relative risks and odds ratios are commonly used in medical literature to describe the association between a variable of interest and an outcome. Before understanding relative risks and odds ratios, it is important to understand the difference between probability (used to calculate relative risks) and odds (used to calculate odds ratios). Probability is the likelihood of an injury occurring, with zero indicating no chance of an injury occurring and one indicating an injury will certainly occur (

A probability of 20% suggests that one in five athletes were likely to sustain an injury. Odds, however, is a ratio of the likelihood of an injury occurring compared to the likelihood of an injury not occurring, and is therefore calculated differently to probability (

Odds of 0.25 actually indicates a ratio of 1:4, which means that for every one athlete that sustains an injury, four athletes will remain uninjured. This may be misinterpreted as equaling a probability of 25%. However, a probability of 20% and odds of 0.25 ultimately indicate the same likelihood.

Relative risk, in the current example, is the ratio of the probability of injury occurring in the previously injured group compared to the probability of injury occurring in the previously uninjured group (

Using the current data (

In the current example, the odds ratio is the ratio between the odds of injury occurring in the previously injured group compared to odds of injury occurring in the previously uninjured group (

Using the data in

Sensitivity and specificity are measures of the performance of a binary classification test (

Specificity is calculated as:

The sensitivity indicates that injury history was able to correctly classify 75% of the prospectively injured athletes, while the specificity indicates that 88% of the uninjured athletes were correctly classified. Sensitivity and specificity are often calculated alongside the relative risk and odds ratio to give an indication of how well a variable classified the injured and uninjured athletes at a group level (

The previously discussed methods can be used to identify the influence a variable has on the risk of injury, but only in one group relative to another. They do not take into account the base rate of injury. Bayes’ theorem can be used to explain the likelihood of an event occurring given the baseline probability of that event occurring as well as the introduction of new evidence (the presence or absence of the variable of interest) (

The next step requires us to transition from probability to odds. The pre-test odds can be calculated using the previously outlined equation (see section “Relative risks and odds ratios”), or can be calculated using the pre-test probability:

The post-test odds and subsequently the post-test probability can be calculated using likelihood ratios (

The positive likelihood ratio indicates that having a previous injury increased the odds of sustaining a future injury 6-fold (see section “Sensitivity and specificity” for sensitivity and specificity calculations). The negative likelihood ratio can also be calculated for athletes without a history of injury, but this is typically less relevant for practitioners that are interested in the impact a variable has on injury risk. The post-test odds of sustaining a future injury is simply the pre-test odds multiplied by our positive likelihood ratio:

Following this, the post-test odds can be used to transition back to probability and to calculate the post-test probability of sustaining a future injury:

Before considering injury history, the probability of injury for the 200 athletes was 20%, or a 2 in 10 chance. After taking into account injury history (or the ‘new evidence’), the probability of injury for the previously injured athletes increased to 60%, or a 6 in 10 chance. A concise summary of these steps and the calculations involved can be found in

A summary of the steps involved in calculating the post-test probability of an injury occurring given a history of injury.

1. Pre-test | Odds (as a decimal) | 0.25 | The decimal odds of sustaining a future injury for all athletes, prior to accounting for previous injury. This can also be calculated using the pre-test probability (see section “Pre-test and Post-test Probabilities”). | |

Odds (as a ratio) | 1:4 | As above, calculated as a fraction | The likelihood of a future injury occurring (1) compared to the likelihood of a future injury not occurring (4) for all athletes. | |

Probability | 20% | The percentage of athletes likely to sustain a future injury (prior to accounting for previous injury). | ||

Explanation | 2 in 10 chance | − | This can simplified to a 1 in 5 chance. | |

2. Likelihood ratio | Positive likelihood ratio | 6 | The magnitude by which having a previous injury increases the odds of sustaining a future injury. This is calculated using sensitivity and specificity (see section “Sensitivity and Specificity”). | |

3. Post-test | Odds (as a decimal) | 1.5 | The decimal odds of athletes with a previous injury sustaining a future injury. | |

Odds (as a ratio) | 6:4 | As above, calculated as a fraction | The likelihood of a future injury occurring (6) compared to the likelihood of a future injury not occurring (4) for athletes with a previous injury. | |

Probability | 60% | The percentage of previously injured athletes likely to sustain a future injury. This is calculated using the post-test odds. | ||

Explanation | 6 in 10 chance | − | This can be simplified to a 3 in 5 chance. |

Up to this point, previous injury has been used as an example to explain methodologies that can be used to determine the association between a factor and the risk of injury. However, in the current example, injury history is a binary categorical variable. This means there are only two possible options: previously injured or previously uninjured. Such data can be easily expressed in a contingency table (

The ROC curve was first developed during the Second World War and was used to analyze the classification accuracy of radar operators in distinguishing a signal from noise in radar detection (

More recently, ROC curves have been used in the medical sphere for the evaluation of diagnostic tests (

An example of a receiver operating characteristic curve, which can be used to illustrate how well a continuous variable performs as a binary classifier. The true positive rate (sensitivity) is plotted against the false positive rate (1 – specificity) at every conceivable cut point for a continuous variable. The gray shaded area indicates the area under the curve.

An optimal cut point, however, is highly specific to the spread of the data from which it is derived. While it can provide information about a variable and its application to a specific cohort, in reality, a statistically derived cut point has little clinical relevance. A more important use of a ROC curve is the ability to calculate the area under the ROC curve, commonly referred to as simply area under the curve (AUC). The higher the sensitivity and the lower the 1 – specificity at every point on a ROC curve, the greater the AUC will be. Illustrated in

The methodologies discussed up to this point are appropriate for investigating the association between a variable and the risk of injury. It can be assumed that two variables are associated when one variable provides information about the other (

Difficulties in understanding the nuances of association versus prediction may result in practitioners concluding that a factor associated with injury risk can be used to predict (and ultimately prevent) injury (

It has long been suggested that a univariable approach (that is, investigating a single variable’s impact on injury risk) may be too simplistic and that in order to better understand the etiology of injuries, the collective contribution of multiple factors to injury risk must be examined (a multivariable approach) (^{2} coefficient = 0.31) (

The previously discussed statistical approaches are reductionist in nature. Reductionism assumes that all the parts of a system (in this case, injury etiology) can be broken down and examined individually and then summed together to represent the system as a whole (

A complex systems approach for modeling the risk of injury, adapted from

Machine learning is a field of computer science which involves building algorithms to learn from data and make predictions without being programmed what to look for or where to look for it. Machine learning techniques can be either supervised or unsupervised. Unsupervised learning is the process by which predictions are made on a dataset with no corresponding outcome variable (

A typical supervised learning modeling approach. A dataset with a known outcome variable (i.e., injured or uninjured), referred to as training data, is used to identify patterns and predict the withheld outcome variable of an independent dataset, referred to as testing data. The performance of the model can then be assessed by comparing the predicted outcomes against the withheld outcome variable of the testing data.

There are a number of different types of algorithms that can be used to build predictive models (

Naïve Bayes

Logistic regression

Decision tree

Random forest

K-nearest neighbors

Generalized estimating equation

Support vector machine

Neural network

When using different algorithms to build a predictive model, the goal is to select a combination of parameters that optimize an algorithm’s ability to perform on the testing data (

There are a number of other important considerations when implementing a machine learning approach. When using a variety of continuous variables as predictors, machine learning algorithms can be sensitive to the vastly different scales and magnitudes of the different variables (

Where ^{1} equals the normalized value.

Normalization, however, can result in a loss of information, particularly when it comes to outliers (

Where ^{1} equals the standardized value.

Another machine learning challenge is class imbalance (

When predicting whether an athlete will sustain an injury or remain uninjured, the predicted outcomes versus the actual outcomes can be expressed in a contingency table, similar to

True positive (TP) = the athlete was predicted as injured and was injured.

False positive (FP) = the athlete was predicted as injured but avoided injury.

False negative (FN) = the athlete was predicted as uninjured but was injured.

True negative (TN) = the athlete was predicted as uninjured and avoided injury.

Accuracy is the simplest metric that can be used to evaluate the performance of a predictive model (

A contingency table expressing the outcomes of a mock dataset. The frequency distribution of athletes predicted as sustaining an injury and athletes predicted as remaining uninjured is displayed against the frequency distribution of athletes that were actually injured and uninjured.

Accuracy, however, is a poor indicator of performance when the class distribution is not equal, as a predictive model can achieve high accuracy by always predicting the over-represented class (^{1}):

The next step is to calculate the probability of a true negative occurring by chance (^{2}):

The overall probability of a correct classification occurring by chance (^{3}) is then calculated as:

Cohen’s kappa coefficient is then calculated as:

Both accuracy and kappa, however, are calculated using only the number of correct and incorrect predictions and do not account for the predicted probability of injury. An athlete will be predicted as injured if the model returns a probability of injury greater than 50%. If Athlete A has a 49% probability of injury and Athlete B has 1% probability of injury, both these athletes are more likely to remain uninjured and will be predicted as such. Accuracy and kappa do not account for the fact that Athlete A, despite being predicted as uninjured, was still 48% more likely to sustain an injury than Athlete B. An alternative method that accounts for the magnitude of the probability rather than just the binary prediction is AUC. As outlined previously (see section “Continuous Variables”), a ROC curve can be constructed by plotting the true positive rate against the false positive rate at every conceivable cut point for a continuous variable. In this case, however, the curve can be constructed by plotting the true and false positive rates at every conceivable cut point for the estimated injury probabilities (0% to 100%). The AUC is equal to the proportion of cases where a prospectively injured athlete had a higher estimated probability of injury than an uninjured athlete (

Machine learning has been used to predict outcomes in a variety of fields for a number of years (

It is suggested that the lack of predictive performance may be for a number of reasons. Firstly, data were only collected at the beginning of pre-season and it is unknown whether more frequent measures of the variables included in the models would have improved performance. The methods implemented in this study (

Similar research has also investigated whether training load data could be used to predict non-contact injuries in a single team of elite Australian footballers (

When implementing complex approaches to model the risk of injury, the primary considerations for researchers (as well as practitioners contributing to research) should be what data to collect and when to collect them. It has been suggested that in the medical sphere, researchers often use the data available to them to shape research questions or areas of exploration (

This narrative review aims to serve as a guide to help the reader understand and implement commonly used methods when modeling the risk of injury in team sports. There are a number of methods that can be used to determine factors that are associated with injury risk (

The variables that are examined; research implementing reductionist approaches to identifying injury risk factors should be used to inform the inclusion/exclusion of relevant variables when implementing complex approaches to identifying injury risk.

The types of variables; analyses pertaining to categorical (e.g., binary) variables and continuous variables should be interpreted appropriately.

The amount of data; a larger amount of observations (i.e., time points) and events (i.e., injuries) will improve the ability to identify patterns (should any patterns exist) and make more meaningful predictions.

Modeling considerations; the method of data transformation and model validation, as well as the impact that class imbalances may have on a model, should be considered carefully.

The performance metric used; the performance metric (whether it be predictive or associative) should be considered and interpreted appropriately.

Data replication and sharing; researchers and practitioners should consider making datasets available to other researchers, so that analyses and results can be replicated and verified.

With these considerations in mind, implementing complex approaches and improving our ability to identify risk and predict injuries may lead to a better understanding as to why they happen (

JR: conceptual outline, writing and editing of the manuscript. DO, SC, RW, RT, and MW: writing and editing of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.