Consideration 1—theoretical theme—multifactorial aetiology

Sports injury aetiology models of the last two decades have highlighted the multifactorial nature of athletic injury.19 21 We asked whether the burgeoning body of research relating workloads and injury is using modern statistical methods to capture workloads while incorporating known risk factors. Few articles in this review incorporated previously identified risk factors and workload into the same analysis. In some instances, the analytical approach prevented this from being an option. For example, simple analyses like t-tests, correlations and Χ² tests do not allow for multiple variables to be included. In other instances, the statistical approaches allowed a multifactorial approach (eg, GEEs) but researchers opted to focus on the effects of workloads in isolation.58 59

Including known risk factors in workload–injury investigations is important from an aetiological perspective in at least two ways. First, failing to control for known risk factors may mean that key confounding variables are not included in the analysis and the relationship between workloads and injury are spurious. For example, women have a 2–6 times higher risk of ACL injury in soccer than their male counterparts.60 61 If a study included both male and female soccer players and did not account for sex in the analysis, then differences in workload may be spuriously correlated with injury rates if male and female players performed varying levels of workload. Depending on the injury type and sporting group, previous injury, age, sex, physiological and/or biomechanical variables may all be important to include.

Second, by including additional risk factors into the analysis, the investigator may be able to identify moderation or effect-measure modification to better understand how risk factors and workload jointly contribute to injury risk.62 63 As a reminder, there are subtle, but important differences between mediation, moderation and effect measure modification that will influence analytical choices.64 65 Effect modification occurs when the effect of a treatment or condition (eg, a given workload demand), differs among different athlete groups. Interaction (or moderation), although similar, examines the joint effect of two or more variables on an outcome. Finally, mediation is concerned with the pathway of exposure to a given outcome, and what are potentially intermediate variables. Previously identified risk factors may aetiologically relate to workload in each of these three ways and may be explored through different modelling strategies.

Statistical approaches that allow multivariable analyses enabled researchers to examine the effects of workloads while controlling for known risk factors. Malisoux et al 48 used a Cox proportional hazards model to control for age and sex while examining the effects of average training volume and intensity. The frailty model by Gabbett and Ullah66 incorporated previous injury—a proven injury risk factor—into the evaluation of the influence of different GPS workloads on injury risk. When investigating multifactorial phenomena, statistical approaches that enable multiple explanatory variables provide a more appropriate option.

Consideration 2—theoretical theme—between-athlete and within-athlete differences

One of the primary benefits of ILD is that it enables researchers (when using certain analyses) to differentiate within-person and between-person effects.3 In the sports medicine field, this would correspond to researchers asking (1) why do some athletes suffer few injuries (between-person inquiry) while others appear ‘injury-prone’? and on the other hand, (2) at what point is a given athlete (within-person inquiry) more likely to sustain an injury? The simpler statistical approaches used by researchers in our included studies (correlation, t-tests, ANOVAs, regular regression) are limited in the number of variables they can include, and consequently cannot differentiate risk between-athletes and within-athletes. Tests of group differences (independent sample t-tests and one-way ANOVAs) only differentiate between athletes (eg, injured vs uninjured), while repeated measures tests (repeated measures ANOVA and paired t-tests) only examine within-athlete differences (eg, loads preceding injuries vs loads during non-injury weeks).

GEEs were commonly used to address some of the longitudinal data challenges. Although this approach accounts for the clustering within-persons, it assumes the effects of predictor variables are constant across all athletes.67 Simple Cox proportional hazards models48 are common in survival analyses, but do not differentiate between-person and within-person effects.68

Only two statistical tools were used in a way that examined between-athlete and within-athlete differences in injury risk. The frailty model by Gabbett and Ullah66 modelled each athlete as a random effect with a given frailty. The multilevel model by Windt et al57 incorporated athlete-level variables (age, position, preseason sessions) and observation-level variables (weekly workload measures). In the latter case, athletes’ weekly distances did not affect their risk of injury in the subsequent week (OR 0.82 for 1 SD increase, 95% CI 0.55 to 1.21)—a within-athlete inquiry. However, controlling for weekly distance and the proportion of distance at high speeds, athletes who had completed a greater number of preseason training sessions had significantly reduced odds of injury (OR 0.83 for each 10 preseason sessions, 95% CI 0.70 to 0.99)—a between-athlete inquiry. These two examples highlight that certain analyses carry a distinct advantage of allowing researchers to tease out differences both between-study and within-study participants

Consideration 3—theoretical theme—injury risk as a complex dynamic system

Complex systems are defined, among other things, by the interaction between multiple internal and external variables that interact to produce an outcome. Simple analyses (t-tests, correlations), which cannot incorporate multiple variables, cannot examine the interaction between multiple factors. However, even other traditional analyses which are more effective in handling the challenges of longitudinal data (eg, GEEs, Cox proportional hazards models) were not used to incorporate non-linear interactions between predictor variables.

The most recent reviews of athletic injury aetiology have highlighted complex systems models.24 69 None of the analyses included in our review analysed intensive longitudinal workload–injury data with statistical analyses that fit within a complex systems framework. This lack of research may reflect the fact that the suggestion that injury aetiology fits within a dynamic, complex systems framework is still relatively ‘new’ in this field. It remains to be seen whether a complex systems approach and the analyses recommended in such reviews (eg, self-organising feature maps, classification and regression trees, agent-based models, etc) are more effective for evaluating the association between workloads and injury.24

Consideration 4—ILD challenge—including time-varying and time-invariant variables

Tying back to the theoretical model of workloads and injury, some relevant factors may be relatively stable (time-invariant) over the course of an observation period (eg, height, age), while others are time-varying (eg, workload). Some analyses can incorporate both time-varying and time-invariant variables, while others are limited in this respect. All analyses that cannot or did not address the multifactorial nature of injury cannot include time-varying and time-invariant variables concurrently. Group difference tests (t-tests, ANOVAs, etc) may collect time-varying measures, but must aggregate them into a single average for analysis.

Including time-varying and stable variables in the same analysis links closely to between-athlete and within-athlete differences—with the frailty model66 and multilevel model57 both used in a way that allowed the researchers to include both. The one exception in our included studies was the GEE approach. As mentioned earlier, the GEE assumes an ‘overall’ effect for each explanatory variable, such that between-athlete and within-athlete differences cannot be differentiated.70 However, the major benefit to a GEE is that it accounts for the repeated measures for each participant and can therefore include both time-invariant and time-varying variables for each participant.

Consideration 5—ILD challenge—handling missing and unbalanced data

Dealing with missing and unbalanced data is a near certainty when collecting ILD, and is common in applied workload-monitoring settings.71 Such missing data decrease statistical power and increases bias, and may be missing at completely at random, missing at random or missing not at random. When analysing aggregated data or using analyses that require balanced data, strategies may include complete-case analysis, last observation carried forward or various imputation methods.72 73 Multiple imputation methods, of which there are many, involves replacing missing values with values imputed from the observed data and is preferred over single imputation. Finally, if interactions are included in regression analyses, the transform-then-impute method has been recommended.74

However, these missing data approaches are not recommended for longitudinal analyses, since researchers have statistical analyses that are robust to missing and unbalanced data at their disposal.75 Statistically, four types of analyses used in this review are robust to missing and unbalanced data—Cox proportional hazards models, GEEs, multilevel models and frailty models, where all observations can be included in the analysis, and athletes can have different numbers of observations. Since mixed/multilevel models have less stringent assumptions for missing data (ie, missing at random) than GEEs (ie, missing completely at random), they have been suggested over GEEs.75

While the statistical concerns related to unbalanced data may be addressed with these analyses, missing data may also affect derived variables, which are common in workload–injury research. These derived variables include rolling workload averages (eg, 1 week, ‘acute’, workloads, 4 weeks average, ‘chronic’, workloads, etc),33 41 ‘monotony’ (average weekly workload divided by the SD of that workload) or ‘strain’ (the monotony multiplied by the average weekly workload).30 Since these measures are all calculated from workloads accumulated over time, failing to estimate workloads for these missing sessions (that end up being treated as ‘0’ workload days) means inferences from these derived measures may be underestimated and unreliable. Few authors discussed how they handled missing data. In these instances, it is important that researchers report how they accounted for missing data, whether they be strategies employed in the past, for example, full team average values,41 weekly individual averages,42 player-specific per-minute values by time played43 or whether through other advanced imputation methods recommended for ILD.72 74

Challenge 6—ILD challenge—dependencies created by repeated measures

Collecting ILD in applied sport settings means repeated (often daily) measurements of the same athlete, such that observations are clustered within athletes. Comparisons of independent groups, through Χ² tests, independent sample t-tests and one-way/two-way ANOVAs all assume participants contribute a single observation to the analysis and force an aggregated variable (eg, average number of balls bowled in a week) to conduct the analysis.37 Similarly, correlation and simple regression (in its linear, logistic and multinomial forms) assume independence of observations.76 Paired t-tests and repeated measures ANOVA were used to deal with repeated measurements by comparing the same athletes’ workloads at different periods (eg, the week before injury vs weeks that did no precede injury).

Of the analyses that addressed this challenge, GEEs were used most commonly (six studies). GEE’s ability to handle clustering was also used in one article to control for players clustering within teams.39 Cox proportional hazard models, used in one article,48 can handle repeated measurements for participants.77 Multilevel models57 and frailty models66an extension of the Cox proportional hazards model—were also used in a single instance each, where repeated measures were clustered within players through a random player effect.

As mentioned in our introduction, there may be additional data dependency created by recurrent injuries.78 Previous recommendations to handle the recurrent injury challenges have included frailty models,79 and a multistate framework.80 However, as so few articles reported collecting information on recurrent injuries (n=5), we focused primarily on the dependencies caused by repeated measures across participants.

Challenge 7—ILD challenge—incorporating time into the analysis/temporality

One of the most relevant questions in ILD analyses is the way that time is accounted for.1 3 Some authors used one-way32 and two-way repeated measures ANOVAs81 to compare loading in different seasons or season-periods—a very simple way of accounting for time. Repeated measures ANOVAs44 48 82 and paired t-tests37 46 also account for time by categorising time-periods as preinjury blocks or non-injury blocks. Multilevel models have been used to examine change through the interactions of variables with time, but the one multilevel model used in this review did not include time as a covariate.57 Survival analyses explicitly account for time by calculating the effects of variables on the predicted time-to-event.48 66 Notably, only one analysis—the frailty model66adjusted the probability of long-term outcomes (eg, injury) based on variations after an initial capture of risk, something few traditional analyses accomplish.26

Temporality is also vital in considering potential causal associations. While making causal inferences from observational data is a topic beyond the scope of this paper, temporality is a well-accepted component of causality dating back, at least, to Bradford Hill’s ‘criteria’.83 Without temporality—where a postulated cause precedes the outcome—directional associations cannot be made.84 85 A lack of temporality can also skew associations since it allows for reverse causality. In the workload–injury field, findings that high weekly workloads are sometimes associated with lower odds of injury in a given week53 57 may be in part because players who get injured in a given week are less likely to accumulate high weekly workloads.

Trying to account for temporality, some researchers have included a latent period—where workload variables are examined for their association with injury occurrence in a given proceeding time window, like the subsequent week.33 57 While recent work has noted that the length of the latent period may affect model findings,86 it is clear that without some type of latent period, any directional inferences between workloads and injury cannot be made.

Methodological, statistical and reporting considerations

Researcher ‘trade-offs’, consequences of misalignment

We used the workload–injury field to highlight seven themes that relate to theoretical injury aetiology models and temporal design (ILD). In many cases, highlighted published studies’ statistical models either could not, or were not used in a way that addresses these themes. In some cases, misalignment may carry a severe cost—like assumption violations that may bias study results.29 This is akin to building conclusions on an unstable foundation. Other times, researchers have properly employed their chosen statistical approach, but the approaches themselves were limited, and unable to answer research questions that ILD can address. This is more akin to having a grand building plan and all the necessary supplies, but only using a screwdriver to construct the building.

Simple regression models provide an ideal example of researchers’ trade-offs when using traditional statistical analyses on ILD, and the potential costs of misalignment. Although 13 papers used regular regression to analyse the association between workloads and injury outcome, they chose one of three paths when dealing with ILD. First, many proceeded to analyse each daily or weekly data point as an independent observation—not addressing the violation of the independence assumption.33 47 88 Second, some researchers aggregated the workload data into an average weekly workload or total workload exposure over the course of the year, such that each participant contributed only one observation to a classic logistic regression.40 87 Although the regression assumptions were not violated, workload was aggregated into a single metric, the temporal relationship between workload and injury was lost, and there was then no way to analyse the effects of workload fluctuations on injury risk. Third, some researchers converted individual data to team level data and examined team workloads with team injury incidence in a linear regression.36 89 In this final case, no differentiation could then be made between players or within-players, and inferences were only possible at the team level. This may be sufficient to inform research on the association of workloads and injury at the team level, but the theoretical model underpinning team injury rates may differ from those that underpin individual athletes’ injury risk.

Review limitations

Previous systematic reviews investigating the workload–injury relationship have documented the challenges of identifying articles through classic systematic review search strategies.7 9 Heterogeneous keywords and the breadth of sporting contexts have meant previous systematic reviews include many articles post hoc that were not originally identified by their systematic searches (eg, 29 of 67 articles in the paper by Jones et al,7 12 of 35 articles in the paper by Drew and Finch9). Therefore, although we worked to identify articles through six systematic reviews7–10 17 18 and the 2016 IOC consensus statement on athletic workloads and injury,11 we may have missed potentially eligible articles.

We used the cut-off for ILD (>20 observations) proposed by Collins.14 However, there is no universal cut-off for ILD, with previous thresholds of ‘more than a handful’,1 10 observations,90 or 40.3

In some instances, authors’ analytical choices may have been attributable to factors outside of statistical considerations. For example, in lower level competitions, or in organisations with lower budgets, it may not have been feasible to collect multiple variables longitudinally with the available equipment or staff. In these types of instances, the authors would be unable to employ a multifactorial approach, instead of choosing not to use one. Such external factors may have influenced the findings of this methodological review.

Finally, it was beyond the scope of this review to list every challenge posed by ILD, and we were not exhaustive in our discussion of different analyses and their capacity to handle the challenges. Where possible, we tried to identify the themes that are most common within the research field of sport and exercise medicine field. Ultimately, our call to action is that statistical tools be chosen more thoughtfully so that the extensive work put into theory building and data collection is not short-changed by a suboptimal statistical model.

Longitudinal improvements in ILD analysis

Methods and statistical analyses evolve over time, as with all scientific inquiry. Therefore, it is possible that we were a little unfair to some earlier papers. For example, researchers may have chosen analyses that aligned with ‘their’ theoretical model at the time, not what is considered the most current theoretical model. However, most papers were published since 2010—the dynamic, recursive aetiology model was introduced in 2007, and the multifactorial nature of injury risk has been highlighted since 1994.21 As complex systems approaches are the most recently proposed theoretical model,24 69 it is not surprising that none of the included articles analysed the data within this type of framework, with the first analysis of its kind in sport injury research only appearing recently.91 Furthermore, some techniques for longitudinal data analysis have been developed and grown in popularity recently, so researchers may not have been aware of alternative approaches at the time of their studies.

As more statistical methods are developed and refined for longitudinal data analysis, researchers will continue to gain awareness and skills with these analyses and their implementation is likely to become more common. Some evidence for that progression can be seen in this review. If we were to assign a ‘method’ score to each analytical approach outlined in table 1, assigning 0 for each red box, 0.5 for each yellow box and 1 for each green box (eg, correlation would score 0, while GEEs would score a 3.5), and then assign that score to each paper in the study, we could obtain a rough estimate of whether analytical approaches were improving over time. Breaking the papers roughly into four periods, the ‘average score’ for papers up to 2005 (n=6) is 1.6, papers between 2006 and 2010 (n=7) score an average of 1.9, papers between 2011 and 2015 (n=11) score 1.7 and papers since 2016 (n=10) score an average of 2.3. Moreover, since the search for this current review was conducted, there have been promising developments in the sports medicine field and a continued improvement in longitudinal analysis. Recent publications have applied statistical models that more appropriately take advantage of the strengths inherent to ILD, and better align with the theoretical frameworks.92–97

Mediation, effect measure modification and interaction/moderation are all causal models, which may also contribute to aetiological frameworks.98 We recently proposed that traditional intrinsic and extrinsic risk factors may act as moderators or effect measure modifiers of the workload–injury association.62 If that is true, the most appropriate statistical model would include workload measures as the independent variable of interest, and incorporate other risk factors such that these causal models can be investigated, whether by stratifying effects across different levels of these risk factors, or including an interaction term within regression.63 While no included articles performed such an analysis, recent studies (not included in this review because it was published after our search) have started to adopt these approaches.94 99 100 For example, Møller et al used a frailty model with weekly workload fluctuations (decrease or <20% increase, 20%–60% increase and >60% increase) as the primary predictor variable in a frailty model. Known shoulder risk factors were treated as ‘effect measure modifiers’, so the model was stratified based on the presence or absence of a given risk factor (eg, scapular dyskinesis).65 In so doing, the researchers used a statistical tool (component 3) that addressed all the challenges inherent to longitudinal data (component 2), conducting a multifactorial analysis that clearly differentiated both within-athlete and between-athlete injury risk—key aspects of the theoretical model (component 1).

Future directions and recommendations for ILD analysis

Researchers in the sports medicine field should be encouraged that the increased availability of ILD may improve understanding of athletes’ fluctuating injury risks—as articulated by their theoretical models. More advanced statistical techniques for longitudinal data are increasingly being developed and implemented across disciplines. This will enable sports medicine researchers to more accurately answer their theory-driven questions by taking advantage of the benefits of ILD. To capitalise on this understanding, researchers must choose statistical models that most closely align with their theory and that address longitudinal data challenges. GEEs, a Cox proportional hazards model, a multilevel logistic model, and a frailty model were the four analyses that most closely approached this alignment within our included papers. However, there remains some clear room for improvement in the future.

First, although mixed modelling was only used in one study, these forms of analyses have inherent values over GEE methods and have been recommended for this reason.101 Because of sample structure, mixed models prevent false-positive associations and have an applied correction method that increases the power of the analysis102; a finding that is useful with the commonly smaller samples. Mixed models also carry a less stringent missing data assumption (missing at random) when compared with GEEs (missing completely at random). Furthermore, whereas GEEs require the correlation structure to be chosen by the researcher (which may be wrong), mixed models model the correlation structure so that it can be investigated. Finally, GEEs assume a constant effect across all individuals in the model, while mixed models allow for individual level effects and for differentiating these individual effects.

To borrow an example from another field and demonstrate the flexibility and utility of mixed effect models, Russell et al used daily stressor values from students during their first three college years to demonstrate that students consumed more alcohol on high-stress days than low-stress days (within-person fixed effect).103 However, a significant random effect between students suggested that some students experienced this increase in alcohol consumption, while others did not. Finally, those students with a tendency to increase alcohol consumption with stressors were more likely to have drinking-related problems in their fourth year.103 For more information on multilevel/mixed effect models for longitudinal analysis, readers are referred to a other helpful resources.1 28 75 104 105

Time-to-event models are another family of statistical models that have become a very common in clinical research articles—reported in 61% of original articles in the New England Journal of Medicine in 2004–2005106but were used infrequently within our included articles. Notably, these models answer a different research question— when does an event occur? These approaches can account for many of the ILD challenges.107–109 Time-to-event models account for censoring, can incorporate time-varying exposures, time-varying effect measure modifiers and time-varying changes in injury status, and may be used to control for competing risks.107 As with other modelling techniques, the appropriate number of events per variable has been investigated, and at least 5–10 events per variable are recommended for these types of models to prevent sparse data bias.110 As long as this and other model assumptions are met, more advanced time-to-event models may be a valuable tool for researchers analysing ILD.77 111 112

Lastly, computational modelling methods, which involve computer simulation, have both pros and cons when modelling injuries. They may provide insight on the best ways to model certain predictor variables,113 and open the door to more complex systems modelling (eg, agent-based modelling).91 Although they show promise, such simulation studies are based on artificially generated data and must be interpreted carefully.114

More analytical approaches are available for ILD, but a full discussion of each of these is beyond the scope of this paper. For the interested reader, functional data analysis,115 machine learning approaches,92 95 time series analysis116 and time-varying effect models117 all show promise. Such analyses and others for ILD can be found in the landmark ILD textbook by Walls and Schafer,1 and more recently, in the work of Bolger and Laurenceau.104

We believe ILD provide an exciting opportunity for applied researchers and statisticians to collaborate moving forward. As the field continues to progress to more advanced analytical approaches that may better suit ILD, the need for collaboration with statisticians will be vital. In our included papers, few researchers referenced methodological or statistical references to justify their analytical approaches. In some instances, this may be attributable to using common, relatively simple analyses—one likely does not expect a citation for a t-test. Where such references existed, they were often to previous papers in the field, not statistical sources. In future longitudinal analyses, we encourage researchers to partner with a statistician, psychometrician, epidemiologist, biostatistician, etc.118 Such fruitful collaborations may lead to statistical approaches that take full advantage of ILD by aligning theory, data collection and statistical analyses as seamlessly as possible.