Not straightforward: modelling non-linearity in training load and injury research

Abstract

ObjectivesTo determine whether the relationship between training load and injury risk is non-linear and investigate ways of handling non-linearity.MethodsWe analysed daily training load and injury data from three cohorts: Norwegian elite U-19 football (n=81, 55% male, mean age 17 years (SD 1)), Norwegian Premier League football (n=36, 100% male, mean age 26 years (SD 4)) and elite youth handball (n=205, 36% male, mean age 17 years (SD 1)). The relationship between session rating of perceived exertion (sRPE) and probability of injury was estimated with restricted cubic splines in mixed-effects logistic regression models. Simulations were carried out to compare the ability of seven methods to model non-linear relationships, using visualisations, root-mean-squared error and coverage of prediction intervals as performance metrics.ResultsNo relationships were identified in the football cohorts; however, a J-shaped relationship was found between sRPE and the probability of injury on the same day for elite youth handball players (p<0.001). In the simulations, the only methods capable of non-linear modelling relationships were the quadratic model, fractional polynomials and restricted cubic splines.ConclusionThe relationship between training load and injury risk should be assumed to be non-linear. Future research should apply appropriate methods to account for non-linearity, such as fractional polynomials or restricted cubic splines. We propose a guide for which method(s) to use in a range of different situations.

Assessing the cumulative effect of long-term training load on the risk of injury in team sports

“…Using splines or fractional polynomials, it can explore non-linearity in both the magnitude of the effect of absolute training load and in the time-dependent effects. 15 …”

“…The relationship between absolute training load and injury risk was simulated to be J-shaped ( online supplemental file 1 figure S2A ). 15 Under this assumption, the lowest point of risk was intermediate levels of training load. The highest point of risk was set at high levels of training load.…”

“… 34 DLNM combines a function on the magnitude of sRPE and a function of the distance since day 0 up to lag 27 (4 weeks). The sRPE was modelled with restricted cubic splines 15 and the lag function with a linear model. The model predictions were visualised to assess the ability of DLNM to explore effects.…”

“… 9 13 A statistical model is a generalisation that is unlikely to tailor the prognostic course of an individual accurately, 14 but it may inform researchers and clinicians about causation and patterns of injury risk. Among others, statistical solutions have been proposed to handle the time-varying effects, 9 the potential for non-linear effects, 15 the cumulative effect, 13 16 and the effect of relative training load 17 in the risk of injury. While statistical models and approaches have been recommended to handle these challenges in isolation, it is still unknown how to explore all the raised challenges in symphony.…”

Incidence and risk factors of intraoperative periprosthetic femoral fractures during primary total hip arthroplasty: 218,423 cases reported to the Norwegian Arthroplasty Register between 1987 and 2020

“…For ease of presentation, we used categorized age in the main analyses, even though categorization of continuous exposure variables has been shown to reduce statistical power ( 25 ), is suboptimal for exploring nonlinear effects ( 26 ), and unreasonably assumes that the relationship between the exposure and the outcome is flat within intervals. Data-driven categorization such as quartile cut-offs exacerbates the issue, and we therefore chose intervals based on clinical rationale.…”