Bayesian estimation of small effects in exercise and sports science

Mengersen, Kerrie, Drovandi, Christopher C., Robert, Christian P., Pyne, David B., & Gore, Christopher G. (2016) Bayesian estimation of small effects in exercise and sports science. PLoS ONE, 11(4), Article Number-e0147311.

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The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a ‘magnitude-based inference’ approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

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ID Code: 95118
Item Type: Journal Article
Refereed: Yes
DOI: 10.1371/journal.pone.0147311
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > HUMAN MOVEMENT AND SPORTS SCIENCE (110600)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: 2016 The Author(s)
Copyright Statement: This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
Deposited On: 26 Apr 2016 00:52
Last Modified: 27 Apr 2016 01:28

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