Prediction of males' physical work capacity in various simulated altitudes using an incremental cycle ergometer exercise test at sea level

Standard approach to predict the decrease in physical fitness that will occur following a transition to a higher altitude is unavailable. Therefore, the study aimed to design simple mathematical models to predict submaximal exercise performance in various altitude environments, using a simple physical work capacity test conducted at sea level involving > 200 subjects. After splitting the subjects’ data in a ratio of 7:3, we used 70% of the data for regression model development and employed 30% for cross-validation testing. All subjects performed submaximal exercise tests using a cycle ergometer at artificial altitudes of 2000 m, 3000 m, 4000 m, 5000 m


Introduction
It is established that temporary exposure to high altitude causes a decrease in physical work capacity [1]. In addition, exposure of low-altitude dwellers to high-altitude environments positively improves metabolic and cardiac responses, triggering an improvement in physical athletic performance [2]. Therefore, hypoxic training is a suitable choice for pre-adaptation to a high-altitude environment [3,4]. In addition to high-altitude climbers, the athletes of endurance events also use hypoxic training to improve their performance [5][6][7][8].
Sinex and Chapman [9] suggested methods of general hypoxic training for athletes and demonstrated that there are differences in individual responses to hypoxic training. Therefore, individual reaction characteristics should be considered to improve physical exercise ability in a high-altitude environment. Based on the extent of change in physical exercise ability in a high-altitude environment, the exercise training goal could be customised for pre-acclimatization. For instance, if an athlete targets to climb Mt. Mont Blanc at (an altitude of 4807 m), a physical fitness test needs to be taken. If the test predicts that the physical work capacity would decrease by 20% at an altitude of 5000 m, participating in an exercise program that improves physical work capacity by 20% before climbing would be advantageous. However, there is no standard approach to predict the decrease in physical fitness that will occur in a high-altitude environment.
In general, measuring athletic ability and fitness level is the most accurate. However, when direct measurement is not feasible, a method for predicting the capacity of exercise or physical fitness level using simple test results or biological information is applied. We reviewed previous studies that predicted fitness levels to identify methods for predicting maximum exercise capacity using only the age of the subject [9,10], or a simple physical fitness test [11,12], and predicting the anaerobic threshold using a simple physical fitness test [13].
However, very few studies have predicted exercise ability and fitness levels in high-altitude environments. Most of the previous studies predict the onset of acute mountain sickness [14][15][16]. Moreover, the exercise tolerance (% HRmax) in a high-altitude environment (3500 m) has also been predicted using the results of a step test conducted in a low-altitude condition (600 m) [17]. However, very few studies have predicted 1 Simulated altitude is a normobaric hypoxic environment.
fitness levels in various altitude environments. The reason is that it is environmentally and technically very difficult to measure physical fitness in various high-altitude environments. Therefore, the purpose of this study was to create simple mathematical models to predict submaximal exercise performance in various altitude environments using the results of a simple physical work capacity test conducted at sea level with more than 200 subjects.

Participants
The participants were recruited into the study after obtaining informed consent. We presented the subject's age distribution in Table 1. Each subject performed a submaximal exercise test in four artificial hypoxic and sea level environments and only the data from subjects who completed all measurements required for analysis were used ( Table 2).

Research Design
The study subjects were equally into four teams. In addition, we set the measurement order of each team to eliminate systematic errors due to the measurement order. In addition, we removed the training effect by setting the interval between individual tests to more than two days. The measurement sequences for each team are listed in Table 3.
All subjects participating in the experiment underwent incremental submaximal exercise tests at artificial altitudes of 2000 m, 3000 m, 4000 m, 5000 m, and at sea level. We performed an incremental submaximal exercise test using a cycle ergometer (Combi 75XLⅡ, Konami Corporation, Tokyo, Japan) and ramp protocol [9]. The team name is defined to distinguish the measurement sequence and is unrelated to the data-analysis process.

Measurement of Physique
We measured the height and weight of all subjects using Inbody 3.0 (Inbody, Seoul, Korea), between 8 and 9 AM. The subjects fasted for at least four hours before the measurement. We instructed the subjects to wear light clothing for the measurements. And we pressed the measurement button after confirming that the subject was standing on the measuring board with bare feet and holding the measuring electrodes in both hands. We instructed the subjects to remove all metal accessories they had for accurate measurements.

Physical Work Capacity Test
The age and sex of the subjects were entered into the cycle ergometer. Then, the cycle ergometer calculated the subject's target heart rate (75% HRmax) according to Miyashita's formula (HRmax = 209 − 0.69 × age) [9]. Next, the subject attached a heart rate sensor connected to the cycle ergometer to the earlobe and started the measurement. After beginning the measurement, the subject pedaled the cycle ergometer at a constant speed of 50 rpm. Subsequently, the exercise load was increased every 1 minute, and the measurement was automatically terminated when the subject's heart rate reached the target heart rate (75% HRmax). After the measurement, the examiner recorded the subject's exercise load (watt) corresponding to 75% HRmax. We performed all tests in an environmental hypoxic chamber (Submersible Systems Technology, Huntington Beach, CA, USA). Each subject was acclimatized in the hypoxic chamber for 30 min for each test before exercise tests were performed [2]. A constant temperature (23 ± 2 • C) and humidity (50 ± 2%) were maintained in the chamber during the test.

Sample size calculation
The G*Power program (ver. 3.1.9.7, Heinrich-Heine-Universität Düsseldorf Univ., Düsseldorf, Germany) was used for power analysis to estimate the appropriate sample size. We calculated the sample size based on the study by Burtscher et al. [17]. We queried by entering 40 for the total sample size, 3 for the number of predictors, and 0.5, for the observed coefficient of determination (R 2 ). As a result, the coefficient of determination of the research hypothesis was calculated to be 0.443. Subsequently, we entered the statistical significance level as 0.05, statistical power as 0.9, and the number of predictors as 4, and obtained the result for the total sample size of 32 subjects. Since this study did not pose a severe risk to the subjects and considering that the submaximal fitness test was simple, 233 males aged 18-68 years were recruited as subjects to increase the statistical power of the results of this study which was 0.9 or higher.

Statistical Analysis
We used age, height, weight, and physical work capacity at sea level as independent variables to predict physical work capacity at each artificial altitude. A multiple regression analysis (stepwise method) was used to develop a regression model. In addition, we checked linearity, continuity, normality of residuals, independence of residuals, homogeneity of residual variance, multicollinearity, and outliers to create an accurate regression model. We set the statistical significance level to less than 5%.

Division of Data (Bernoulli trials)
We split the final data in a ratio of 7:3 using Bernoulli's trial. Subsequently, we used 70% of the data for regression model development and 30% of the data for cross-validation tests ( Table 4).

Outliers
We defined an outlier as a value with an absolute value of three or more standardized residuals. We repeated the analysis after removing outliers found during the regression analysis. The status of the outliers removed is presented in Table 5. The proportion of outliers removed during the development of each regression model was less than 2.4%.

Cross-Validation Test
We checked the cross-validation of our predictive model by using 30% of the total data. We calculated the predicted values of the cross-validation data by using the regression equation developed in this study. We then calculated the mean absolute percentage error (MAPE) using the residuals between the predicted and measured values, as in Eqn. 1 [18]. In addition, we calculated the standard error of the estimation using Eqn. 2 [12].
The MAPE is the mean absolute percentage error (%), where Watt real is the actual measured value of physical work capacity at 75% HRmax and Watt pred. is the predicted value of physical work capacity at 75% HRmax. The "N" is the sample size.
SEE is the standard error of estimate (watt). Watt real is the actual measured value of physical work capacity at 75% HRmax and Watt pred. is the predicted value of physical work capacity at 75% HRmax. The "n" is the sample size. Table 5 presents the descriptive statistics, the amount of change, and the coefficient of variation for the physical work capacity measured in each artificial altitude environment.

Descriptive Statistics of Physical Work Capacity in Each Hypoxic Condition
The decrease in physical work capacity at 75% HRmax above 4000 m artificial altitude was greater than that below 4000 m artificial altitude. In addition, considering the coefficient of variation between the artificial altitudes, the relative variance of the artificial altitude above 4000 m was greater than that of the artificial altitude below 3000 m ( Table 6).

Determination of the Regression Models
In this study, we applied multiple regression analysis (stepwise method) with age, height, weight, and physical work ability at sea level as independent variables. As a result, there was only one independent variable in each regression model below the artificial altitude of 4000 m: the physical work capacity at sea level. In contrast, there were two regression models at an artificial altitude of 5000 m. In one of the regression models, only physical work capacity at sea level was an independent variable, whereas, in the other, height and physical work capacity at sea level were independent variables. By comparing the two regression models, we confirmed that the coefficient of determination (R 2 ) increased by only 2.7%, even when height was added as an independent variable in the regression model. Therefore, we concluded that it was not efficient to include height as an independent variable. Therefore, we used only the physical work capacity at sea level as the independent variable for each regression model.
The coefficient of determination (R 2 ) of the simple regression models using only the physical work capacity at sea level as an independent variable was 0.398-0.578 (Table 7).

Linearity
We constructed a scatter plot to check the linearity between the independent and dependent variables (Fig. 1) and confirmed that each regression model had linearity between independent and dependent variables.

Independence of Residuals
We calculated the Durbin-Watson index to confirm the independence of the residuals. Since the Durbin-Watson index of each regression model was close to 2, we concluded that each regression model was independent of the residuals (Table 8).

F-test for Each Regression Model
We carried out F-test to confirm the significance of the regression model which confirmed that the null hypothesis "the regression coefficient of the independent variable is 0" was rejected in each regression model. Hence, each regression model was found to be statistically significant (Table 9).

The Goodness of Fit for Each Regression Model
We calculated MAPE to confirm the goodness of fit of each regression model. The MAPE range of each regression model was 0.08~0.14%, and the MAPE range in the cross-validation test was 8.09~17.0%. In particular, the MAPE at an artificial F I G U R E 1. Scatter plot. PWC: physical work capacity.

Normality of Residuals for Each Regression Model
We conducted the Shapiro-Wilk test to confirm the normality of the residuals of each regression model and confirmed that the residuals of each regression model were normal (Table 11).

Regression Equations to Estimate Physical Work Capacity at Each Simulated Altitude
In Table 12, we present the regression models that predict the physical work capacity at each artificial altitude, along with the standard error of estimation.

Discussion
This study aimed to create simple mathematical models to predict submaximal exercise performance in various altitude environments using the results of a simple physical work capacity test conducted at sea level. In our study, we used only physical work capacity at sea level as the independent variable of the regression model at each artificial altitude.
Previous studies [19,20] reported that physical work capacity decreased with increasing age; therefore, we expected age to be a significant independent variable. However, the statistical analysis showed that age was not a significant independent variable in any regression model. Therefore, we concluded that there was no relationship between the decrease in physical work capacity with increasing age and the reduction in physical work capacity in the high-altitude environment.
The MAPE of each regression model applied to an artificial altitude of ≤4000 m was ≤10%. According to previous studies [18,[21][22][23], "the estimation result is valid if the estimation error of physical strength is within 10%". Therefore, most of the regression models we developed had no issues with the validity of the estimates. However, the MAPE of the regression model applied to the artificial altitude of 5000 m was 17.0% which indicated a large estimation error. Similarly, Nelson et al. [18] suggest that estimating methods with a MAPE greater than 10% should be cautiously used. The MAPE of the regression model applied to an artificial altitude of 4000 m was 10.2%. It is unclear why the estimation error was large at an artificial altitude of 4000 m or higher. Considering the CV in Table 5, the relative variance of the measured values above 4000 m was larger than the relative variance of the measured values below 4000 m. In general, if the variance is large, the estimation error of the linear equation is also large. The large dispersion of physical fitness measurements at altitudes above 4000 m may be due to significant differences in responses between individuals in a high-altitude environment [1]. In similar previous studies, Buskirk [24] demonstrated that individual conditions, such as acute mountain sickness, pulmonary hypertension, and edema, and one's work capacity could be problematic at high altitudes. Imray et al. [25] reported that acute mountain sickness occurs rapidly at altitudes above 3000 m. Additionally, Honigman et al. [26] reported that acute mountain sickness is more frequent in younger, unhealthy individuals, those living at sea level, having a history of acute mountain sickness, and having underlying lung problems. Therefore, to estimate exercise ability at an altitude of ≥4000 m, individual differences may be significant due to various reasons.
By checking the primary assumptions in the regression anal-ysis developed in this study, we confirmed that all basic assumptions of the regression analysis were satisfied. The coefficient of determination of our regression model was in the range of 0.398-0.578. These values are slightly smaller than 0.6, the coefficient of determination of the regression model developed by Burtscher et al. [17]. However, our result was larger than the coefficient of determination (0.297-0.520) calculated using the correlation coefficient (0.545-0.721) suggested by Gibson et al. [27].
Burtscher et al. [17] created a regression model to predict exercise tolerance at 3500 m altitude using the results of the step test at an altitude of 600 m and additional independent variables. Gibson et al. [27] compared a 6-minute treadmill walking test conducted in a hypoxic chamber (simulated altitude of 3400 m) with a 6-minute outdoor walking test performed at an actual altitude of 3400 m (Cuzco, Peru). However, we created regression models to predict physical work capacity in environments with various altitudes using only simple physical fitness measurement results at sea level as an independent variable. Therefore, our regression models have a performance similar to that of previous studies, although it is a more straightforward method compared to previous studies.

Conclusions
The method of predicting submaximal exercise capacity in various high-altitude environments with submaximal exercise performance measured at sea level has an explanatory power of approximately 40-58% and an estimation error of 8-17%. Among the regression models we developed, the regression model applied to an artificial altitude below 4000 m had no problem with generalization because the cross-validation was less than 10%. However, the regression model applied to an artificial altitude of 5000 m had a cross-validity of 17%; therefore, it should be used with caution. This method we've created will be able to tell someone in advance how much their physical work capacity will decrease in the high-altitude environment when they want to travel to high altitude.

A B B RE VI AT IO NS
MAPE, mean absolute percentage error; SEE, standard error of estimation; CV, coefficient of variation; PWC, physical work capacity.

A U TH OR CO NT RI BU TI ONS
SSN and HYP-designed the research study; drafted the manuscript. HYP and JWK-performed experiments. SSNanalyzed the data. SSN, HYP, and JWK-discussed the results. All authors contributed to the editorial changes in the manuscript. All authors have read and approved the final manuscript.

E THICS APPROVAL AND CONSENT TO PA R TICIPATE
This study was conducted according to the Helsinki Declaration's guidelines and approved by the local ethics committee of Kyunghee University (KHSIRB 2015-024). Also, informed consent was obtained from all subjects involved in the study.

ACK NOWLEDGMENT
This study involved several participants. We thank the participants of this study.

F UNDING
This research received no external funding.