Dear Editor,
I am writing in regard Edouard et al’s recent publication in your journal to bring your attention to what I think are some errors that have perhaps slipped through the editing process.
The paper describes the results of their protocol (Lahti et al 2020): “… to compare if there is a significant effect of the intervention on the (hamstring muscle injury) occurrence using Cox regression analysis” where the intervention was “a multifactorial and individualised HMI risk reduction programme”.
The pre-specified outcome (hamstring injury risk) was found to be no different for those undertaking the novel programme compared to the control group at any time – i.e. the complex multifactorial individualized programme did not reduce hamstring injury incidence, risk, or burden. The authors have subsequently reported the findings of secondary analyses not outlined in the published protocol. These reported secondary analyses also found no difference in hamstring muscle injury risk/incidence, but they did report that for a sub-group of 31/90 selected participants there was a reduction in hamstring injury burden (but not others, some of whom reported an increase).
Specifically, these apparent errors (reporting a reduction in incidence/risk for the secondary analyses where the data do not support this) are:
1. in the abstract: “… and additional secondary analyses showed a significant association between the intervention and lower HMI burden, incidenc...
Dear Editor,
I am writing in regard Edouard et al’s recent publication in your journal to bring your attention to what I think are some errors that have perhaps slipped through the editing process.
The paper describes the results of their protocol (Lahti et al 2020): “… to compare if there is a significant effect of the intervention on the (hamstring muscle injury) occurrence using Cox regression analysis” where the intervention was “a multifactorial and individualised HMI risk reduction programme”.
The pre-specified outcome (hamstring injury risk) was found to be no different for those undertaking the novel programme compared to the control group at any time – i.e. the complex multifactorial individualized programme did not reduce hamstring injury incidence, risk, or burden. The authors have subsequently reported the findings of secondary analyses not outlined in the published protocol. These reported secondary analyses also found no difference in hamstring muscle injury risk/incidence, but they did report that for a sub-group of 31/90 selected participants there was a reduction in hamstring injury burden (but not others, some of whom reported an increase).
Specifically, these apparent errors (reporting a reduction in incidence/risk for the secondary analyses where the data do not support this) are:
1. in the abstract: “… and additional secondary analyses showed a significant association between the intervention and lower HMI burden, incidence and risk.”
2. In the “Practical implications” section: “…programme was feasible and associated with reduction of HMI burden, incidence and risk for some aspects.”
3. In the conclusions section: “…secondary analyses showed a significant association between the intervention and lower HMI burden, incidence and risk.”
I believe this is important as many clinicians, perhaps time-poor, may only scan these sections, and not the details of the results, and erroneously conclude that the programme was successful in reducing hamstring injury risk/incidence.
References:
Lahti J, Fleres L, et al. A musculoskeletal multifactorial individualised programme for hamstring muscle injury risk reduction in professional football: results of a prospective cohort study. BMJ Open Sport & Exercise Medicine 2024;10:e001866. doi:10.1136/ bmjsem-2023-001866
Lahti J, Mendiguchia J, Ahtiainen J, et al. Multifactorial individualised programme for hamstring muscle injury risk reduction in professional football: protocol for a prospective cohort study. BMJ Open Sport Exerc Med 2020;6:e000758.
Solle et al. argue that our study “supports a conclusion for the relationship between sex and race time, as a result of the poorly constructed and likely miscategorized sex variable”. However, if this view were correct, some other explanation would be needed to explain the statistically significant correlations we found between sex and race time. Solle et al. do not provide any such explanation.
They state that our methodology is “unreliable”. But we do not assume that our model for sex is perfectly reliable, and we emphasize throughout that we model sex probabilistically. As we explain in the appendix to our paper, and illustrate with a numerical example, if one increases the uncertainty in our model this would indicate that there is an even stronger relationship between sex and race times. Solle et al. do not consider this point in their response, and as a result they fail to explain how their theory can be reconciled with the data.
In the absence of such an argument, we believe that their theory cannot be reconciled with the data and so must be in some way flawed. We believe that the flaw in their argument is to overstate the difficulty in ascribing a sex to a non-binary athlete. For example, Solle et al. give the impression that we modelled non-binary athletes’ sex using only their names, yet for the majority of non-binary athletes we could determine their sex from their race history.
Solle et al. go on to argue that our use of the terminology “na...
Solle et al. argue that our study “supports a conclusion for the relationship between sex and race time, as a result of the poorly constructed and likely miscategorized sex variable”. However, if this view were correct, some other explanation would be needed to explain the statistically significant correlations we found between sex and race time. Solle et al. do not provide any such explanation.
They state that our methodology is “unreliable”. But we do not assume that our model for sex is perfectly reliable, and we emphasize throughout that we model sex probabilistically. As we explain in the appendix to our paper, and illustrate with a numerical example, if one increases the uncertainty in our model this would indicate that there is an even stronger relationship between sex and race times. Solle et al. do not consider this point in their response, and as a result they fail to explain how their theory can be reconciled with the data.
In the absence of such an argument, we believe that their theory cannot be reconciled with the data and so must be in some way flawed. We believe that the flaw in their argument is to overstate the difficulty in ascribing a sex to a non-binary athlete. For example, Solle et al. give the impression that we modelled non-binary athletes’ sex using only their names, yet for the majority of non-binary athletes we could determine their sex from their race history.
Solle et al. go on to argue that our use of the terminology “natal sex” is “pathologizing and stigmatizing”. This could be seen as ruling out the use of a gender-critical operationalization of sex in our analysis irrespective of the data. However, to determine the effectiveness of a scientific model, one should be guided by empirical evidence. Solle et al.’s argument would appear to be ideological rather than scientific.
Solle et al. also state that our findings “should not have any implication in law or policy”. However, in the UK, the Equality Act 2010 it is unlawful for service providers to indirectly discriminate on the basis of sex. Our results therefore suggest that, as males would be more likely to win than females, a single non-binary race category is likely to be unlawful.
Inclusion for non-binary athletes in racing events has progressed in the last three years, with five of the six Abbott Major Marathons offering non-binary running categories in 2023. Given that the “main issue for non-binary people is that they cannot compete authentically” without the non-binary category1, non-binary race divisions were created, in part, as inclusion measures for non-binary individuals. As the number of non-binary athletes participating in running is increasing2, the representation and needs of non-binary athletes should be studied using appropriate methods that are in line with current best practices3, particularly in assessing gender and sex measurement and analyses. In their paper, “Performance of non-binary athletes in mass-participation running events,” Armstrong et al. utilize several methodological approaches and analyses that do not appropriately assess the performance of non-binary athletes. As a consequence, the conclusions of the paper introduce numerous biases with results that do not accurately reflect the reality of non-binary athletes.
In designing their study, the authors attempt to determine the sex assigned at birth (labeled natal sex in their model) of non-binary athletes based on the presumed sex assigned at birth of their names. This approach is methodologically unreliable and flawed4. Specifically, the authors fail to distinguish between sex assigned at birth, legal sex, and any sex-related medical intervention that the athle...
Inclusion for non-binary athletes in racing events has progressed in the last three years, with five of the six Abbott Major Marathons offering non-binary running categories in 2023. Given that the “main issue for non-binary people is that they cannot compete authentically” without the non-binary category1, non-binary race divisions were created, in part, as inclusion measures for non-binary individuals. As the number of non-binary athletes participating in running is increasing2, the representation and needs of non-binary athletes should be studied using appropriate methods that are in line with current best practices3, particularly in assessing gender and sex measurement and analyses. In their paper, “Performance of non-binary athletes in mass-participation running events,” Armstrong et al. utilize several methodological approaches and analyses that do not appropriately assess the performance of non-binary athletes. As a consequence, the conclusions of the paper introduce numerous biases with results that do not accurately reflect the reality of non-binary athletes.
In designing their study, the authors attempt to determine the sex assigned at birth (labeled natal sex in their model) of non-binary athletes based on the presumed sex assigned at birth of their names. This approach is methodologically unreliable and flawed4. Specifically, the authors fail to distinguish between sex assigned at birth, legal sex, and any sex-related medical intervention that the athletes may have had, conflating them. This technique is not novel, but rather a misapplication of methods. As a result, the authors are analyzing assumed sex assigned at birth and race times, but assume that it accounts for gender. The model does not analyze gender. As a member of an organization whose athletes are a part of this analysis, we can confirm that errors are present.
Principles of research methods dictate that the design of a study must align with the study's objectives and the context of the phenomenon. However, in Amstrong’s case, the authors’ particular use of language describing natal sex shows their use of a pathologizing and stigmatizing framework in viewing the phenomenon, which is misaligned with current best practices in trans health research5. Confirmation bias is present in the way the authors attempt to guess sex assigned at birth and design the independent variable labels. Treating gender identity as “natal-female nonbinary” or “natal-male nonbinary” is still miscategorizing non-binary athletes. Finally, the authors introduce non-neutrality bias as they favor sex assigned at birth as a concept over gender identity by saying “sex has considerable explanatory advantages over gender identity” without providing evidence to support this.
These poorly chosen methods, apparent biases, and lack of reasonable evidence lead to inaccurate conclusions. The authors state that "...if one wishes to understand the needs of gender non-conforming individuals, it is vital to control for sex as it is likely to play a significant role in any analysis." Because the analysis only supports a conclusion for the relationship between sex and race time, as a result of the poorly constructed and likely miscategorized sex variable, we know nothing about the needs of gender non-confirming individuals at all.
The methods of this paper are misapplied and not robust. Importantly, the non-binary category in running helps to validate the identities of non-binary individuals1. The author's conclusion that sex and gender data should both be collected does not disprove any concepts regarding the importance of gender identity and relating to social determinants is an inappropriate conclusion. As a result of these misapplications, the findings cannot and should not have any implication in law or policy. Future research to better understand the needs of this population should include non-binary runners themselves, as non-binary runners are likely experts in their own needs6,7.
References
1. Erikainen, S., Vincent, B., & Hopkins, A.. Specific Detriment: Barriers and Opportunities for Non-Binary Inclusive Sports in Scotland. Journal of Sport and Social Issues, 2022; 46(1), 75-102.
2. Bernhard, J. What Does It Take to Design an Inclusive Running Race? - Uncommon Path – An REI Co-op Publication. REI. 2023. https://www.rei.com/blog/run/inclusion-in-running (accessed 11 January, 2024)
3. Reisner SL, Deutsch MB, Bhasin S, et al. Advancing methods for US transgender health research. Curr Opin Endocrinol Diabetes Obes. 2016 Apr;23(2):198-207.
4. Blevins, C., & Mullen, L. DHQ: Digital Humanities Quarterly: Jane, John … Leslie? A Historical Method for Algorithmic Gender Prediction. Alliance of Digital Humanities Organizations. 2015
5. Ruane, J. M. Essentials of research methods: A guide to social science research. Malden, MA: Blackwell Publishing. 2005
6. Solle JC, Steinberg A, Marathe P, Gray TF, Emmert A, Abel GA. Patients as experts: characterizing the most relevant patient-reported outcomes after hematopoietic cell transplantation. Bone Marrow Transplant. 2020 Jan;55(1):242-244.
7. Streed CG Jr, Perlson JE, Abrams MP, Lett E. On, With, By-Advancing Transgender Health Research and Clinical Practice. Health Equity. 2023 Mar 3;7(1):161-165.
Many thanks for producing the thoroughly enjoyable article on SEM practitioners around the world. We would like to add that SEM in Malaysia has also been well established as a standalone speciality since 2002. The impetus for for kickstarting the speciality was having being appointed the host city for Commonwealth Games 1998 (Kuala Lumpur). Our training programme, was in effect a combined 4 year run-through standalone clinical training, in its inception together with Rehabilitation Medicine originally, of which very early then branched out into an independent Sports Medicine Masters training program in the early 2000s, with on average 4 to 6 trainees a year qualifying out of the program. At the moment, we have approximately nearly 60 practitioners throughout the broader Malaysia with a large number of my contemporaries working within the Ministry of Health Malaysia. Our core service focuses on optimising musculoskeletal health across all spectrum of age and health, performing diagnostic imaging and guided-pain interventional, therapeutic and regenerative procedures, sideline and team physician management, prescriptive exercise clinics and fitness/performance testing, and various collaborative work with public health in being an advocate for healthy living. The training program is indeed quite similar as to how the Australasian and British FSEM curriculum content-wise, and has been traditionally done at the University of Malaya throughout the whole clinical course. Many of...
Many thanks for producing the thoroughly enjoyable article on SEM practitioners around the world. We would like to add that SEM in Malaysia has also been well established as a standalone speciality since 2002. The impetus for for kickstarting the speciality was having being appointed the host city for Commonwealth Games 1998 (Kuala Lumpur). Our training programme, was in effect a combined 4 year run-through standalone clinical training, in its inception together with Rehabilitation Medicine originally, of which very early then branched out into an independent Sports Medicine Masters training program in the early 2000s, with on average 4 to 6 trainees a year qualifying out of the program. At the moment, we have approximately nearly 60 practitioners throughout the broader Malaysia with a large number of my contemporaries working within the Ministry of Health Malaysia. Our core service focuses on optimising musculoskeletal health across all spectrum of age and health, performing diagnostic imaging and guided-pain interventional, therapeutic and regenerative procedures, sideline and team physician management, prescriptive exercise clinics and fitness/performance testing, and various collaborative work with public health in being an advocate for healthy living. The training program is indeed quite similar as to how the Australasian and British FSEM curriculum content-wise, and has been traditionally done at the University of Malaya throughout the whole clinical course. Many of us are also attached with the broader sporting teams across the country. We are presently actively engaging medical students during their undergraduate program to build the awareness of the speciality and services going forward. Collectively, SEM Malaysia are presently represented by the Malaysian Association of Sports Medicine (MASM) and we are currently working to create a collegiate under the Academy of Medicine Malaysia (AMM) to get better advocacy and visibility nationally and internationally.
The systematic review by Paultre et al. supports the use of turmeric or curcumin extract for knee osteoarthritis pain.
They did not perform a formal meta-analysis but summarize the results of individual studies by calculating effect sizes based on the data in the original papers. Unfortunately there are two problems with these, one major and the other more modest.
The major issue is with the last study reported in table 3, Srivastava (2016). Paultre et al. report very large effect sizes for this study, such as 8.6, 9.5, and even 11 for a visual analogue scale. These effect sizes are the usual "d" value, that is the mean difference divided by the standard deviation. Effect sizes of such high magnitudes should raise a red flag that something is wrong, as they are rarely attained in clinical studies.
The authors' impressive effect sizes for Srivastava are errors due to using a standard error of the mean (SE) as if it were a standard deviation (SD). Srivastava et al. define the statistic used in the statistical methods: "The results are presented as mean ± SE." The values shown are also impossibly small to be standard deviations, which is what caught my attention. Both at 60 days and 120 days, the "standard deviations" shown for a 10-point VAS scale are around 0.1. This suggests a range of responses of about 0.5, which is not plausible.
The SEM is the SD divided by the square root of the sample size and represents...
The systematic review by Paultre et al. supports the use of turmeric or curcumin extract for knee osteoarthritis pain.
They did not perform a formal meta-analysis but summarize the results of individual studies by calculating effect sizes based on the data in the original papers. Unfortunately there are two problems with these, one major and the other more modest.
The major issue is with the last study reported in table 3, Srivastava (2016). Paultre et al. report very large effect sizes for this study, such as 8.6, 9.5, and even 11 for a visual analogue scale. These effect sizes are the usual "d" value, that is the mean difference divided by the standard deviation. Effect sizes of such high magnitudes should raise a red flag that something is wrong, as they are rarely attained in clinical studies.
The authors' impressive effect sizes for Srivastava are errors due to using a standard error of the mean (SE) as if it were a standard deviation (SD). Srivastava et al. define the statistic used in the statistical methods: "The results are presented as mean ± SE." The values shown are also impossibly small to be standard deviations, which is what caught my attention. Both at 60 days and 120 days, the "standard deviations" shown for a 10-point VAS scale are around 0.1. This suggests a range of responses of about 0.5, which is not plausible.
The SEM is the SD divided by the square root of the sample size and represents the accuracy of the sample mean, not the distribution of individual subject values. Effect sizes incorrectly calculated using the SEM will thus be inflated by a factor of the square root of the sample size. Correcting for this leaves several still large effects (near 1) but other effect sizes drop to below 0.5. None are over 2.
The modest issue is with the first study in the table, Panda. I don't see any actual errors, but the standard deviations on the VAS are smaller than is typical for a 100 point scale. I believe this is because an inclusion criterion for that study was, "VAS score during the most painful knee movement between 40-70mm." Restricting to a max of 70 for "most painful" is a significant restriction and results in rather small standard deviations for the VAS.
On a 100-point scale a mean difference of 10 is not a large effect clinically, but Paultre et al. show differences of 5 and 7 as "large" for the Panda study because of the small standard deviations. Not until day 60 is there a mean difference much bigger than 10 on the VAS.
I would be interested to see if the authors would modify their conclusions after addressing these issues.
====
References (both are from the reviewed paper)
Srivastava S, Saksena AK, Khattri S, et al. Curcuma longa extract reduces inflammatory and oxidative stress biomarkers in osteoarthritis of knee: a four-month, double-blind, randomized, placebo-controlled trial. Inflammopharmacology 2016;24:377–88
Panda SK, Nirvanashetty S, Parachur VA, et al. A randomized, double blind, placebo controlled, parallel-group study to evaluate the safety and efficacy of Curene® versus placebo in reducing symptoms of knee oa. Biomed Res Int 2018;2018:1–8.
We read with interest your editorial ‘Sport and exercise medicine around the world: global challenges for a unique healthcare discipline’ [1] in BMJ Open Sport and Exercise Medicine. We would like to congratulate the authors for bringing the challenges of our speciality back into the spotlight again.
While Sports and Exercise Medicine (SEM) may be a modern and more inclusive terminology than sports medicine, many of the challenges of our speciality have remained the same over the years. Societies such as the European College of Sports and Exercise Physicians (ECOSEP) have championed for years for the advancement of sports medicine/ SEM speciality across Europe by providing education, publishing research, organising congresses, collaborating with other organisations and serving as a source of information to the public [2–4]. ECOSEP has been promoting exercise for prevention and treatment to policy holders, creating post-graduate programmes and seminars to provide further training for physicians and bringing practitioners together, not only with biannual congress but also through promoting professional dialogue and standards [2–4]. Other societies, like the European Federation of Sports Medicine Associations (EFSMA) have been champing for a common sports medicine speciality within Europe for over 20 years, providing a detailed curriculum for sports medicine practitioners [5]. Even back then they recognised that sports medicine is a m...
We read with interest your editorial ‘Sport and exercise medicine around the world: global challenges for a unique healthcare discipline’ [1] in BMJ Open Sport and Exercise Medicine. We would like to congratulate the authors for bringing the challenges of our speciality back into the spotlight again.
While Sports and Exercise Medicine (SEM) may be a modern and more inclusive terminology than sports medicine, many of the challenges of our speciality have remained the same over the years. Societies such as the European College of Sports and Exercise Physicians (ECOSEP) have championed for years for the advancement of sports medicine/ SEM speciality across Europe by providing education, publishing research, organising congresses, collaborating with other organisations and serving as a source of information to the public [2–4]. ECOSEP has been promoting exercise for prevention and treatment to policy holders, creating post-graduate programmes and seminars to provide further training for physicians and bringing practitioners together, not only with biannual congress but also through promoting professional dialogue and standards [2–4]. Other societies, like the European Federation of Sports Medicine Associations (EFSMA) have been champing for a common sports medicine speciality within Europe for over 20 years, providing a detailed curriculum for sports medicine practitioners [5]. Even back then they recognised that sports medicine is a multidisciplinary speciality dealing with health promotion for the general population by stimulating a physically active lifestyle as well as providing diagnoses, retreatment, prevention programmes and rehabilitation following injuries or illnesses sustained by participation in physical activities, exercises and sport at all levels [5]. So, while the terminology SEM may be new, the goals and challenges to the speciality have remained the same.
Another challenge is the common recognition of the speciality across countries; however, this has not even been achieved within Europe, even after years of negotiations with governments and stakeholder. In an open market such as the European Union it makes it challenging for health care professionals, working and traveling with sports teams across Europe as well as being disadvantaged in seeking job opportunitiesin the common market.
We believe adequate employment opportunities for SEM/ sports physicians are another important challenge to be addressed. Historically sports doctors did not receive payment for attending match days or overseeing competitions/ training camps and although this has changed in some countries, this type of work remains voluntary or poorly paid in other countries. Many big international sporting events such as Olympic Games, Athletic European or World Championship and others rely on SEMs as volunteers and while this may be interesting for some SEM to gain experience or for other reasons, we believe it is a practice that should also be addressed. Many SEMs have a portfolio career, e.g., combining working with a sports team, health prevention programmes, private practice, university etc., however employers/ institutions often do not recognise this working type of pattern and are reluctant or unwilling to adapt to modern ways of working.
We agree with your statements that ‘SEM should be more visible in the health-based undergraduate curricula’ [1], and we believe it should be taught by appropriately qualified staff with the necessary qualifications. In some countries, however it is still possible to hold a university chair/ professorship in SEM/ sports medicine without even having obtained the necessary country specific sports medicine qualification or specialised training. What message does this send for the promotion of our speciality?
While we understand that an editorial cannot address all the challenges of our speciality, we hope that some of our challenges maybe also be addressed in future consultations, and we wish the current ‘generation’ of SEMs more success in tackling those challenges compared to previous generations of sports physicians.
References
1 Carrard J, Morais Azevedo A, Gojanovic B, et al. Sport and exercise medicine around the world: global challenges for a unique healthcare discipline. BMJ Open Sport Exerc Med 2023;9:e001603. doi:10.1136/bmjsem-2023-001603
2 ECOSEP. 2023.https://ecosep.eu (accessed 4 May 2023).
3 Heron N, Malliaropoulos NG. International differences in sport medicine access and clinical management. Muscles Ligaments Tendons J 2012;2:248–52.
4 West L, Malliaropoulos N, De Jonge S. ECOSEP: bringing the European SEM family together. Br J Sports Med 2014;48:1585–1585. doi:10.1136/bjsports-2014-094167
5 Ergen E, Pigozzi F, Bachl N, et al. Sport medicine specialty training core curriculum for European countries. J Sports Med Phys Fitness 2008;48:419–33.
We thank Shrier et al. for a thoughtful expansion on the topic of non-linearity.1 The comments from the authors provide valuable insights and detail to both the handling and the interpretation of fractional polynomials and splines, and may interest readers who seek more information than the short introduction in Bache-Mathiesen, et al. 2.
We are especially grateful for elaborating on the interpretation of restricted cubic splines, and the solution of adding a small constant (i.e. 0.1) to all values to handle the value “0” when using fractional polynomials. These topics could not be sufficiently addressed within the limited wordcount of the original article, and we encourage readers to consider these comments.
Conflict of Interest:
None declared.
References
1. Shrier I, Wang C, Stokes T, et al. Important Nuances for Non-Linear Modeling. BMJ Open Sport & Exercise Medicine 2021
2. Bache-Mathiesen LK, Andersen TE, Dalen-Lorentsen T, et al. Not straightforward: modelling non-linearity in training load and injury research. BMJ Open Sport & Exercise Medicine 2021;7(3):e001119. doi: 10.1136/bmjsem-2021-001119
We would like to thank Bache-Matiesen et al.(1) for their thoughtful article on non-linear modelling in sport medicine. Our own study on the non-linear relationship between acute: chronic workload ratio (ACWR) and injury risk in children was published as a preprint (2) and recently accepted by the American Journal of Epidemiology.(3) Below, we highlight some additional underlying principles in non-linear modelling that readers should understand.
GENERAL CONCEPTS
Models are based on information, which includes both data and assumptions. Simple linear models are more prone to bias because they assume a data generating process that is likely incorrect. The flexibility of non-linear models leads to less risk of bias, but also less precision. The optimal choice between bias and uncertainty depends on the context.(4)
Bache-Matiesen describe three non-linear modelling options: quadratic modelling, fractional polynomials (FP), and restricted cubic splines (RCS, where knots are determined by either data driven or a priori methods). These all fall under generalized additive models (GAMs), or generalized additive mixed models (GAMMs; if one uses “random effects” to adjust for repeated measures on participants).
FP methods use a single polynomial function over the entire range of exposures to predict the outcome. Quadratic models are special cases of FP (with exponents of 0, 1 and 2) and are too restrictive to be generally recommended. RCS separate data i...
We would like to thank Bache-Matiesen et al.(1) for their thoughtful article on non-linear modelling in sport medicine. Our own study on the non-linear relationship between acute: chronic workload ratio (ACWR) and injury risk in children was published as a preprint (2) and recently accepted by the American Journal of Epidemiology.(3) Below, we highlight some additional underlying principles in non-linear modelling that readers should understand.
GENERAL CONCEPTS
Models are based on information, which includes both data and assumptions. Simple linear models are more prone to bias because they assume a data generating process that is likely incorrect. The flexibility of non-linear models leads to less risk of bias, but also less precision. The optimal choice between bias and uncertainty depends on the context.(4)
Bache-Matiesen describe three non-linear modelling options: quadratic modelling, fractional polynomials (FP), and restricted cubic splines (RCS, where knots are determined by either data driven or a priori methods). These all fall under generalized additive models (GAMs), or generalized additive mixed models (GAMMs; if one uses “random effects” to adjust for repeated measures on participants).
FP methods use a single polynomial function over the entire range of exposures to predict the outcome. Quadratic models are special cases of FP (with exponents of 0, 1 and 2) and are too restrictive to be generally recommended. RCS separate data into sections by “knots”, determine which polynomials best predict the observed data within the sections defined by the knots, and apply a smoothing function to join the polynomials. The placement of the knots is important. In simulations, we know the true data generating process. In real-world observational data, we do not. Although we believe subjective a priori knot placement is sometimes better than data driven methods, researchers should be aware that gross errors may occur if the assumptions are incorrect.
RCS methods are more flexible than FP because they allow the functions between knots to be different from each other. We highlight two technical points. First, the “restriction” in the RCS method used by Bache-Matiesen appears restricted to using linear functions before the first knot and after the last knot. RCS can include other types of restrictions as well. Second, FP and RCS are just two forms of GAM(M)s. Two other popular forms are penalized regression spline and thin plate regression spline (e.g. default in mgcv package in the statistical program R (5)). The major difference between RCS and the penalized/thin plate regression splines is the shape of the polynomial that is used. The optimal choice depends partly on the research question and partly on the observed data.
SPECIFIC COMMENTS ON RECOMMENDATIONS BY BACHE-MATIESEN
1. Based on their simulations, Bache-Matiesen suggests RCS performs better than FP for predictive modeling. We believe the conclusion is too strong. RCS can be used in situations when there is a more complex underlying structure than FP. However, fitting more complex structure requires more data. When there is limited data and less complex structure, FP could outperform RCS.
2. Bache-Matiesen claim that RCS allowed the authors to model the relationship at high training loads where there were few data points. We caution against this due to the limited information. In our own study on children,(3) we restricted our conclusions about the relationship between acute:chronic workload ratio (ACWR) and injury risk to ACWR <3 where there were enough data. We show the full range of the relationship in the supplementary material to be fully transparent and to help generate hypotheses for future studies but did not feel it appropriate to make inferences.
3. We disagree with Bache-Matiesen that FP is more interpretable than RCS for causal effects, and that RCS results “can only be interpreted in the form of p values and visualisation”. First, we hope that most sport medicine researchers have moved beyond making inferences on p-values because of its severe limitations.(6, 7) Second, for causal questions, we generally estimate the difference in outcome when exposure is set to two different levels. When causal inference assumptions are reasonable, one estimates the causal effect with g-computation using predicted data from the model;(8) this is applicable for both linear and non-linear models. In brief, the magnitude of the causal effect in a non-linear model necessarily depends on the two chosen exposure levels. Although FP has only a single function over its entire range, the causal effect between the chosen exposure levels still requires using g-computation and the predicted values from the FP function. The causal effect using other GAM(M) methods is obtained with the same process; one uses the predicted values provided by the statistical software over the chosen exposure range.
4. The authors discuss the need to add a small constant to training load when it can equal 0, in order to allow for analyses on the log scale. The choice should have theoretical justification. For example, if activity (i.e. training load) is a proxy for time at risk (e.g. game injuries and a game was not played), adding a constant is inconsistent with the research question. However, in the ACWR, activity is a proxy for fatigue in the numerator and a proxy for fitness in the denominator. Both fatigue and fitness are affected by activities of daily living (e.g. occupation, transportation) outside of regular sports. In our analysis on children, we added a constant of 0.1 to activity to reflect our belief that activities of daily living might contribute 10% to each of fatigue and fitness. In supplementary analyses, we explored the effects if the contribution were 25% or 50%.
5. Finally, if we believe tripling the activity will triple the injury risk (e.g. 3 games vs 1 game), then activity (or ACWR) should be plotted on the log scale.(3)
REFERENCES
1. Bache-Mathiesen LK, Andersen TE, Dalen-Lorentsen T, et al. Not straightforward: modelling non-linearity in training load and injury research. BMJ Open Sport Exerc Med. 2021;7(3):e001119.
2. Wang C, Stokes T, Vargas JT, et al. Injury risk increases minimally over a large range of changes in activity level in children. arXiv. 2021;2010.02952v2 [q-bio.QM].
3. Wang C, Stokes T, Vargas JT, et al. Injury risk increases minimally over a large range of changes in activity level in children (In Press). Am J Epidemiol. 2021.
4. Kaufman JS. Commentary: Why are we biased against bias? Int J Epidemiol. 2008;37(3):624-626.
5. Wood S. mgcv. In: R: A language and environment for statistical computing R Foundation for Statistical Computing Vienna, Austria; 2021.
6. Amrhein V, Greenland S, McShane B. Scientists rise up against statistical significance. Nature. 2019;567(7748):305-307.
7. Wasserstein RL, Lazar NA. The ASA statement on p-values: context, process, and purpose. Am Stat. 2019;70(2):129-133.
8. Hernán MA, Robins JM. Causal inference: What if. Boca Raton: Chapman & Hall/CRC, 2020.
Thanks to the authors for providing some preliminary data on the potential effectiveness of bike-fitting to reduce pain and discomfort in cycling.
Very interesting study, but probably some questions are worth comments from authors:
1- Was there a proper ethics approval for this study? It seems that data was obtained retrospectively from clinical records.
2- How transferable to training is 100W of cycling?
3- Would authors be able to disclose the source of the 'measurement reference values'? Elaborating the criteria used for changes in bike-fit is critical to understand how and why cyclists improved their posture on the bike.
It would have been nice to see a control group to determine how much of the perceived changes are from placebo-effect.
Dear Editor,
Show MoreI am writing in regard Edouard et al’s recent publication in your journal to bring your attention to what I think are some errors that have perhaps slipped through the editing process.
The paper describes the results of their protocol (Lahti et al 2020): “… to compare if there is a significant effect of the intervention on the (hamstring muscle injury) occurrence using Cox regression analysis” where the intervention was “a multifactorial and individualised HMI risk reduction programme”.
The pre-specified outcome (hamstring injury risk) was found to be no different for those undertaking the novel programme compared to the control group at any time – i.e. the complex multifactorial individualized programme did not reduce hamstring injury incidence, risk, or burden. The authors have subsequently reported the findings of secondary analyses not outlined in the published protocol. These reported secondary analyses also found no difference in hamstring muscle injury risk/incidence, but they did report that for a sub-group of 31/90 selected participants there was a reduction in hamstring injury burden (but not others, some of whom reported an increase).
Specifically, these apparent errors (reporting a reduction in incidence/risk for the secondary analyses where the data do not support this) are:
1. in the abstract: “… and additional secondary analyses showed a significant association between the intervention and lower HMI burden, incidenc...
Solle et al. argue that our study “supports a conclusion for the relationship between sex and race time, as a result of the poorly constructed and likely miscategorized sex variable”. However, if this view were correct, some other explanation would be needed to explain the statistically significant correlations we found between sex and race time. Solle et al. do not provide any such explanation.
They state that our methodology is “unreliable”. But we do not assume that our model for sex is perfectly reliable, and we emphasize throughout that we model sex probabilistically. As we explain in the appendix to our paper, and illustrate with a numerical example, if one increases the uncertainty in our model this would indicate that there is an even stronger relationship between sex and race times. Solle et al. do not consider this point in their response, and as a result they fail to explain how their theory can be reconciled with the data.
In the absence of such an argument, we believe that their theory cannot be reconciled with the data and so must be in some way flawed. We believe that the flaw in their argument is to overstate the difficulty in ascribing a sex to a non-binary athlete. For example, Solle et al. give the impression that we modelled non-binary athletes’ sex using only their names, yet for the majority of non-binary athletes we could determine their sex from their race history.
Solle et al. go on to argue that our use of the terminology “na...
Show MoreInclusion for non-binary athletes in racing events has progressed in the last three years, with five of the six Abbott Major Marathons offering non-binary running categories in 2023. Given that the “main issue for non-binary people is that they cannot compete authentically” without the non-binary category1, non-binary race divisions were created, in part, as inclusion measures for non-binary individuals. As the number of non-binary athletes participating in running is increasing2, the representation and needs of non-binary athletes should be studied using appropriate methods that are in line with current best practices3, particularly in assessing gender and sex measurement and analyses. In their paper, “Performance of non-binary athletes in mass-participation running events,” Armstrong et al. utilize several methodological approaches and analyses that do not appropriately assess the performance of non-binary athletes. As a consequence, the conclusions of the paper introduce numerous biases with results that do not accurately reflect the reality of non-binary athletes.
In designing their study, the authors attempt to determine the sex assigned at birth (labeled natal sex in their model) of non-binary athletes based on the presumed sex assigned at birth of their names. This approach is methodologically unreliable and flawed4. Specifically, the authors fail to distinguish between sex assigned at birth, legal sex, and any sex-related medical intervention that the athle...
Show MoreMany thanks for producing the thoroughly enjoyable article on SEM practitioners around the world. We would like to add that SEM in Malaysia has also been well established as a standalone speciality since 2002. The impetus for for kickstarting the speciality was having being appointed the host city for Commonwealth Games 1998 (Kuala Lumpur). Our training programme, was in effect a combined 4 year run-through standalone clinical training, in its inception together with Rehabilitation Medicine originally, of which very early then branched out into an independent Sports Medicine Masters training program in the early 2000s, with on average 4 to 6 trainees a year qualifying out of the program. At the moment, we have approximately nearly 60 practitioners throughout the broader Malaysia with a large number of my contemporaries working within the Ministry of Health Malaysia. Our core service focuses on optimising musculoskeletal health across all spectrum of age and health, performing diagnostic imaging and guided-pain interventional, therapeutic and regenerative procedures, sideline and team physician management, prescriptive exercise clinics and fitness/performance testing, and various collaborative work with public health in being an advocate for healthy living. The training program is indeed quite similar as to how the Australasian and British FSEM curriculum content-wise, and has been traditionally done at the University of Malaya throughout the whole clinical course. Many of...
Show MoreThe systematic review by Paultre et al. supports the use of turmeric or curcumin extract for knee osteoarthritis pain.
They did not perform a formal meta-analysis but summarize the results of individual studies by calculating effect sizes based on the data in the original papers. Unfortunately there are two problems with these, one major and the other more modest.
The major issue is with the last study reported in table 3, Srivastava (2016). Paultre et al. report very large effect sizes for this study, such as 8.6, 9.5, and even 11 for a visual analogue scale. These effect sizes are the usual "d" value, that is the mean difference divided by the standard deviation. Effect sizes of such high magnitudes should raise a red flag that something is wrong, as they are rarely attained in clinical studies.
The authors' impressive effect sizes for Srivastava are errors due to using a standard error of the mean (SE) as if it were a standard deviation (SD). Srivastava et al. define the statistic used in the statistical methods: "The results are presented as mean ± SE." The values shown are also impossibly small to be standard deviations, which is what caught my attention. Both at 60 days and 120 days, the "standard deviations" shown for a 10-point VAS scale are around 0.1. This suggests a range of responses of about 0.5, which is not plausible.
The SEM is the SD divided by the square root of the sample size and represents...
Show MoreAn implementation of REDI as a dedicated R package is now available: https://grenouil.github.io/REDI/.
A code-free web app is also provided to compute REDI directly on your datasets: https://arthurleroy.shinyapps.io/REDI/
Dear editor/ dear authors,
We read with interest your editorial ‘Sport and exercise medicine around the world: global challenges for a unique healthcare discipline’ [1] in BMJ Open Sport and Exercise Medicine. We would like to congratulate the authors for bringing the challenges of our speciality back into the spotlight again.
While Sports and Exercise Medicine (SEM) may be a modern and more inclusive terminology than sports medicine, many of the challenges of our speciality have remained the same over the years. Societies such as the European College of Sports and Exercise Physicians (ECOSEP) have championed for years for the advancement of sports medicine/ SEM speciality across Europe by providing education, publishing research, organising congresses, collaborating with other organisations and serving as a source of information to the public [2–4]. ECOSEP has been promoting exercise for prevention and treatment to policy holders, creating post-graduate programmes and seminars to provide further training for physicians and bringing practitioners together, not only with biannual congress but also through promoting professional dialogue and standards [2–4]. Other societies, like the European Federation of Sports Medicine Associations (EFSMA) have been champing for a common sports medicine speciality within Europe for over 20 years, providing a detailed curriculum for sports medicine practitioners [5]. Even back then they recognised that sports medicine is a m...
Show MoreWe thank Shrier et al. for a thoughtful expansion on the topic of non-linearity.1 The comments from the authors provide valuable insights and detail to both the handling and the interpretation of fractional polynomials and splines, and may interest readers who seek more information than the short introduction in Bache-Mathiesen, et al. 2.
We are especially grateful for elaborating on the interpretation of restricted cubic splines, and the solution of adding a small constant (i.e. 0.1) to all values to handle the value “0” when using fractional polynomials. These topics could not be sufficiently addressed within the limited wordcount of the original article, and we encourage readers to consider these comments.
Conflict of Interest:
None declared.
References
1. Shrier I, Wang C, Stokes T, et al. Important Nuances for Non-Linear Modeling. BMJ Open Sport & Exercise Medicine 2021
2. Bache-Mathiesen LK, Andersen TE, Dalen-Lorentsen T, et al. Not straightforward: modelling non-linearity in training load and injury research. BMJ Open Sport & Exercise Medicine 2021;7(3):e001119. doi: 10.1136/bmjsem-2021-001119
We would like to thank Bache-Matiesen et al.(1) for their thoughtful article on non-linear modelling in sport medicine. Our own study on the non-linear relationship between acute: chronic workload ratio (ACWR) and injury risk in children was published as a preprint (2) and recently accepted by the American Journal of Epidemiology.(3) Below, we highlight some additional underlying principles in non-linear modelling that readers should understand.
GENERAL CONCEPTS
Models are based on information, which includes both data and assumptions. Simple linear models are more prone to bias because they assume a data generating process that is likely incorrect. The flexibility of non-linear models leads to less risk of bias, but also less precision. The optimal choice between bias and uncertainty depends on the context.(4)
Bache-Matiesen describe three non-linear modelling options: quadratic modelling, fractional polynomials (FP), and restricted cubic splines (RCS, where knots are determined by either data driven or a priori methods). These all fall under generalized additive models (GAMs), or generalized additive mixed models (GAMMs; if one uses “random effects” to adjust for repeated measures on participants).
FP methods use a single polynomial function over the entire range of exposures to predict the outcome. Quadratic models are special cases of FP (with exponents of 0, 1 and 2) and are too restrictive to be generally recommended. RCS separate data i...
Show MoreThanks to the authors for providing some preliminary data on the potential effectiveness of bike-fitting to reduce pain and discomfort in cycling.
Very interesting study, but probably some questions are worth comments from authors:
1- Was there a proper ethics approval for this study? It seems that data was obtained retrospectively from clinical records.
2- How transferable to training is 100W of cycling?
3- Would authors be able to disclose the source of the 'measurement reference values'? Elaborating the criteria used for changes in bike-fit is critical to understand how and why cyclists improved their posture on the bike.
It would have been nice to see a control group to determine how much of the perceived changes are from placebo-effect.
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