Abstract
Studies in sport and exercise medicine routinely use samples of highly trained individuals in order to understand what characterizes elite endurance performance, such as running economy and maximal oxygen uptake (\({\rm V}{\rm O}_{\mathrm {2max}}\)). However, it is not well understood in the literature that using such samples most certainly leads to biased findings and accordingly potentially erroneous conclusions because of endogenous selection bias. In this paper, I review the current literature on running economy and \({\rm V}{\rm O}_{\mathrm {2max}}\), and discuss the literature in light of endogenous selection bias. I demonstrate that the results in a large part of the literature may be misleading, and provide some practical suggestions as to how future studies may alleviate endogenous selection bias.
Similar content being viewed by others
Notes
Note that although most studies express economy and efficiency directly as the oxygen cost, some studies define economy and efficiency such that a high value indicates higher efficiency [21]. For instance, in the study by Lucia et al. [20], the correlations between \({\rm V}{\rm O}_{\mathrm {2max}}\) and CE/GE are negative.
Statistical generalization from a sample to a population (of interest) depends on assumptions such as random sampling. When using convenience samples, which are commonly used in the literature, the statistical significance of the correlations may be misleading [5]. With convenience samples, not all elites or highly trained individuals are equally likely to be included in the sample, and the study participants are likely to be more alike with regard to for instance training principles (e.g., amount of high-intensity interval training) than the participants would have been had they been selected through a probability sample. I suspect that this will lead to P values that are too small and that the uncertainty in the results is underestimated. However, the literature routinely report P values without any discussion. To explain their sampling procedure, and discuss any potential bias, researchers should consider using guidelines for reporting observational studies, for instance the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement [53].
Following the counterfactual model of causality, causal effects are defined as contrasts between potential outcomes [33].
Linear path models allow us to calculate coefficients under the assumption of linearity and homogeneous effects (no interactions). Restricting the analysis to elite athletes is the same as adding a control for elite athletes and interactions between elite athletes and all independent variables.
The coefficient of determination (\(R^2\)) can be calculated by summing the squared semipartial correlations, which in this case is identical to the pairwise correlations (Fig. 1a): \(R^2=\pi ^2+\gamma ^2\). Since \(\pi\) and \(\gamma\) are constrained to be equal, \(\pi\) and \(\gamma\) can be calculated from the figure using \((R^2\times \frac{1}{2})^{\frac{1}{2}}\).
This study also found an inverse relationship between RE and \({\rm V}{\rm O}_{\mathrm {2max}}\) (\(r=0.42\)), which, as discussed in Sect. 3.1, is at least partially spurious.
This means that studies which estimate within-subject correlations with small sample sizes and find significant effects most likely exaggerate the correlation.
This association is also biased by endogenous selection, but the bias is likely small and the findings accordingly informative. Given the following model: anthropometric variable \(\rightarrow\) RE \(\rightarrow\) RP \(\rightarrow\) elite, then the elite variable is a descendant of the outcome variable RE, and restricting the sample to elites amounts to conditioning on the outcome variable. However, since the effects of RE on elite are less than the effects of RP on elite, the bias would most likely be small.
References
Atkinson G, Davidson R, Passfield L, et al. Could the correlation between maximal oxygen uptake and “ECONOMY” be spurious? Med Sports Exerc. 2003;35(7):1242–3.
Atkinson G, Davison R, Nevill AM. Response: inverse relationship between \({\rm V}{\rm O}_{\mathrm {2max}}\) and economy in world class cyclists. Med Sports Exerc. 2004;36(6):1085–6.
Allison PD. Fixed effects regression models, vol. 160. Thousand Oaks: SAGE Publishing; 2009.
Berkson J. Limitations of the application of fourfold table analysis to hospital data. Biometrics. 1946;2(3):47–53.
Berk RA, Freedman DA. Statistical assumptions as empirical commitments. In: Blomberg TG, Cohen S, editors. Law, punishment, and social control: essays in honor of Sheldon Messinger. 2nd ed. New York: Aldine de Gruyter; 2003. p. 235–54.
Bland JM, Altman DG. Statistics notes: calculating correlation coefficients with repeated observations: part 1—correlation within subjects. BMJ. 1995;310(6977):446.
Bleakley C, MacAuley D. The quality of research in sports journals. Br J Sports Med. 2002;36(2):124–5.
Borgen NT. Fixed effects in unconditional quantile regression. Stata J. 2016;16(2):403–15.
Brandon LJ. Physiological factors associated with middle distance running performance. Sports Med. 1995;19(4):268–77.
Elwert F, Winship C. Endogenous selection bias: the problem of conditioning on a collider variable. Annu Rev Sociol. 2014;40:31–53.
Fay L, Londeree BR, LaFontaine TP, et al. Physiological parameters related to distance running performance in female athletes. Med Sci Sports Exerc. 1989;21(3):319–24.
Foster C, Lucia A. Running economy. Sports Med. 2007;37(4–5):316–9.
Firpo S, Fortin NM, Lemieux T. Unconditional quantile regressions. Econometrica. 2009;77(3):953–73.
Gelman A, Carlin J. Beyond power calculations: assessing Type S (sign) and Type M (magnitude) errors. Perspect Psychol Sci. 2014;9(6):641–51.
Grant S, Craig I, Wilson J, et al. The relationship between 3 km running performance and selected physiological variables. J Sports Sci. 1997;15(4):403–10.
Harris JD, Cvetanovich G, Erickson BJ, et al. Current status of evidence-based sports medicine. Arthroscopy. 2014;30(3):362–71.
Hopkins WG. Measures of reliability in sports medicine and science. Sports Med. 2000;30(1):1–15.
Legaz-Arrese AL, Ostáriz ES, Mallen JC, et al. The changes in running performance and maximal oxygen uptake after long-term training in elite athletes. J Sports Med Phys Fitness. 2005;45(4):435.
Legaz-Arrese A, Munguía-Izquierdo D, Nuviala AN, et al. Average \({\rm V}{\rm O}_{\mathrm {2max}}\) as a function of running performances on different distances. Sci Sports. 2007;22(1):43–9.
Lucia A, Hoyos J, Perez M, et al. Inverse relationship between \({\rm V}{\rm O}_{\mathrm {2max}}\) and economy/efficiency in world-class cyclists. Med Sci Sports Exerc. 2002;34(12):2079–84.
Lucia A, Hoyos J, Perez M, et al. Could the correlation between maximal oxygen uptake and “ECONOMY” be spurious? Med Sci Sports Exerc. 2003;35(7):1244.
Jones A. The physiology of the world record holder for the women’s marathon. Int J Sports Sci Coach. 2006;1(2):101–16.
Joyner MJ. Modeling: optimal marathon performance on the basis of physiological factors. J Appl Physiol. 1991;70(2):683–7.
Joyner MJ, Ruiz JR, Lucia A. The two-hour marathon: who and when? J Appl Physiol. 2011;110(1):275–7.
Joyner MJ, Coyle EF. Endurance exercise performance: the physiology of champions. J Physiol. 2008;586(1):35–44.
Maughan RJ, Leiper JB. Aerobic capacity and fractional utilisation of aerobic capacity in elite and non-elite male and female marathon runners. Eur J Appl Physiol Occup Physiol. 1983;52(1):80–7.
Marcora SM, Staiano W, Manning V. Mental fatigue impairs physical performance in humans. J Appl Physiol. 2009;106(3):857–64.
Mooses M, Mooses K, Haile DW, et al. Dissociation between running economy and running performance in elite Kenyan distance runners. J Sports Sci. 2015;33(2):136–44.
Morgan DW, Baldini FD, Martin PE, et al. Ten kilometer performance and predicted velocity at \({\rm V}{\rm O}_{\mathrm {2max}}\) among well-trained male runners. Med Sci Sports Exerc. 1989;21(1):78–83.
Morgan DW, Daniels JT. Relationship between \({\rm V}{\rm O}_{\mathrm {2max}}\) and the aerobic demand of running in elite distance runners. Int J Sports Med. 1994;15(07):426–9.
Morgan DW, Pate R. Could the correlation between maximal oxygen uptake and economy be spurious? Med Sci Sports Exerc. 2004;36(2):345.
McLaughlin JE, Howley ET, Bassett DR Jr, et al. Test of the classic model for predicting endurance running performance. Med Sci Sports Exerc. 2010;42(5):991–7.
Morgan SL, Winship C. Counterfactuals and causal inference: methods and principles for social research. 2nd ed. Oxford: Oxford University Press; 2015.
Midgley AW, McNaughton LR, Wilkinson M. Is there an optimal training intensity for enhancing the maximal oxygen uptake of distance runners? Sports Med. 2006;36(2):117–32.
Noakes TD, Myburgh KH, Schall R. Peak treadmill running velocity during the \({\rm V}{\rm O}_{\mathrm {2max}}\) test predicts running performance. J Sports Sci. 1990;8(1):35–45.
Noakes TD. The central governor model of exercise regulation applied to the marathon. Sports Med. 2007;37(4):374–7.
Ogueta-Alday A, Rodríguez-Marroyo JO, García-López J. Rearfoot striking runners are more economical than midfoot strikers. Med Sci Sports Exerc. 2014;46(3):580–5.
Pate RR, Macera CA, Bailey SP, et al. Physiological, anthropometric, and training correlates of running economy. Med Sci Sports Exerc. 1992;24(10):1128–33.
Paavolainen L, Häkkinen K, Hämäläinen I, et al. Explosive-strength training improves 5-km running time by improving running economy and muscle power. J Appl Physiol. 1999;86(5):1527–33.
Pearl J. Causality: models, reasoning, and inference. 2nd ed. Cambridge: Cambridge University Press; 2009.
Pearl J. Linear models: a useful “microscope” for causal analysis. J Causal Inference. 2013;1(1):155–70.
Pitsiladis Y, Wang G, Wolfarth B, et al. Genomics of elite sporting performance: what little we know and necessary advances. Br J Sports Med. 2013;47(9):550–5.
Pollock ML. Submaximal and maximal working capacity of elite distance runners. Part I: cardiorespiratory aspects. Ann N Y Acad Sci. 1977;301(1):310–22.
Ramsbottom R, Williams C, Fleming N, et al. Training induced physiological and metabolic changes associated with improvements in running performance. Br J Sports Med. 1989;23(3):171–6.
Rothman KJ, Greenland S, Lash TL. Case-control studies. In: Rothman KJ, Greenland S, Lash TL, editors. Modern epidemiology. Philadelphia: Wolters Kluwer; 2008. p. 111–27.
Saltin B, Larsen H, Terrados N, et al. Aerobic exercise capacity at sea level and at altitude in Kenyan boys, junior and senior runners compared with Scandinavian runners. Scand J Med Sci Sports. 1995;5(4):209–21.
Saunders PU, Pyne DB, Telford RD, et al. Factors affecting running economy in trained distance runners. Sports Med. 2004;34(7):465–85.
Saunders PU, Pyne DB, Telford RD, et al. Reliability and variability of running economy in elite distance runners. Med Sci Sports Exerc. 2004;36(11):1972–6.
Smoliga JM. What is running economy? A clinician’s guide to key concepts, applications and myths. Br J Sports Med. 2017;51(10):831–2.
Tartaruga MP, Brisswalter J, Peyré-Tartaruga LA, et al. The relationship between running economy and biomechanical variables in distance runners. Res Q Exerc Sport. 2012;83(3):367–75.
Shaw AJ, Ingham SA, Atkinson G, et al. The correlation between running economy and maximal oxygen uptake: cross-sectional and longitudinal relationships in highly trained distance runners. PLoS One. 2015;10:e0123101.
Vollaard NB, Constantin-Teodosiu D, Fredriksson K, et al. Systematic analysis of adaptations in aerobic capacity and submaximal energy metabolism provides a unique insight into determinants of human aerobic performance. J Appl Physiol. 2009;106(5):1479–86.
Von Elm E, Altman DG, Egger M, et al. The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies. Int J Surg. 2014;12(12):1495–9.
Winship C, Mare RD. Models for sample selection bias. Annu Rev Sociol. 1992;18:327–50.
Wang CY, Haskell WL, Farrell SW, et al. Cardiorespiratory fitness levels among US adults 20–49 years of age: findings from the 1999–2004 National Health and Nutrition Examination Survey. Am J Epidemiol. 2010;171(4):426–35.
Wilber RL, Pitsiladis YP. Kenyan and Ethiopian distance runners: what makes them so good? Int J Sports Physiol Perform. 2012;7(2):92–102.
Acknowledgements
The author thanks Solveig T. Borgen, and two anonymous reviewers for useful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Funding
No sources of funding were used to assist in the preparation of this article.
Conflict of interest
Nicolai T. Borgen declares that he has no conflict of interest relevant to the content of this review.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Borgen, N.T. Running Performance, \({\rm V}{\rm O}_{\rm {2max}}\), and Running Economy: The Widespread Issue of Endogenous Selection Bias. Sports Med 48, 1049–1058 (2018). https://doi.org/10.1007/s40279-017-0789-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40279-017-0789-9