We applied the recommendations for observational studies by the EQUATOR Network–STROBE Guidelines for cross-sectional studies (Supplementary Table S1). CPET was performed by endurance athletes in the years 2022–2023. Exercise tests took place at the Institute of Sport–National Research Institute in Warsaw. The study was reviewed and approved by the Bioethics Committee of the Medical University of Warsaw (AKBE/277/2023). Written informed consent was obtained for each subject. In particular, we did not initially refer to the CPET potential study candidates who had past medical or family histories and evident medical conditions (diagnosed during pre-participation physical examination).

Only adult subjects of age ≥18 years were included. To be eligible for this study, endurance athletes had to be free from a) cardiovascular or pulmonary conditions, b) psychiatric or neurological diseases, d) orthopedic conditions restricting effort at CPET, e) divergences in complete blood count, f) and tobacco smoking. All athletes had at least a 4-year experience in regular endurance training and were members of a training club and elite or development national teams in Olympic sports. They periodically participated in both national and international competitions, including the Olympic Games. The participants of this study belonged to tiers 3–5, according to the McKay classification system (McKay et al., 2022). The full participant selection process is detailed in Figure 1.

All endurance athletes performed maximal-graded symptom-limited CPET. We considered the maximal exercise response when there was a a) ≥30-s VO₂ plateau, b) respiratory exchange ratio (RER) ≥1.05, c) declaration of fatigue confirmed by a Borg’s RPE ≥18, and d) measured heart rate ≥80% of the age-predicted value. Experienced physiologists supervised the CPET, and the athletes were verbally motivated to reach maximal effort.

The athletes underwent ramp cycling CPET on a Cyclus2 Ergometer (RBM, Leipzig, Germany). At the beginning of CPET, there was a brief 2–3 min warm-up of freewheeling pedaling. The initial load began with 55–70 W and was progressively raised by 0.17–0.28 W s⁻¹. The resistance was modified individually in provided ranges to adjust the intensity in agreement with each participant.

We obtained the following anthropometric measurements: age, weight, height, and body mass index (BMI). The weight was measured prior to breakfast by a TANITA weight scale (TANITA Corporation, Arlington Heights, IL, United States). The height was measured in the morning (in the same time as weight) with a stadiometer (Seca GmbH and Co., Hamburg, Germany).

Polar H10 (Polar Electro Oy, Kempele, Finland) was used to monitor the heart rate (HR). Gas-exchange variables were taken breath-by-breath with a V2 Mask (Hans Rudolph, Inc., Shawnee, KS, United States) and a Cortex B3 Metamax system (CORTEX Biophysik GmbH, Leipzig, Germany). All the pieces of equipment used were calibrated according to the manufacturer’s guidelines before each CPET. We applied 15-s intervals to average the measurements. The measured VO₂peak was compared with the VO₂peak predicted by the Wasserman and Hansen equation (Wasserman et al., 1987).

OUES was defined according to the method of Baba et al. (1996): VO₂ = a · log₁₀ · VE + b., where “a” represents the OUES. OUES was calculated at 75%, 90%, and 100% of the exercise duration. The first minute of the loaded protocol was not included in the analysis, as recommended by Hollenberg and Tager (2000). The body surface area was calculated using the Du Bois and Du Bois formula: 0.007184 · height (cm)^0.725 · weight (kg)^0.425 (Burton, 2008). We additionally calculated the HR (both absolute and percentage of peak HR) for each intensity zone (OUES₇₅, OUES₉₀, and OUES₁₀₀).

Prediction equations for external validation were chosen from the review by Akkerman et al. (2010) up to year 2010 and through additional search for studies published in years 2010–2024. The applied keywords were “oxygen uptake efficiency slope,” “OUES,” “prediction model,” “prediction equation,” “cardiopulmonary exercise testing,” “reference values,” and “linear regression” in the scientific literature. Equations derived from clinical cohorts (with comorbidities) were excluded to ensure maximal similarity. To sum up, 11 reference equations from seven studies fulfilled the inclusion criteria. Their characteristics are provided in Table 1.

First, data distribution was evaluated with the Shapiro–Wilk test and quantile–quantile plots. The continuous measures have been shown as mean (standard deviation [±]). The categorical measures have been shown as numbers (percentage [%]). An athlete was removed from the analysis when there were any missing measurements, with the aim of supporting maximal credibility of the results. The significance borderline was set at a two-sided p-value < 0.05.

For applied statistical tests, we verified the cohorts’ sizes. The whole population or particular subgroups (males and females) fulfilled the required numbers to achieve a large effect size, statistical significance (p < 0.05), and high power (>0.8).

Differences between all measurements (OUES₇₅, OUES₉₀, and OUES₁₀₀) were compared by one-way ANOVA. Additionally, Student’s t-test for independent means was conducted to compare differences between paired measurements (OUES₇₅ and OUES₉₀, OUES₇₅ and OUES₁₀₀, and OUES₉₀ and OUES₁₀₀). Linear regression was used to examine the prediction power of OUES₇₅, OUES₉₀, and OUES₁₀₀ on VO₂peak. Each calculation was carried out independently for male and female individuals.

The model’s derivation was preceded by an assessment of the data assumptions (correlations, collinearity, independence of observations, analysis of residuals, and leverage or influence plots). We used multiple linear regression to derive new prediction equations. The performance of new models was presented with the root-mean-square error (RMSE) and two-way mixed-effects interclass correlation coefficient (ICC_3,1) (Koo and Li, 2016). The Bland–Altman plots and 10-fold cross-validation were used to evaluate the model’s agreement (Jung and Hu, 2015). Linear models were developed to externally validate equations by regressing the predicted OUES against the observed OUES. In analysis, the coefficient of determination (R ²) was considered as the adjusted R ².

The results have been shown in line with the APA style guidelines. IBM SPSS (version 29.0, IBM, Chicago, IL, United States) was used for analysis, and GraphPad Prism (version 10.1.0, GraphPad Software, San Diego, California, United States) was used to prepare figures.

A total of 140 healthy endurance athletes were qualified. A total of 45.0% (n = 63) of the study population were female individuals, and 55.0% (n = 77) of the population were male individuals. The participants represented sports from endurance-oriented Olympic disciplines. A total of 40.0% (n = 56) were specified in triathlon or cycling, 42.1% (n = 59) in speedskating, and 17.9% (n = 25) chose other disciplines. Percent-predicted VO₂peak equals 144.5% ± 25.9% according to the Wasserman and Hansen equation. The demographic characteristics and exercise results are stratified by sex in Table 2.

For males, the mean OUES₇₅ (4.53 ± 0.90 mL·min⁻¹/L·min⁻¹) was not significantly different than OUES₉₀ [(4.52 ± 0.91 mL·min⁻¹/L·min⁻¹); t (152) = 0.08, p = 0.94] or OUES₁₀₀ [(4.41 ± 0.87 mL·min⁻¹/L·min⁻¹); t (152) = −0.85, p = 0.398]. Similarly, OUES₉₀ did not differ significantly from OUES₁₀₀ [t (152) = −0.76, p = 0.45]. The same relationship was observed among female subjects. Average OUES₇₅ (3.50 ± 0.65 mL·min⁻¹/L·min⁻¹) did not differ significantly from OUES₉₀ [(3.49 ± 0.62 mL·min⁻¹/L·min⁻¹); t (124) = 0.07, p = 0.95] or OUES₁₀₀ [(3.41 ± 0.58 mL·min⁻¹/L·min⁻¹); t (124) = 0.79, p = 0.43]. Moreover, OUES₉₀ did not differ significantly from OUES₁₀₀ [t (124) = 0.73, p = 0.46]. One-way ANOVA revealed that there was no significant difference in all OUES measurements both for male [F (2,228) = 0.43, p = 0.65] and female subjects [F (2,168) = 0.38, p = 0.69]. On average, the difference between OUES₇₅ and OUES₉₀ was 0.11 ± 0.11 mL·min⁻¹/L·min⁻¹ for male individuals and 0.12 ± 0.12 mL·min⁻¹/L·min⁻¹ for female individuals, that between OUES₇₅ and OUES₉₀ was 0.21 ± 0.19 mL·min⁻¹/L·min⁻¹ for male individuals and 0.18 ± 0.20 mL·min⁻¹/L·min⁻¹ for female individuals, and that between OUES₉₀ and OUES₁₀₀ was 0.13 ± 0.11 mL·min⁻¹/L·min⁻¹ for male individuals and 0.10 ± 0.12 mL·min⁻¹/L·min⁻¹ for female individuals. OUES dependencies among the endurance athletes are shown independently for male and female individuals in the lower rows of Table 2 and Figure 2.

Univariable models were developed to examine OUES prediction power on VO₂peak. OUES presented a high ability to predict VO₂peak. OUES explained up to 63% of the variance in VO₂peak in male subjects and up to 62% of the variance in VO₂peak in female subjects. VO₂peak increased simultaneously with OUES calculated from all time intervals. This relationship was more noticeable in male individuals (β = 0.73–0.80) than in female individuals (β = 0.71–0.79). The RMSE was consistently lower in female individuals than in male individuals. For the presented models, the predicted VO₂peak is in L·min⁻¹ and OUES should be calculated in mL·min⁻¹/L·min⁻¹.

The fitted univariable models for male subjects were expressed as follows:

(a) VO₂peak = 2.07 + 0.51 · OUES₇₅

The regression model covered 52% of the variance in VO₂peak (R ² = 0.52, F (1, 75) = 83.6, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.73, p < 0.001). The RMSE was 0.44 L·min⁻¹.

(b) VO₂peak = 1.97 + 0.54 · OUES₉₀

The regression model covered 59% of the variance in VO₂peak (R ² = 0.59, F (1, 75) = 108.2, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.77, p < 0.001). The RMSE was 0.44 L·min⁻¹.

(c) VO₂peak = 1.81 + 0.59 · OUES₁₀₀

The regression model covered 63% of the variance in VO₂peak (R ² = 0.63, F (1, 75) = 131.5, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.80, p < 0.001). The RMSE was 0.39 L·min⁻¹.

The fitted univariable models for female subjects were expressed as follows:

(a) VO₂peak = 1.36 + 0.53 · OUES₇₅

The regression model covered 50% of the variance in VO₂peak (R ² = 0.50, F (1, 61) = 63.0, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.71, p < 0.001). The RMSE was 0.34 L·min⁻¹.

(b) VO₂peak = 1.18 + 0.58 · OUES₉₀

The regression model covered 56% of the variance in VO₂peak (R ² = 0.56, F (1, 61) = 79.2, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.75, p < 0.001). The RMSE was 0.32 L·min⁻¹.

(c) VO₂peak = 0.96 + 0.66 · OUES₁₀₀

The regression model covered 62% of the variance in VO₂peak (R ² = 0.62, F (1, 61) = 100.1, p < 0.001), and OUES₇₅ significantly predicted VO₂peak (β = 0.79, p < 0.001). The RMSE was 0.30 L·min⁻¹.

Plots visualizing the prediction powers are shown in Figure 3.

We predicted OUES using several variables: age, sex, and BSA. Models for OUES₇₅, OUES₉₀, and OUES₁₀₀ showed similar and promising accuracy. In the developed equations, BSA should be in m², age in years, and the sex coefficients are 2 if female and 1 if male. The RMSE was similar in all three equations (0.72–0.77 mL·min⁻¹/L·min⁻¹) developed to predict OUES obtained from different portions of the exercise data.

The new prediction equations for OUES are as follows:

(a) OUES₇₅ = 1.09 + 2.87 · BSA—0.0030 · (age · sex)

The prediction equation explained 34% of variance in OUES₇₅ (R = 0.59, R ² = 0.34, F (2, 137) = 36.1, p < 0.001). The overall RMSE was 0.77 mL·min⁻¹/L·min⁻¹.

(b) OUES₉₀ = 1.46–3.02 · BSA—0.0010 · (age · sex)

The prediction equation explained 35% of variance in OUES₇₅ (R = 0.60; R ² = 0.35, F (2, 137) = 37.5, p < 0.001). The overall RMSE was 0.77 mL·min⁻¹/L·min⁻¹.

(c) OUES₁₀₀ = 1.54–2.99 · BSA—0.0014 · (age · sex)

The prediction equation explained 36% of variance in OUES₇₅ (R = 0.61; R ² = 0.36, F (2, 137) = 40.3, p < 0.001). The overall RMSE was 0.72 mL·min⁻¹/L·min⁻¹.

In all external models, a high variability was observed between the observed and predicted data sets (only 4 out of 11 models have ICC>0.5). The best alignment was noted in Milani et al. (2023) (equation adjusted to age) (ICC = 0.510 [0.491, 0.529] for OUES₇₅, ICC = 0.512 [0.492, 0.531] for OUES₉₀, and ICC = 0.529 [0.511, 0.548] for OUES₁₀₀). The equations underestimated all OUES₇₅, OUES₉₀, and OUES₁₀₀. Underestimation ranged up to 186.8% for the formula proposed by Marinov et al. (2007). However, the overall prediction trend in endurance athletes was maintained. The predicted values followed those directly observed, but the degree of explained variance was wide (R ² = 0.004–0.388). For detailed external validation, see Table 3. The agreement was lower in equations for OUES₉₀ (R ² = 0.290) and OUES₇₅ (R ² = 0.346). Bland–Altman plots showing the validity of our models are shown in Figure 4. All the equations slightly underestimated OUES. The best-performing model was the one for OUES₉₀, with the bias of only −0.001 mL·min⁻¹/L·min⁻¹. The next was the model for OUES₁₀₀ (bias = −0.04 mL·min⁻¹/L·min⁻¹). The least-performing model was for OUES₇₅, with an error of −0.13 mL·min⁻¹/L·min⁻¹. The limits of agreement were narrow and similar in all models. For OUES₇₅, it ranged between −1.51 and 1.50 mL·min⁻¹/L·min⁻¹. The limit of agreement in the equation for OUES₉₀ was from −1.49 to 1.49 mL·min⁻¹/L·min⁻¹. Finally, in the model for OUES₁₀₀, it ranged between −1.36 and 1.44 mL·min⁻¹/L·min⁻¹. As presented in Figure 4, some athletes exceeded the upper limits of agreement, but no one exceeded the lower limits.

So far, the diagnostic value of submaximal cardiorespiratory fitness has been mostly discussed in clinical populations when the maximal strenuous effort is not recommended, e.g., in heart failure (Metra et al., 1998). However, among healthy, highly trained individuals, the holistic approach should include an evaluation of the whole exercise duration (Shushan et al., 2022). Submaximal performance could also deteriorate in elite endurance athletes, e.g., after a viral infection (Sliz et al., 2022). Sheridan et al. noticed limited prediction power of OUES for VO₂peak when measured from the start to the ventilatory threshold in endurance athletes (Sheridan et al., 2021). OUES measured from the percentage of exercise duration is a more objective and replicable index because it includes the precisely truncated parts of exercise data (in our study, 75%, 90%, and 100%, respectively) (Baba, 2000). Even in elite athletes, OUES links well with the most reliable index of cardiorespiratory fitness, i.e., VO₂peak. Therefore, considering OUES as a prognostic indicator is justified when we suspect CVD in the athletic population. Furthermore, comparing OUES of a single participant between 75%, 90%, and 100% intervals would be beneficial to determine how an athlete’s heart responds to increasing intensity. Furthermore, the developed new prediction equations could be applied when direct CPET is not possible.

Our study also has some points that have to be mentioned to ensure correct interpretation. The population was homogenous in age and ethnicity. The other studies for OUES prediction models included a higher number of participants than our study. In this research, the average age of the participants was roughly 22 years. The subjects were younger and had above-average endurance capacity when compared to other studies in this field. Our athletes were healthy. Thus, the results have limited application in patients with pathologies. We conducted CPET on cycle ergometry. Testing modality could influence the achieved performance, and exercise tests performed on other machines (treadmill and rowing ergometry) could provide slightly different results (Price et al., 2022). The participants usually achieve a lower performance on the cycle ergometer than on the treadmill, and our models are mostly tailored for cycling exercise tests. We expect that applying the presented models to other testing protocols could cause some inaccuracies. Therefore, we recommend considering all the above-mentioned aspects when deriving future reference equations. This is the first study of OUES predictions in highly fit participants, so we recommend careful extrapolation when considering the results. The external validation of our equations is welcome. Moreover, the development of formulas from other testing machines is also needed.