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Methods to Estimate V˙O2max upon Acute Hypoxia Exposure


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Medicine & Science in Sports & Exercise: September 2015 - Volume 47 - Issue 9 - p 1869-1876
doi: 10.1249/MSS.0000000000000628


Maximal oxygen uptake (V˙O2max) is a ubiquitous measure in exercise science that is relevant to performance, health, and disease (30). Physiologically, V˙O2max represents the maximum rate at which oxygen (O2) can be taken up and used by the body during exercise (5). This rate is dependent on the transport of O2 from the environment to the mitochondria, where it is used as the final electron acceptor in the production of ATP via oxidative phosphorylation (5). Partial pressure of O2 (PO2) decreases progressively with increases in altitude (45) or with decreases in the fraction of inspired O2, leading to consequent reductions of PO2 at all levels of the O2 cascade. Thus, hypoxia impairs O2 delivery, which decreases an individual’s V˙O2max relative to normoxia (43)—a concept that has been demonstrated by numerous studies (20). Although V˙O2max is not an exact proxy for aerobic exercise performance, V˙O2max is still a key determinant of aerobic exercise performance and can be thought of as the “ceiling” for aerobic work (5,30). Accordingly, decreases in V˙O2max (e.g., resulting from hypoxic exposure) impair aerobic exercise performance (14,20).

Meaningful decrements in V˙O2max (∼7%) have been detected at altitudes as low as 580 m (21), and much larger decrements in V˙O2max are apparent at high altitudes (e.g., ∼50% at 5300 m (10)). Furthermore, multiple studies have reported progressive declines in V˙O2max with stepwise reductions in PO2 (29,38,46). Thus, it is clear that reductions in PO2 reduce V˙O2max; however, at any given hypoxic dose, there is still substantial interindividual variation in the effects of hypoxia on V˙O2max.

Relative and absolute decreases in V˙O2max are larger in trained humans than in untrained humans at low (21,40), moderate (29), high (6), and severe altitudes (29). The physiological basis for the interacting effects of hypoxia and baseline V˙O2max on a decrease in V˙O2max in hypoxia may be a result of relatively greater reductions in O2 transport or a smaller capacity to increase O2 extraction in aerobically trained subjects relative to untrained subjects (32). Other studies suggested that the interaction was due to greater exercise-induced arterial hypoxemia (EIAH) in trained subjects (21,29), which, at sea level, is known to be more prevalent in trained individuals than in untrained individuals, as well as in females relative to males (17,19,23,25).

Individual studies of the effects of hypoxia on V˙O2max are supported by a comprehensive literature review of four decades of research (20). In that review, the authors demonstrated relationships between i) altitude and decrease in V˙O2max, and ii) baseline V˙O2max and decrease in V˙O2max. While very useful, this review did not provide a quantitative analysis of these data. Building on that narrative review, the purposes of our analyses were to i) update the data with recent research in order to ii) quantitatively determine the individual and interacting effects of altitude and baseline V˙O2max on the decrease in V˙O2max upon acute exposure to hypoxia. As a result, the primary purpose of this analysis was to iii) develop a robust predictive model that would allow us to predict an individual’s decline in V˙O2max under hypoxic conditions with reasonable accuracy. The main hypotheses were that altitude and baseline V˙O2max would explain much of the variation in the decrease in V˙O2max upon acute exposure to hypoxia and that our meta-regression model would accurately predict individual-level decreases in V˙O2max upon acute exposure to hypoxia. We also hypothesized that the decrease in V˙O2max upon acute exposure to hypoxia would be independent of the mode of hypoxia (i.e., normobaric or hypobaric).


Systematic literature review

Relevant studies were identified by searching PubMed with combinations of the following words as queries: “altitude,” “hypoxia,” “V˙O2max,” and “aerobic capacity.” Studies were included if i) V˙O2max was assessed at two or more altitudes; ii) baseline V˙O2max was assessed at an altitude below 600 m; iii) relevant summary data (means and SD) were provided; iv) subjects were “healthy” (i.e., the study was not of a clinical population); and v) altitude V˙O2max was assessed in the first 24 h of exposure (to limit any effects of acclimatization). We also included studies that assessed V˙O2peak (rather than V˙O2max) to increase the number of included studies. The rationale was that the two values are often very similar, even in the absence of a plateau in V˙O2 (35), and sea-level criteria for establishing V˙O2max might not be evidence of a true V˙O2max at altitude (e.g., hypoxia lowers maximum heart rate (4,9)). To be concise, we will use the term “V˙O2max” throughout the article. An initial 855 titles were identified; after screening of titles and abstracts, 112 articles were screened by full text (Figure, Supplemental Digital Content 1, flow diagram, A total of 80 studies were included (Document, Supplemental Digital Content 2, references, Multiple groups of participants from a single study (e.g., “trained” and “untrained” groups) were separated for analysis. Thus, data from 105 independent groups of participants were included in the analysis, with a total of 958 subjects (850 males and 108 females). Cohorts were categorized as being exposed to normobaric (n = 66) or hypobaric (n = 39) hypoxia.

Data collection

From each included study, the following data were collected for our analysis: i) mean and SD of V˙O2max at baseline; ii) mean and SD of V˙O2max at a higher altitude; iii) number of subjects; iv) mean weight of subjects; v) mode of exercise; vi) altitudes or barometric pressures of testing sites; and vii) mode of hypoxia (normobaric or hypobaric). When unavailable, the lower altitude was estimated from the location of the study, which was often approximately sea level (e.g., Brussels, Copenhagen). When hypoxic gas was used to simulate altitude, the altitude was estimated with the formula provided by West (45). For those studies that measured V˙O2max at more than two altitudes, V˙O2max at the highest altitude was compared to V˙O2max at the lowest altitude (i.e., V˙O2max values from intermediate altitudes were disregarded) to ensure that groups were statistically independent (i.e., the analysis only included one measure from any given subject).

Risk of bias

Risks of bias were identified through evaluation of each included study based on the following criteria: selection bias (randomization and concealed allocation), performance bias (blinding of treatment), detection bias (blinding of outcome assessment), attrition bias, and reporting bias. For each criterion, studies were rated as low, high, or unclear.

Quantitative analysis

Means, SD, and sample sizes for the independent participant groups were entered into a spreadsheet and used to calculate standardized effect sizes (Hedges g) and variances (Vg) (8). Because change in V˙O2max occurs within a subject, correct calculation of effect-size variance (Vg) requires an estimate of the correlation between pretest and posttest measures (8). This correlation is not provided in most academic publications, but it is generally positive for the case of V˙O2max (i.e., those with the highest V˙O2max at low altitude generally have the highest V˙O2max at higher altitude). While the exact correlation for each study was not known, we were able to estimate the correlation between pretest and posttest scores from a dataset of 74 participants. The correlation between baseline and altitude V˙O2max was r = 0.75. We analyzed our data by assuming this positive correlation and assuming that pretest scores were independent of posttest scores (r = 0). Results from both analyses agreed in the direction, magnitude, and statistical significance of effects. The results presented later are based on an estimated correlation of r = 0.75.

Effect sizes were computed from the difference between V˙O2max at baseline and V˙O2max at a higher altitude (with negative effect sizes indicating decreases in V˙O2max), divided by the pooled within-group SD. Pooled SD were calculated from between-participant variances within a group at two different sample collection times (baseline and altitude) to create a single estimate of variability among participants. Effect-size measures were analyzed using the “metafor” package (42) in R (

Custom scripts (Document, Supplemental Digital Content 3, appendix, tested a random-effects model for the overall decline in V˙O2max, averaging across different test altitudes. While this overall decrease in V˙O2max is informative, the goal of this first model is to calculate τ2, an estimate of the variance between observed effect sizes (estimated using restricted maximum likelihood). Meta-regression was used in subsequent analyses to explain this variance. i) We tested the linear relationship between the test altitude and the observed decline in V˙O2max. ii) We tested the effect of baseline V˙O2max on the observed decline in V˙O2max, controlling for the effects of test altitude, iii) the interaction of these terms, and (iv) the curvilinear effects of altitude and baseline V˙O2max.

In order to compare the “fit” of our different models, we calculated the more familiar metric of r2 based on τ2 (8). Furthermore, we also examined the predictive utility of these models by comparing the predictions of our models to a dataset of 74 participants obtained from a subset of studies in the meta-analysis (3,7,16,26,28,36,37,39) that reported participant-level data. Scores for individual participants are fundamentally different from group-level data in the meta-analysis. Thus, successfully predicting individual decreases in V˙O2max would greatly increase the external validity of our regressions. The predicted decrease in V˙O2max from the model (ĝ) was backtransformed into appropriate units by multiplying by the average pooled SD in our metadata (

= 5.59) and subtracting this predicted decrease (

) from each participant’s baseline to obtain a predicted V˙O2max at altitude (

). As shown in equations 1 and 2, this predicted V˙O2max was then compared to the participant’s observed V˙O2max at altitude (Max) so that we could calculate the root-mean-squared error (RMSE). This RMSE represents the average deviation of predicted V˙O2max to actual V˙O2max. Thus, a smaller RMSE means better prediction for a given model:

To our knowledge, predictive models based on group-level summary data have not been validated against participant-level data in previous research. This validation technique is a unique feature of our design that adds to the external validity of our regression models.


Study quality

None of the included studies reported that the allocation of subjects to groups was concealed (i.e., hypoxic test before/after normoxic test). However, 27 of the included studies randomized the order of testing when participants arrived in the laboratory (analogous to a concealed allocation). An additional four studies used a counterbalanced design but did not explicitly state that subjects were randomized between the predetermined orders. Furthermore, 26 studies always performed normoxic testing first, and one study always performed hypoxic testing first. The remaining studies did not state how the order of exposures was determined. Thus, although there was an overall high risk of bias for allocation and randomization, the objective nature of the testing minimized the impact of this bias. Subject blinding was performed in 18 of the included studies, and researcher blinding was performed in three of the included studies; however, because the V˙O2max tests are objective, the risks of bias for performance and detection were mostly unclear. Even still, only 21 studies reported that the objective criteria for ensuring V˙O2max were reached during the test. Lastly, dropouts were very rare, and V˙O2max was a primary variable in all studies; therefore, risks of attrition and reporting bias were low.

Random-effects model for overall effect of altitude

Across studies, V˙O2max decreased at altitude (g = −1.77; 95% confidence interval, −2.05 to −1.49). The random-effects model had the following values: τ2 = 1.85 (estimate of variance between effects), I2 = 95.1 (percentage of total variability attributable to heterogeneity), and H2 = 20.46 (ratio of total variability to sampling variability). Thus, the overall effect of altitude on V˙O2max was clearly negative; however, there was also substantial variability between effects that we wanted to explain with meta-regression.

Descriptive statistics for regression models

Figure 1 shows scatter plots for the observed decrease in V˙O2max (g), the altitude of the highest altitude test (in kilometers), the baseline V˙O2max of participants (in milliliters per kilogram per minute), and a bar plot with the frequency of different testing modalities. The mean ± SD baseline V˙O2max was 53.5 ± 9.8 mL·kg−1·min−1. The mean ± SD altitude of the altitude test was 3.1 ± 1.4 km, and the mean ± SD altitude of the baseline test was 0.006 ± 0.006 km. As shown in the figures, i) there was a negative relationship between observed effect and testing altitude across studies (r = −0.53; 95% confidence interval, −0.66 to −0.38); ii) there was a negative relationship between observed effect and baseline V˙O2max across studies (r = −0.27; 95% confidence interval, −0.44 to −0.09); and iii) there was a negative correlation between testing altitude and baseline V˙O2max across studies (r = −0.31; 95% confidence interval, −0.47 to −0.13). The relationship between testing altitude and baseline V˙O2max appears to be driven by a lack of studies of well-trained athletes (baseline V˙O2max ≥70 mL·kg−1·min−1) being tested at altitudes above 3 km. Indeed, removing these studies reduces the strength of this correlation (rless fit = −0.16; 95% confidence interval, −0.34 to 0.05).

Scatter plots (upper left, upper right, and lower left) showing the relationship between observed effect (g), test altitude, and baseline V˙O2max for each study. A bar plot (bottom right) showing the frequency of different modalities for V˙O2max testing.

Increasing altitude negatively affects V˙O2max

To quantify the relationship between testing altitude and the observed decrease in V˙O2max, we regressed the highest test altitude (in kilometers) in each study onto the standardized effect size (g). As shown in Table 1, there was a strong negative relationship between testing altitude and the observed decline in V˙O2max. Addition of the altitude predictor accounted for 48% of the residual variance from the random-effects model.

Regression statistics from the four models (τ 2 estimator = restricted maximum likelihood).

Higher baseline V˙O2max is associated with a larger decrease in V˙O2max (controlling for altitude)

In order to quantify the relationship between baseline V˙O2max and the observed decrease in V˙O2max at altitude, we first created a new variable, BV˙O2.c, centering baseline V˙O2 on the grand mean. Thus, a positive BV˙O2.c represents a study of fitter participants with higher baseline V˙O2max than other studies in the meta-analysis. We regressed BV˙O2.c (in milliliters per kilogram per minute) and test altitude (in kilometers) in each study onto the standardized effect size (g). As shown in Table 1, there was a strong negative relationship between testing altitude and effect size, and between BV˙O2.c and effect size. Controlling for altitude and baseline V˙O2max accounted for 72% of the residual variance of the random-effects model.

We were also interested in the potential interaction between baseline V˙O2max and altitude, so we added an interaction term to the main-effects model presented previously. As shown in Table 1, there was a strong negative relationship between testing altitude and V˙O2max. Furthermore, the point estimate for the interaction coefficient was β = −0.02, suggesting that the negative effect of altitude was larger in individuals with higher baseline V˙O2max. Controlling for altitude, baseline V˙O2max, and their interaction accounted for 75% of the residual variance of the random-effects model—a 3% improvement over the main-effects model.

Controlling for curvilinear effects of altitude and V˙O2max improves model fit

Visual inspection of the relationship between the decrease in V˙O2max and altitude (Fig. 2) suggests the possibility of a nonlinear decline in V˙O2max as altitude increases. This curvilinear relationship is not only suggested by the data but also supported by physiological reasons suggesting an accelerated decline in V˙O2max at higher altitude: the relationship between PO2 and O2 saturation (SaO2) is nonlinear, and SaO2 is related to V˙O2max (14). Similarly, trained individuals are more likely to demonstrate EIAH at sea level (18) and have also been shown to desaturate more at altitude compared with untrained subjects (29). Thus, we added the variables Alt2 and BV˙O2.c2 to test for curvilinear relationships in the decline in V˙O2max.

A. Observed V˙O2max at high-altitude test (circles) for each independent participant group as a function of average baseline V˙O2max and test altitude. The size of each circle is inversely proportional to the variance of each study. B. Predicted V˙O2max at high-altitude test as a function of test altitude and baseline V˙O2max (shown as separate lines). These predictions are based on the curvilinear model.

Controlling for other factors in the model (Table 1), we found was a negative effect of Alt2, suggesting that the already negative effect of altitude is exacerbated as altitude increases. Similarly, there was a negative effect of BV˙O2.c2 such that the effect of baseline V˙O2max was less negative in participants with low baseline V˙O2max and progressively more negative in participants with higher baseline V˙O2max. Furthermore, the interaction of altitude and BV˙O2.c was negative, again showing that the negative effect of altitude was larger in individuals with higher baseline V˙O2max. Adding the Alt2 and BV˙O2.c2 predictors to the interaction model accounted for 80% of the residual variance of the random-effects model, which is a 5% improvement over the interaction model. Model predictions are shown plotted against the observed data in Figure 2.

Meta-regression models reasonably predict V˙O2max in participant-level data

In order to validate the predictive utility of our different models, we used the regression equations provided in Table 1 to predict the decrease in V˙O2max for a dataset consisting of 74 participants’ raw data. The average baseline V˙O2max for participants in this dataset was 46.8 ± 9.2 mL·kg−1·min−1, and the average test altitude for participants in this dataset was 3.1 ± 0.9 km.

The RMSE for the main-effects model was 3.8 mL·kg−1·min−1, the RMSE for the interaction model was 3.8 mL·kg−1·min−1, and the RMSE for the curvilinear interaction model was 3.9 mL·kg−1·min−1. For all of these models, there was no evidence of a relationship between residual errors and altitude or between residual errors and baseline V˙O2max, suggesting that the models were not biased in their predictions at different levels of the predictors (Figure, Supplemental Digital Content 4, residual plots,

No evidence of difference between normobaric and hypobaric testing conditions

In our dataset, there were 66 normobaric hypoxia and 39 hypobaric hypoxia independent cohorts (descriptive statistics shown in Table 2). For the decline in V˙O2max, there was no significant difference between normobaric and hypobaric hypoxia (β = 0.24, P = 0.39). Although the mean effect size was larger for studies using normobaric hypoxia than for studies using hypobaric hypoxia, the higher average test altitude for studies conducted in normobaric hypoxia likely drove this trend. Indeed, after controlling for altitude, the difference between conditions was even smaller (β = −0.06, P = 0.79). We also added the variable hypobaric hypoxia versus normobaric hypoxia to the regression models described previously; however, this variable was never statistically significant nor did it interact with any other factors (Document, Supplemental Digital Content 3, appendix,

Descriptive statistics for normobaric and hypobaric studies.


This is not the first study to report on relationships between decrease in V˙O2max at altitude and testing altitude and baseline V˙O2max; however, this is the first study to quantify the acute decrease in V˙O2max that occurs at altitude as a function of these factors. Using a meta-regression approach, we created and tested models to predict the decrease in V˙O2max upon acute exposure to altitude (real or simulated) based on change in altitude and the baseline V˙O2max of an individual. Finally, hypobaric and normobaric hypoxia had similar effects on the decrease in V˙O2max, suggesting that hypoxia, not hypobaria per se, is the predominant environmental factor decreasing V˙O2max upon acute exposure to altitude.

Importantly, when predictions from group-level models were compared to a dataset of individual participants tested at several altitudes, our best model (nonlinear effects and interactions) had an average error of 3.9 mL·kg−1·min−1, which is similar to measurement error in repeated V˙O2max testing (i.e., ∼2–4 mL·kg−1·min−1) (2,27,33,44). This validation is important because it suggests that our predictive models generalize beyond the metadata on which they are based. Furthermore, the low RMSE of these models suggests that they have sufficient precision to be used in applied settings, in addition to being statistically significant. To our knowledge, this validation procedure is relatively unique in meta-analysis. In this case, the predictions of group-level data generalized very well to a dataset of individual-level data, greatly improving the external validity of the models; however, it is not clear how or when such models should generalize. After all, aggregation from individual-level to group-level data fundamentally transforms the variables in any analysis, so the utility of this validation procedure is an area of future research.

In the cross-validation, all models produced similar RMSE for participant-level data; however, we argue that the curvilinear interaction model is preferable for three reasons: i) the curvilinear interaction model explained the most variance in the metadata; ii) simple linear models produce unrealistic predictions at very low altitudes (e.g., participants with low baseline V˙O2max would have supramaximal V˙O2max at low altitudes); and iii) there is a known nonlinear relationship between PO2 and SaO2, making the curvilinear model the most biologically plausible.

While this study provides quantitative certainty to the decrease in V˙O2max experienced at altitude, it does not provide mechanistic insight into this decrease. This topic has been reviewed extensively elsewhere; in brief, hypoxia reduces V˙O2max by limiting O2 diffusion in the lungs and—although perhaps to a lesser extent—in the muscle (11,43). Similarly, our analysis does not probe the mechanisms related to the greater V˙O2max reduction in aerobically trained versus untrained subjects, but many studies have investigated the effects of aerobic training status on V˙O2max at altitude (6,21,29,32,40). Several studies have demonstrated that SaO2 is correlated with the decrease in V˙O2max that occurs in hypoxia and that aerobically trained subjects exhibit greater hypoxemia than untrained subjects while exercising in hypoxia (12,21,29,46). At sea level, trained subjects are more likely to develop EIAH, likely owing to insufficient pulmonary diffusion at high workloads, and pulmonary diffusion limitations are exacerbated by hypoxia (18,41). Thus, the greater arterial desaturation experienced by exercising trained subjects partially explains the greater decrease in V˙O2max at altitude in trained versus untrained subjects.

Chapman (14) suggested that the decrease in SaO2 during normoxic testing (not baseline V˙O2max) is the best predictor of the decrease in V˙O2max in hypoxia. While this was demonstrated for groups of highly trained subjects (12), there would be far less variation in SaO2 among untrained subjects exercising at sea level, as they are less likely to demonstrate EIAH at sea level (18). In contrast, our analysis is applicable to individuals of varying aerobic fitness levels.

The ability to accurately predict V˙O2max for an individual ascending to a known altitude (or being exposed to a hypoxic inspirate) is useful for athletes, coaches, and researchers. V˙O2max sets the “ceiling” for aerobic exercise, and the O2 cost of constant-load submaximal work is not affected by hypoxia (38). Therefore, by knowing the O2 cost of a particular exercise task (i.e., exercise economy), one can calculate the percentage of the predicted altitude V˙O2max at which the individual would need to exercise and can determine the feasibility of the task. More simply, for cycling, one could calculate a new maximum power output (1,24) and derive intensities for workouts and racing from this new value. Similarly, these data are useful for researchers designing studies in which subjects are asked to exercise in hypoxia (e.g., determining an appropriate intensity for steady-state exercise in hypoxia). Figure 2 shows these predictions in units of V˙O2max (see the table of predicted decreases in V˙O2max (Supplemental Digital Content 3, Appendix, and the curvilinear equation for generating predictions). A priori estimates of effect size can also be used directly in power calculations when designing experimental studies (15). Furthermore, these estimates can be used indirectly as reference values for interpreting data in other experiments. That is, decreases in V˙O2max observed due to other factors (e.g., pollution) could be compared to observed decreases due to altitude as reference standard.

That the mode of hypoxia (i.e., whether subjects were exposed to normobaric or hypobaric hypoxia) did not influence the decline in V˙O2max suggests that the acute decline in V˙O2max observed in hypoxia was dependent on the change in the partial pressure of inspired O2 rather than on the change in barometric pressure. Given the current contention of the comparability of these two modes of hypoxia (e.g., (31,34)), this is an interesting finding that will also increase the utility of our model: our results suggest that normobaric hypoxia can be used to determine V˙O2max at the altitude of a competition (e.g., in hypobaric hypoxia). This hypothesis should be addressed experimentally to confirm our findings.

Study limitations

A major limitation of this study is that altitude was the only variable that was experimentally manipulated in the primary data. Baseline V˙O2max was always a quasi-experimental variable. As participants were not randomly assigned to groups that differed in V˙O2max, this negates a causal interpretation of the decreases due to baseline V˙O2max. However, it does suggest an interesting area of future work: using random assignment in a training study to increase the V˙O2max of an experimental group of participants and comparing their hypoxia-induced decreases to a control group whose V˙O2max has not been augmented through training.

Another limitation of these data is the lack of elite endurance athletes (V˙O2max >70 mL·kg−1·min−1) studied at high altitudes (Fig. 2). Without primary data for these participants, the predictions of our model are circumspect for very aerobically fit individuals at higher altitudes, as this would be an extrapolation beyond the available data. Similarly, very unfit individuals are rarely tested at altitudes below 2 km (Fig. 2). We also cannot address the effects of EIAH on V˙O2max at altitude, which is discussed in a recent review (14). To our knowledge, this has not been demonstrated experimentally, but studies with highly trained individuals exercising at high altitudes are currently missing from the research literature.

The cross-validation data ameliorate this concern somewhat, as there was no evidence that the residuals were larger for participants with higher baseline V˙O2max in that dataset (Figure, Supplemental Digital Content 4, residual plots, Furthermore, the highest baseline V˙O2max in that dataset was 66.8 mL·kg−1·min−1, and that participant’s V˙O2max decreased by 8.7 mL·kg−1·min−1 when tested at an altitude of 2 km. The curvilinear model predicted a decrease of 10.4 mL·kg−1·min−1 for that participant (ŶY = 1.7), which is a reasonably accurate prediction. However, that V˙O2max was not higher than 70 mL·kg−1·min−1, and the 2-km test altitude was not particularly high. Thus, in future research, we would be very interested to see fitter athletes exposed to higher altitudes (and unfit individuals exposed to relatively low altitudes) to see how the model’s predictions perform.

Only ∼10% of included subjects were female, preventing us from investigating the potential for sex differences in response to hypoxia. Studies directly comparing the responses of males and females reported similar declines in V˙O2max across sexes (13,22). While EIAH is typically more prevalent in females than in males (19), this is not a universal finding (22). Thus, while we cannot determine with our analysis the effects of sex on the decline in V˙O2max upon acute exposure to hypoxia, these studies suggest that our model might approximate the effects of altitude on females and males equally well. Even still, including more females in future studies should be a priority to clarify the applicability of our model to females.


This systematic review and meta-analysis provides a quantitative framework for the relationship between baseline V˙O2max, altitude, and V˙O2max at altitude. Data suggest the curvilinear and interacting effects of altitude and baseline V˙O2max on the effective V˙O2max at altitude:

where ŷ is the predicted decrease in V˙O2max (in milliliters per kilogram per minute), Alt is altitude (in kilometers), and BV˙O2 is the participant’s baseline V˙O2max (in milliliters per kilogram per minute). (To backtransform a prediction into an effect size ĝ, divide by the average pooled SD,

Note that the coefficients in this equation are different from those in Table 1 because here we are not centering baseline V˙O2max, making it easier for researchers to enter values into the model (this model is otherwise statistically equivalent to model 4 in Table 1).

The predictions generated from the meta-regression were validated against a dataset of individuals with varying aerobic capacities tested at a variety of altitudes. This cross-validation procedure suggested that the model’s predictions were reasonably accurate and unbiased across the different levels of the predictor variables. Thus, our quantitative framework for the relationship between aerobic capacity, baseline V˙O2max, and altitude appears to be robust, but future experimental work is needed to mechanistically explain the physiology that underlies these changes. This model is useful for hypothesis generation, for power calculations, as reference values in future experimental work, and in applied settings.

The authors would like to thank Michael Koehle and the staff at the Environmental Physiology Laboratory of University of British Columbia for their discussions and ideas during the preparation of the manuscript.

This study received no funding from any source.

The authors declare no conflict of interests.

M. J. MacInnis conceived of the study, and S. F. Nugent and K. E. MacLeod performed systematic review and data extraction. K. R. Lohse designed and conducted statistical analysis with assistance from M. J. MacInnis, S. F. Nugent, and K. E. MacLeod. M. J. MacInnis and K. R. Lohse wrote the first draft of the manuscript. All authors critically reviewed and revised the manuscript before approving the final draft.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.


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