Machine learning and statistical methods for the prediction of maximal oxygen uptake: recent advances

Figures & data

Figure 1 Overview of various types of VO₂max prediction models.

Abbreviations: HRmax, maximal heart rate; RER, respiratory exchange ratio; PFA, perceived functional ability; PAR, physical activity rating; AC, activity code; VO₂max, maximal oxygen uptake.

Table 1 Summary of recent studies in literature that developed maximal models for the prediction of VO₂max

Study	Year	Method	Predictor variables	R	SEE (mL kg^−1 min^−1)
Chatterjee et al^Citation8	2010	MLR	Velocity	0.94	0.53
Bandyopadhyay^Citation9	2011	MLR	Age, height, weight, velocity	0.93a	1.38
Mahar et al^Citation10	2011	MLR	Sex, age, BMI, PACER	0.74a	6.17
Akay et al^Citation11	2012	SVM	Sex, age, BMI, BF%, RER, RPE, HRmax, time	0.92	4.09
Akay et al^Citation11	2012	MLP	Sex, age, BMI, BF%, RER, RPE, time	0.91	3.73
Akay et al^Citation11	2012	GRNN	Sex, age, BMI, BF%, RER, time	0.82	5.03
Akay et al^Citation11	2012	MLR	Sex, age, BMI, BF%, RER, RPE, HRmax, time	0.81a	4.54
Silva et al^Citation13	2012	MLP	Sex, age, height, weight, BMI, SR stage	0.79	5.60
Silva et al^Citation13	2012	MLR	Sex, age, height, weight, BMI, SR stage	0.68a	4.90
Daros et al^Citation14	2012	MLR	Meter	0.76	4.29
Veronese da Costa et al^Citation15	2013	MLR	Weight, NLP, AHR	0.76a	7.21
Machado and Denadai^Citation16	2013	MLR	Weight, velocity	0.92a	4.10
Aktürk and Akay^Citation17	2014	MLP combined with Relief-F	Sex, age, BMI, HRmax, RER, grade	0.86	4.63
Akay et al^Citation12	2014	SVM combined with Relief-F	Sex, age, BMI, HRmax, time	0.90	4.58
Akay et al^Citation12	2014	MLR combined with Relief-F	Sex, age, BMI, HRmax, time	0.88a	4.77
Akay et al^Citation18	2014	SVM	Sex, age, BMI, HRmax, Pr	0.83	4.38
Akay et al^Citation18	2014	MLP	Sex, age, BMI, HRmax, Pr	0.81	4.64
Akay et al^Citation18	2014	MLR	Sex, age, BMI, HRmax, Pr	0.78a	4.73

Note:

a Represents adjusted R (R_adj).

Abbreviations: VO₂max, maximal oxygen uptake; SEE, standard error of estimate; MLR, multiple linear regression; BMI, body mass index; PACER, progressive aerobic cardiovascular endurance run; SVM, support vector machine; BF%, body fat percentage; RER, respiratory exchange ratio from treadmill test; RPE, self-reported rating of perceived exertion from treadmill test; HRmax, maximal heart rate; MLP, multilayer perceptron; GRNN, general regression neural network; SR stage, shuttle run stage; NLP, number of laps performed; AHR, after heart rate; Pr, protocol.

Table 2 Summary of recent studies in literature that developed submaximal models for the prediction of VO₂max

Study	Year	Method	Predictor variables	R	SEE (mL kg^−1 min^−1)
Coquart et al^Citation19	2010	MLR	Age, power	0.81a	0.16
Akay et al^Citation20	2011	MLP	Sex, age, weight, HR, jogging speed	0.95	1.80
Açıkkar et al^Citation21	2012	MLP	Sex, age, BMI, MIN3, HR3	0.89	2.22
Billinger et al^Citation23	2012	MLR	Sex, age, weight, WR, HR	0.91a	4.09
Tönis et al^Citation24	2012	MLR	Sex, age, height, weight, HR, AD	0.87a	2.05
Cao et al^Citation25	2013	MLR	Sex, age, 3MWD, BF%	0.83a	4.57
Akay et al^Citation22	2014	SVM	Sex, age, height, weight, MIN3, HR3	0.87	2.90
Akay et al^Citation22	2014	MLP	Sex, age, height, weight, MIN3, HR3	0.85	3.13
Akay et al^Citation22	2014	MLR	Sex, age, height, weight, MIN3, HR3	0.83a	3.25

Note:

a Represents adjusted R (R_adj).

Abbreviations: VO₂max, maximal oxygen uptake; SEE, standard error of estimate; MLR, multiple linear regression; MLP, multilayer perceptron; HR, heart rate; BMI, body mass index; MIN3, elapsed exercise time at the end of 1.5 mile; HR3, exercise heart rate at the end of 1.5 mile; WR, work rate; AD, accelerometer data; 3MWD, 3-minute walk distance; BF%, body fat percentage; SVM, support vector machine.

Table 3 Summary of recent studies in literature that developed nonexercise models for the prediction of VO₂max

Study	Year	Method	Predictor variables	R	SEE (mL kg^−1 min^−1)
Akay et al^Citation26	2009	SVM	Sex, age, BMI, PFA, PAR	0.93	3.41
Akay et al^Citation26	2009	MLP	Sex, age, BMI, PFA, PAR	0.91	3.23
Cao et al^Citation27	2010	MLR	Age, BMI, SC, VPA	0.85a	3.90
Schembre and Riebe^Citation28	2011	MLR	Sex, VPA	0.63a	5.45
Jang et al^Citation29	2012	MLR	Sex, age, BMI, smoking, LPA, WPA	0.88a	3.36
Shenoy et al^Citation30	2012	MLR	Sex, PFA, BSA	0.89a	0.42
Akay et al^Citation31	2014	SVM	Sex, age, BMI, BF%, AC	0.89	4.68
Akay et al^Citation31	2014	MLP	Sex, age, BMI, BF%, LBM, AC	0.87	5.00
Akay et al^Citation31	2014	MLR	Sex, age, BMI, BF%, AC	0.84a	5.12

Note:

a Represents adjusted R (R_adj).

Abbreviations: VO₂max, maximal oxygen uptake; SEE, standard error of estimate; SVM, support vector machine; BMI, body mass index; PFA, perceived functional ability; PAR, physical activity rating; MLP, multilayer perceptron; MLR, multiple linear regression; SC, step count; VPA, vigorous physical activity; LPA, leisure-time physical activity; WPA, work-related physical activity; BSA, body source area; BF%, body fat percentage; AC, activity code; LBM, lean body mass.

Table 4 Summary of recent studies in literature that developed hybrid models for the prediction of VO₂max

Study	Year	Method	Predictor variables	R	SEE (mL kg^−1 min^−1)
Nielson et al^Citation32	2010	MLR	Sex, weight, HR, WR, PFA	0.90a	3.36
Akay et al^Citation33	2010	MLP	Sex, age, BMI, PAR, HR, stage	0.96	2.01
Akay et al^Citation34	2011	MLP	Sex, age, BMI, HRmax, PFA, PAR	0.94	2.23
Akay et al^Citation34	2011	MLR	Sex, age, BMI, grade, PFA, PAR	0.85a	3.73
Yücel et al^Citation35	2013	MLP	Sex, age, BMI, MPH, PAR, PFA	0.93	3.15
Yücel et al^Citation35	2013	MLR	Sex, age, BMI, MPH, PAR, PFA	0.92a	3.27
Akay et al^Citation36	2014	SVM	Sex, age, weight, height, ES, PFA-1, PAR	0.93	3.25
Akay et al^Citation36	2014	MLR	Sex, age, weight, height, ES, PFA-1, PAR	0.87a	4.20

Note:

a Represents adjusted R (R_adj).

Abbreviations: VO₂max, maximal oxygen uptake; SEE, standard error of estimate; MLR, multiple linear regression; HR, heart rate; WR, ending work rate; PFA, perceived functional ability; MLP, multilayer perceptron; BMI, body mass index; PAR, self-reported level of physical activity; HR, heart rate; HRmax, maximal heart rate; MPH, miles per hour; SVM, support vector machine; RPE, self-reported rating of perceived exertion from treadmill test; ES, ending speed; PFA-1, PFA for one mile distance.

ChatterjeePBanerjeeAKDasPDebnathPA regression equation for the estimation of maximum oxygen uptake in Nepalese adult femalesAsian J Sports Med201011414522375191

 PubMedGoogle Scholar

BandyopadhyayAValidity of 20 meter multi-stage shuttle run test for estimation of maximum oxygen uptake in male university studentsIndian J Physiol Pharmacol201155322122622471228

 PubMedGoogle Scholar

MaharMTGuerieriAMHannaMSKembleCDEstimation of aerobic fitness from 20-m multistage shuttle run test performanceAm J Prev Med2011414117123

 Web of Science ®Google Scholar

AkayMFGhahremanlouNSAktürkEGeorgeJDAktarlaEPerformance comparison of different regression methods for VO₂max prediction7th International Symposium on Electrical and Electronics Engineering and Computer SystemsLefka, North CyprusEuropean University of Lefke2012711

 Google Scholar

SilvaGOliveiraNLAiresLMotaJOliveiraJRibeiroJCCalculation and validation of models for estimating VO2max from the 20-m shuttle run test in children and adolescentsArch Exerc Health Dis201231–2145152

 Google Scholar

DarosLBOsieckiRDouradoACMaximum aerobic power test for soccer playersJ Exerc Physiol201215280

 Google Scholar

Veronese da CostaAManoel da CunhaCMelo de OliveiraSFLima de AlbuquerqueFJosé de Sá Pereira GuimarãesFBarbosaTMValidation of an equation for estimating maximal oxygen consumption of nonexpert adult swimmersOpen Access J Sports Med20134192524379705

 PubMedGoogle Scholar

MachadoFADenadaiBSPredição da potência aeróbia (VO2max) de crianças e dolescents em teste incremental na esteira rolante. [Prediction of aerobic power (VO2max) of children and adolescents during an incremental treadmill test]Motriz2013191126132 Portuguese

 Google Scholar

AktürkEAkayMFPrediction of maximal oxygen uptake using multilayer perceptron combined with feature selection7th Engineering and Technology SymposiumAnkara, TurkeyÇankaya University201436

 Google Scholar

AkayMFAkgölDGeorgeJSupport vector machines combined with feature selection for prediction of maximal oxygen uptakeInternational Symposium on Engineering, Artificial Intelligence and Applications KyreniaNorth CyprusGirne American University201434

 Google Scholar

AkayMFAbutFDaneshvarSHeilDPrediction of maximal oxygen uptake of cross-country skiers using different regression methodsInternational Symposium on Engineering, Artificial Intelligence and ApplicationsKyrenia, North CyprusGirne American University20141819

 Google Scholar

CoquartJBEstonRGGrosboisJMPrediction of peak oxygen uptake from age and power output at RPE 15 in obese womenEur J Appl Physiol2010110364564920532554

 PubMed Web of Science ®Google Scholar

AkayMFZayidEIMAktürkEGeorgeJDArtificial neural network-based model for predicting VO2max from a submaximal exercise testExpert Syst Appl201138320072010

 Web of Science ®Google Scholar

AcikkarMAkayMFGeorgeJDDelilMAktürkEArtificial neural network models for predicting maximum oxygen uptake from submaxiaml exercise involving walking, jogging or runningInternational Symposium on Electrical and Electronics Engineering and Computer SystemsLefka, North CyprusEuropean University of Lefke20121721

 Google Scholar

BillingerSASwearingenEMcClainMLentzAAGoodMBRecumbent stepper submaximal exercise test to predict peak oxygen uptakeMed Sci Sports Exerc20124481539154422382170

 PubMed Web of Science ®Google Scholar

TönisTMGorterKVollenbroek-HuttenMMRHermensHComparing VO2max determined by using the relation between heart rate and accelerometry with submaximal estimated VO2maxJ Sports Med Phys Fitness201252433734322828454

 PubMed Web of Science ®Google Scholar

CaoZ-BMiyatakeNAoyamaTHiguchiMTabataIPrediction of maximal oxygen uptake from a 3-minute walk based on gender, age, and body compositionJ Phys Act Health201310228028722821953

 PubMed Web of Science ®Google Scholar

AkayMFÖzsertGGeorgeJPrediction of maximal oxygen uptake using support vector machines from submaximal dataDEÜ Eng Fac Eng Sci J2014164834248

 Google Scholar

AkayMFInanCBradshawDIGeorgeJDSupport vector regression and multilayer feed forward neural networks for non-exercise prediction of VO2maxExpert Syst Appl20093661011210119

 Web of Science ®Google Scholar

CaoZ-BMiyatakeNHiguchiMMiyachiMTabataIPredicting VO2max with an objectively measured physical activity in Japanese menEur J Appl Physiol2010109346547220145947

 PubMed Web of Science ®Google Scholar

SchembreSMRiebeDANon-exercise estimation of VO2max using the International Physical Activity QuestionnaireMeas Phys Educ Exerc Sci2011153168181

 Google Scholar

JangT-WParkS-GKimH-RKimJ-MHongY-SKimB-GEstimation of maximal oxygen uptake without exercise testing in Korean healthy adult workersTohoku J Exp Med2012227431331922850649

 PubMed Web of Science ®Google Scholar

ShenoySTyagiBSandhuJSenguptaDDevelopment of non-exercise based VO2max prediction equation in college-aged participants in IndiaJ Sports Med Phys Fitness201252546547322976732

 PubMed Web of Science ®Google Scholar

AkayMFÖzsertGGencEGeorgeJDevelopment of new non- exercise maximal oxygen uptake models by using support vector machinesInternational Symposium on Engineering, Artificial Intelligence and ApplicationsKyrenia, North CyprusGirne American University20141112

 Google Scholar

NielsonDEGeorgeJDVehrsPRHagerRLWebbCVPredicting VO2max in college-aged participants using cycle ergometry and perceived functional abilityMeas Phys Educ Exerc Sci2010144252264

 Google Scholar

AkayMFZayidEIMAktürkEKaleGGeorgeJDArtificial neural network-based model for predicting VO₂max from a hybrid exercise test6th International Symposium on Electrical and Computer SystemsLefka, North CyprusEuropean University of Lefke20101620

 Google Scholar

AkayMFShokrollahiNAktürkEGeorgeJDDevelopment of new VO₂max prediction models by using artificial neural networksInternational Symposium on Computing in Science and EngineeringAydin, TurkeyGediz University20113944

 Google Scholar

YücelEAkayMFAktürkEInvestigating the effect of questionnaire variables on the prediction of maximal oxygen uptake using multilayer perceptron and multiple linear regressionInternational Symposium on Engineering, Artificial Intelligence and Applications KyreniaNorth CyprusGirne American University201335

 Google Scholar

AkayMFAbutFGeorgJUsing support vector machines to predict maximal oxygen uptake with the help of questionnaire variablesInternational Symposium on Engineering, Artificial Intelligence and Applications KyreniaNorth CyprusGirne American University201456

 Google Scholar