Predicting physical performance after training: insights from machine learning using small samples

doi:10.21203/rs.3.rs-4707433/v1

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Predicting physical performance after training: insights from machine learning using small samples

https://doi.org/10.21203/rs.3.rs-4707433/v1

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Background

Performance optimization is a major goal in sports science. However, this remains difficult due to the small samples and large individual variation in physiology and training adaptations. Machine learning (ML) solutions seem promising, but have not been tested for their capability to predict performance in this setting. The aim of this study was to predict 4-km cycling performance following a 12-week training intervention based on ML models with predictors from physiological profiling, individual training load and well-being, and to retrieve the most important predictors. Specific techniques were applied to reduce the risk of overfitting.

Results

Twenty-seven recreational cyclists completed the 4-km time trial with a mean power output of 4.1 ± 0.7 W/kg. Changes in time-trial performance after training were not different between moderate-intensity endurance training (n = 6), polarised endurance training (n = 8), concurrent polarised with concentric strength training (n = 7) and concurrent polarised with eccentric strength training (n = 6) groups (P > 0.05), but included substantial inter-individual differences. ML models predicted cycling performance with excellent model performance on unseen data before (R² = 0.923, mean absolute error (MAE) = 0.183 W/kg using a generalized linear model) and after training (R² = 0.758, MAE = 0.338 W/kg using a generalized linear model). Absolute changes in performance were more difficult to predict (R² = 0.483, MAE = 0.191 W/kg using a random forest model). Important predictors included power at V̇O_2max, performance V̇O₂, ventilatory thresholds and efficiency, but also parameters related to body composition, training impulse, sleep, sickness and well-being. Conclusion

ML models allow accurate predictions of cycling performance based on physiological profiling, individual training load and well-being during a 12-week training intervention, even using small sample sizes, although changes in cycling performance were more difficult to predict.

artificial intelligence

concurrent training

cycling

training response

strength training

endurance training

performance optimization

Machine learning models enabled accurate predictions of time-trial performance in recreational cyclists, even though changes in performance were more difficult to predict

Accurate predictions could be obtained even with a small sample size, when applying techniques to reduce overfitting

Key predictors of time-trial performance include physiological determinants of endurance performance, parameters related to body composition, training impulse, sleep, sickness and well-being.

Optimizing physical performance is a central objective in sport science. For instance, athletes are largely identified based on their physiological profiles that enable them to deliver exceptional performances [1]. Coaches seek the best training strategies to improve these physiological traits [2–4] and many sports require a combination of high maximal strength and endurance performance [5, 6]. Concurrent strength and endurance training is encouraged in these sports, but may lead to impaired adaptations [7–9] which can be explained by interference of molecular signalling for protein synthesis and mitochondrial biosynthesis mechanisms [10, 11]. These interference effects following concurrent training have recently been shown to differ between males and females [9] and may very well be different between individuals too.

Training adaptations following the same training intervention deviate substantially in different individuals [12–15], a finding that persists in monozygotic twins possessing the same genotype [14]. On average, increases in knee extensor muscle strength and V̇O_2max were observed following 3 months of strength training and endurance training respectively, but with large inter-individual differences [14]. However, training effects following concurrent training were not assessed. Previous studies suggested that concurrent training focusing specifically on eccentric or plyometric exercise could be (more) effective for combining high strength and endurance performance [11,13,16]. Moreover, executing concurrent strength and endurance training following a polarised design resulted in higher simultaneous endurance and strength gains compared to low-intensity endurance only [17], suggesting that the design of the concurrent training program plays an important role in mitigating the interference effect. In a polarised training design, 80% of the training is spent at a low-to-moderate intensity (i.e. below the first lactate/ventilatory threshold) and the remaining 20% is spent primarily at severe intensities (i.e. above the second lactate/ventilatory threshold). Recently, it was shown that combining polarised endurance training with plyometric strength training resulted in the highest performance gains in elite runners compared to pyramidal endurance training, where 80% of the time was spent in the low-to-moderate intensity domain and the final 20% was spent primarily at heavy intensities (i.e. between the first and second lactate/ventilatory thresholds) [12]. Given that individual training responses differ considerably, even following the same training and in individuals with the same genotype, coaches and athletes could benefit from individual predictions of anticipated changes in performance. To date, however, we are unaware of studies that predict individual sports performance and changes thereof resulting from training based on characteristics from physiological profiling, training load and well-being.

Machine learning (ML) solutions seem promising in this regard. In previous studies, ML models have been successfully applied to predict training load [18], injury [19], cardiorespiratory fitness [20] and (team) sports performance [21, 22]. Whereas ML typically thrives by using datasets with a large number of observations [23], in sport science [24] and concurrent training research [8, 9] the number of observations is typically small, with a median sample size of approximately 20 participants and 10 per training group. The problem with predictive modelling using a small sample size, particularly when combined with a large number of predictors, is the risk of overfitting, which results in a model that is not well generalizable to newly collected data [25]. Rather than increasing the sample size, which could be challenging in sports science, one could benefit from applying techniques that reduce the risk of overfitting. Several techniques exist to mitigate overfitting and improve machine learning modelling [25–28], such as 1) prior selection of predictors, 2) tuning ML model parameters, 3) using ML algorithms that reduce the number of predictors and 4) applying cross-validation. It has yet to be determined how robust or generalizable ML models are for predicting performance following training in a small group of participants.

The aim of this study was to predict 4-km cycling performance following a 12-week training intervention based on ML models with predictors from comprehensive physiological profiling, individual training load and well-being. Here, we developed ML models for the prediction of cycling performance before and after the training intervention, as well as for the changes in cycling performance. Models were developed using a small sample size, while applying techniques to reduce overfitting, and we assessed their generalizability to new data (not used to develop the model). Secondly, we obtained the most important predictors from the ML models. We hypothesized that cycling performance at baseline would be predicted accurately by ML models, even when based on limited number of participants, but that training-induced changes in cycling performance would be more difficult to predict. The largest improvements in cycling performance were hypothesized to occur following concurrent polarised and eccentric strength training. ML models were also expected to provide novel insights into the most important predictors of cycling performance.

2.1 Participants

Thirty-four participants were recruited for this study based on the following inclusion criteria: 1) cycling experience ≥ two years, 2) current training frequency ≥ three sessions per week and 3) absence of known disease or exercise limitations. Information about the procedures and risks associated with the study were provided beforehand and all participants gave written informed consent. Seven participants (20.6%) dropped out during the intervention due to personal reasons (n = 5) or due to injuries unrelated to this research (n = 2). The study was approved by the departmental ethics committee of the Vrije Universiteit Amsterdam, the Netherlands (VCWE-2022-081) and conducted in accordance with the Declaration of Helsinki.

2.2 Experimental design

The study was performed from September to December. The experimental design is illustrated in Fig. 1. Participants performed multiple tests on three separate occasions to establish comprehensive physiological profiles in the two weeks before and after the training intervention. In between testing, participants followed a twelve-week training program consisting of moderate-intensity endurance training only (MIE, n = 6), polarised endurance training (POL, n = 8), concurrent polarised training with concentric strength training (CT_CON n = 7) and concurrent polarised training with strength training using eccentric and plyometric exercises (CT_ECC, n = 6). Group allocation was done by stratified random sampling based on results from the pre-intervention tests. Participants were ranked based on their 4-km time-trial performance, V̇O_2max, Wingate peak power output (PO_peak), body fat percentage, height, weight, age and sex. After ranking, strata consisting of four participants each were used for random sampling without replacement to assign participants across the four groups.

--- Please insert Fig. 1 here ---

2.3. Performance and physiological profiles

2.3.1 Cycling time-trial performance

The primary outcome of this study was the mean power (per kg body mass) obtained during the 4-km cycling time trial, which was performed on an electrically-braked ergometer (Lode Excalibur Sport, Lode Medical Technology, Groningen Netherlands). Prior to the trial, crank torque was calibrated based on the manufacturer’s instructions. Participants performed a 24-minute standardised warm-up consisting of two 6-minute blocks of moderate-intensity exercise (to obtain pulmonary V̇O₂₋kinetics, described below). After the warm-up, participants were instructed to finish the 4-km time trial as fast as possible. Power output during the time trial was determined from cadence and the linear load constant alpha, which was set to correspond to 90% of the power output at V̇O_2max, when cycling at 90 rpm. Subsequently, momentary power output was measured throughout the 4-km time trial. Participants were able to see covered distance and power output and received verbal encouragement of the test supervisor throughout the time trial.

During the time trial, heart rate was recorded using a heart rate monitor (Garmin Ltd., Schaffhausen, Swiss) and pulmonary gas exchange was measured breath-by-breath via a facemask that was connected to a metabolic cart (Cosmed Quark CPET, Cosmed S.R.L., Rome, Italy). Prior to testing, the gas analyser and volume transducer were calibrated according to manufacturer’s instructions. Breath-by-breath data were smoothed and then averaged over the time trial to obtain performance V̇O₂, defined as the mean V̇O₂ during the time trial. Moreover, gross efficiency was determined during warm-up at 90% of the power corresponding to the first ventilatory threshold and was calculated by dividing mechanical power output by the oxidative metabolic power. The latter was derived from V̇O₂ and respiratory exchange ratio [29], with respiratory exchange ratio < 1.0 and V̇O₂ in steady state (< 5% change between min 3 and 6).

2.3.2 Incremental exercise test

V̇O_2max was obtained during an incremental cardiopulmonary exercise test on a bicycle ergometer (Lode Excalibur Sport, Lode Medical Technology, Groningen Netherlands). Participants were instructed to maintain a cadence of 90 rpm throughout the test. Workload started at 100W and increased in stepwise increments of 25W every minute and was stopped at exhaustion, defined as the point at which cadence fell below 80 rpm despite verbal encouragement. Similar to the time trial, participants wore a heart rate monitor and breath-by-breath pulmonary gas exchange was measured. V̇O_2max was calculated as the highest 30-s rolling average value. Exercise thresholds were obtained by two independent researchers using an online application [30], determining the first ventilatory threshold (VT1) using the

V-slope method [31], ventilatory equivalents and end-tidal oxygen tensions, and VT2 from the minute ventilation-V̇CO₂ graph and ventilatory equivalents for CO₂ and end-tidal CO₂ tension [32]. When GE could not be determined during the warm-up of the time trial (n = 2), GE was determined from the incremental test, at the last increment below VT1.

2.3.3 Wingate test

Sprint performance was obtained as 1-s peak power obtained during a 30-s Wingate test on a bicycle ergometer (Monark 894E Peak Bike, Monark Exercise AB, Vansbro, Sweden). Participants first performed a four-minute warm-up with 1kg added to the cradle, with a short 3 s sprint at minute one, two and three. For the Wingate test, workload was set at 7.5% body weight, starting from stand-still and the load was automatically dropped when a cadence of 70 rpm was reached. Participants were instructed to remain seated and pedal maximally throughout the test, with strong verbal encouragement.

2.3.4 Vertical jump test

Vertical jump performance was measured using inertial measurement units (MPU-9150, ± 16.0 g, 500Hz, Invensense, San Jose, USA) that were firmly secured to the participants’ left and right shoe [33]. Warm-up consisted of three sets of ten squats with one-minute rest in between. After warm-up and two practice jumps, participants performed five vertical squat jumps with one minute of rest in-between consecutive jumps. Participants were instructed to put their hands on their hips and to land with extended legs. No further instructions were given on jumping technique. Jump height was determined from flight time, locating take-off and landing time using a custom-written Matlab script (Mathworks Co, Natick, Massachusetts, USA). The highest jump of the five was used for further analysis. Jump height was also normalized by dividing jump height by the participant’s leg length as described in [34].

2.3.5 Anthropometry

Anthropometric measures included height, weight, thigh length, shank length, thigh circumference, shank circumference and fat percentage. All measurements were taken on the right side and in accordance with instructions from the International Society for the Advancement of Kinanthropometry [35]. Participants were measured by the same examiner during pre- and post-measurements. For the segment lengths, a sliding segmometer was used. Fat percentage was estimated from the sum of 4 skinfolds at the biceps, triceps, subscapular and iliac crest locations [36], which were obtained with a Harpenden skinfold calliper (Baty International, West Sussex, UK).

2.3.6 Muscle morphology

Muscle morphology was measured using 3-dimensional (3D) ultrasound imaging of the participants’ right m. vastus lateralis (VL), following the protocol described by Weide et al. [16]. In brief, B-mode ultrasound images of the muscle were collected at 30 Hz using a 5-cm linear array probe (Hitachi L-55, Hitachi Ltd., Tokyo, Japan). A cluster marker set was rigidly connected to the ultrasound probe and was tracked with 30 Hz using a motion detection camera (Polaris Vega, NDI, Waterloo, Canada). Participants were positioned with a knee flexion angle of 120° and a hip angle of 95°. Participants were instructed to remain still during the scans, with their shank fixated to prevent any leg movements. Multiple sweeps were performed along VL, starting on the lateral aspect of the tibia plateau and moving at constant speed in distal-proximal direction. Sweeps were made from lateral to medial direction with slight overlap (approximately 0.5 cm). Subsequently, a 3D voxel reconstruction was generated using the tracked probe coordinates and corresponding ultrasound images, employing bin-filling and inpainting through a custom-written Matlab script.

From the 3D voxel array, origin and distal musculotendinous junction of the VL were obtained using 3D image processing software (MITK; www.mitk.org). Muscle volume was calculated by manually segmenting transverse cross-sections along the muscle belly in MITK, followed by interpolating these cross-sections in ITK-SNAP (www.itksnap.org). Maximal anatomic cross-sectional area was obtained from the reconstructed 3D voxel array. Muscle fascicle length (Lf) was measured at two-third of the length between origin and distal end muscle belly within the mid-longitudinal fascicle plane [16]. The pennation angle (PA) was determined as angle between the distal aponeurosis and the fascicle. Physiological cross-sectional area was calculated by dividing muscle volume by muscle fascicle length.

2.3.7 Muscle oxygenation

During the 4-km time trial, relative changes in deoxygenated haemoglobin and myoglobin (deoxy[heme]) and oxygenated haemoglobin and myoglobin (oxy[heme]) in the m. vastus lateralis were collected with respect to the start of the time trial using continuous-wavelength near-infrared spectroscopy (NIRS) (Portamon; ArtinisMedical Systems, Elst, The Netherlands). The measurement protocol has been described in detail elsewhere [37]. Average oxy[heme] and deoxy[heme] were obtained throughout the time trial.

2.3.8 V̇O₂-kinetics

Pulmonary $\:\dot{V}$O₂ (p$\:\dot{V}$O₂)-kinetics were derived from the 6-minute moderate-intensity cycling bouts in the warming up before the 4 km time trial. Mono-exponential fitting was performed for the transition from cycling at 20W to 90% of the power at VT1. Fitting was performed using an online application (https://www.exphyslab.com/kinetics) based on the ensemble-averaged response of the two individual bouts after filtering for outliers using the 95% confidence interval based on the initial fit (see Eq. 1) and linear interpolation of breath-by-breath data into second-by-second bins. Data were fitted with the following mono-exponential function:

$$\:\begin{array}{c}p\dot{V}{O}_{2}=\:p\dot{V}{O}_{2\:BL}+{A}_{p}\:\left(1-{e}^{\frac{t-{TD}_{p}}{{\tau\:}_{p}}}\right)\:\left(1\right)\end{array}$$

With $\:{p\dot{V}{O}_{2}}_{\:\text{B}\text{L}}$ as the pulmonary mean baseline $\:\dot{\text{V}}{\text{O}}_{2}$ in mL$\:\bullet\:$min⁻¹ at 20W measured over the last 30 s, $\:{\text{A}}_{\text{p}}$ as the amplitude of increase in $\:\dot{\text{V}}{\text{O}}_{2}$ in mL$\:\bullet\:$min⁻¹ above $\:{p\dot{V}{O}_{2}}_{\:\text{B}\text{L}}$,$\:\:t$ the time in seconds, $\:{\text{T}\text{D}}_{\text{p}}$ the time delay in seconds and $\:{{\tau\:}}_{\text{p}}$ the time constant in seconds. One participant (n = 1) did not achieve a steady-state pV̇O₂ but displayed a p$\:\dot{V}$O₂ slow component, indicative of heavy exercise. To account for the slow component, a custom-written Matlab script was applied as previously described [38]. This script iteratively fitted a mono-exponential Eq. (1) on the pV̇O₂ data starting from 20 seconds relative to exercise onset with a window size of 40 seconds and iteratively increasing the window size by one second until the window covered the entire response. The resulting time constants ($\:{{\tau\:}}_{\text{p}}$) of each iteration were then plotted against the window size. Onset of the slow component is defined as a deflection point in this plot of $\:{{\tau\:}}_{\text{p}}$ versus time. The fit corresponding to the deflection point was defined as the fundamental response and was used for further analysis for this particular participant.

2.4 Training intervention and monitoring

The 12-week training period was divided into three mesocycles of four weeks. Each mesocycle consisted of five training sessions with a 3:1 load structure, including three weeks of progressive training load and one deloading week with reduced training volume. Progressive overload was applied with a weekly increase of 5% in training load within and between mesocycles to stimulate training adaptation [39]. Such design was used for both strength and endurance training programs and for all four training groups: MIE, POL, CT_CON and CT_ECC. A complete overview of the scheduled training sessions is provided in supplemental tables 1–3.

Strength training was focused on the most important muscles for power production in cycling, including the mm. vastii, m. gluteus, m. iliopsoas and hamstring muscles [40]. Each strength training started with a 10 minutes cardio warm-up on a cross-trainer, rowing or cycling ergometer.

Endurance training was prescribed according to a three-zone model [41]. Training intensity distribution (TID) was established using zone 1 for moderate intensities below VT1 (Z1), zone 2 for heavy intensities between VT1 and VT2 (Z2) and zone 3 for severe intensities above VT2 (Z3). Training impulse (TRIMP) was calculated by multiplying the number of minutes in each zone by 1, 2 or 3 for Z1, Z2 and Z3, respectively [42]. Average TRIMP per endurance training session was set as 87.5 (A.U.), corresponding to those used in previous studies [43, 44]. All participants received a heart rate monitor (H9 Polar Electro Inc., Lake Success, NYV) to wear during the endurance training sessions.

Participants in the MIE group performed five moderate-intensity endurance sessions per week, and were instructed to keep their heart rate in Z1, between 15 and 5 bpm below the heart rate at VT1. The Z1 sessions were not supervised.

In the POL group, participants performed three Z1 endurance sessions and two interval sessions. Training was prescribed using a TID set at 75%, 10% and 15% for Z1, Z2 and Z3, respectively, corresponding to a polarised index of 2.05 [45]. Z1 sessions were performed similar to MIE. Interval sessions were prescribed based on power output, including 7–8 x 4-min or 2–6 x 8-min interval blocks with 2–3 minutes of rest in between. Intervals were prescribed at 110% of PO_VT2 for Z3, at 50% of the difference between PO_VT1 and PO_VT2 for Z2 and at 80% of PO_VT1 for Z1. Participants were instructed to keep their PO within 5% of the prescribed PO values. The interval sessions were supervised.

The CT_CON group performed two Z1 endurance sessions, one interval session and two traditional or concentric strength training sessions. Interval sessions were supervised and included 7–12 x 4-min interval blocks with 2 minutes of rest in between. Strength sessions consisted of two-legged leg press, half deep squat (90° knee angle), split squat, 1-legged leg press, deadlift, hip thruster and hip flexion exercises (see supplemental table 2). All squats, i.e. the half deep squat and split squat, were performed with direct supervision for safety purposes. Load of the exercises was prescribed at 65–85% of the one-repetition maximum (1RM) that was measured during the first training session. Participants performed 3–5 sets with 6–10 repetitions (~ 30 repetitions per exercise).

In the CT_ECC group, participants performed two Z1 endurance sessions, one interval session and two eccentric strength training sessions. Interval sessions were supervised and included 7–12 x 4-min interval blocks with 2 minutes of rest in between. Strength sessions consisted of a goblet squat jump, jump lunge, 1-legged counter movement jump, 2-legged triple jump, eccentric psoas exercise, nordic hamstring curl and eccentric sliders (for details on sets, reps and load see supplemental table 3). Load was progressively increased by increasing the applied % body mass and/or number of jumps or repetitions. For the jump lunge, depth was set where the knee of the rear leg nearly touched the ground. Depth of the goblet squat and triple jumps was defined as the height where the thigh was parallel to the floor.

Monitoring of internal endurance training load was done based on heart rate measured during the Z1 and interval sessions (H9 Polar Electro Inc., Lake Success, NYV). Furthermore, we monitored the participants’ well-being during the training intervention by daily records of total sleep time, perceived quality of sleep (1–5 scale), fatigue (1–5 scale), stress (1–5 scale) soreness (1–5 scale), mood (1–5 scale) and readiness-to-train (1–5 scale) and weekly records of mental and physical fatigue (1–5 scale) using the SportDataValley-platform (https://app.sportdatavalley.nl) [46–48].

2.5 Data analysis

2.5.1 Feature engineering

Predictions were made based on physiological profiles and characteristics of training load and well-being during the training intervention. For physiological profiles, most of the features (i.e. variables) were obtained directly from the exercise tests and measurements or calculated as described above. For V̇O₂ kinetics, mean response time was calculated as the sum of the time delay and time constant [49]. For training load and well-being data, different aggregate functions were applied to all recordings obtained during the intervention for a specific variable (e.g. mean, standard deviation, 5th, 25th, 50th, 75th, 95th percentiles). For example, the value associated with 75th percentile of sleep duration reflects the threshold value for the top-25% longest sleep durations that were recorded during the intervention. For heart rate recordings during endurance training sessions, when heart rate was missing (e.g. when the heart rate monitor was not connecting well), median imputation was performed based on all prior zone 1 training sessions. Note that this was only done for zone 1 training sessions as it is expected that the heart rate was within the narrow bandwidth of 10 bpm that was prescribed. Afterwards, these heart rate values were used to calculate TRIMP scores according to Lucia’s TRIMP [42]. From all predictors, only oxygenation features contained missing values (n = 2 at baseline and n = 3 for changes), which were imputed by median values. Prior to modelling, all features were centred and standardized to Z-scores removing differences in measurement scales between variables.

2.5.2 Predictive modelling using machine learning

Machine learning was used to predict time-trial performance at baseline, after training or for changes in performance. Time-trial performance was therefore the target we wished to predict. Since time-trial performance was expressed in W/kg, weight was excluded as a predictor in ML models. First, records were split into a training set to create ML models (n = 19) and a test set for model evaluation on unseen data (n = 8) based on randomized stratified sampling based on the target. As we did not know a priori which algorithm may best predict our outcomes, three different algorithms were used. Since we were dealing with a relatively small sample size, we opted for a generalized linear model (glm) that uses regularization to limit the number of predictors in the model and a principal component regression model (pcr) that reduces the number of predictors using principal components. Also, we included a non-linear random forest (rf) model [50] that allows for a more complex ensemble models with high predictive performance, but that is also robust to high-dimensional data [51].

Specific techniques to reduce chances of overfitting were also applied. We performed feature selection based on multicollinearity to reduce the number of predictors prior to modelling [52]. Features were analysed using pairwise correlations and features with an |r| > 0.7 were removed (i.e. the variable that had the strongest relation with other predictors in terms of average absolute correlation was removed from each pair). Moreover, machine learning modelling can be optimized by tuning hyperparameters of the algorithm using the training set. A short description of each model’s hyperparameters can be found in supplemental table S4. Combining hyperparameter tuning with (inner) cross-validation is recommended to retrieve the best combination of hyperparameters based on performance on an independent out-of-sample validation set [53]. Given the small sample size in this study, we used leave-one-out cross-validation to select the best combination of hyperparameters using predictive performance on the hold-out sample of the (inner) validation set. After obtaining the best combination of hyperparameters, we created a new model with these parameters based on all data within the training set.

Model performance was assessed based on the mean absolute error (MAE) and explained variance (R²) between the predicted values and actual values for time-trial performance. Typically, model performance is first evaluated on the training set to perform model selection. Here, MAE scores were used to select the best performing model, with a MAE of 0 presenting a lower bound where the predicted values match the actual values. We created different models for glm, rf and pcr algorithms either with or without filtering and with or without hyperparameter tuning. Subsequently, only the best model was used to predict values on the independent test set containing data that were not seen by the model. Model performance on the test set reflects how well the model generalizes to other datasets. Last, most important predictors were obtained using feature importance based on the best performing model using all available data. Top thirty most important features were presented.

2.6 Statistics

Data are presented as mean ± standard deviation. Normality was checked using Shapiro-Wilk tests. To check for differences between training intervention groups at baseline, we performed one-way analysis of variance (ANOVA) and post-hoc tests with Bonferroni correction. A repeated-measures two-way ANOVA was performed to detect changes in time-trial performance after training for the different intervention groups. If significant main effects were observed, post-hoc tests with Bonferroni correction were performed. To gain insight into the most important predictors, feature importance of each model was evaluated based on permutation. Data analysis was performed in R (v4.2.2). The main packages used were caret package [54] for machine learning, ggplot2 for data visualisation [55] and dplyr for data processing [56]. α was set at 0.05.

3.1 No group differences at baseline

Table 1 displays baseline characteristics per training group. Randomised stratified allocation resulted in similar groups, with no significant differences in age, body composition and performance at baseline. In addition, average V̇O_2max was 52.7 ± 7.7 mL/kg/min across all participants, confirming their recreational training level. Cyclists completed the 4-km time-trial with a mean power output of 4.1 ± 0.7 W/kg.

Table 1

Participant characteristics before training intervention
Group	MIE	POL	CT_CON	CT_ECC	P value
Group	(n = 6)	(n = 7)	(n = 6)	(n = 8)	P value
Age (years)	39 ± 14	41 ± 10	39 ± 9	43 ± 7	0.829
Weight (kg)	71.58 ± 11.9	81.04 ± 10.9	78.39 ± 11.9	78.39 ± 10.2	0.484
Height (m)	1.79 ± 0.08	1.88 ± 0.08	1.84 ± 0.08	1.81 ± 0.10	0.247
Body fat (%)	22.46 ± 6.3	20.51 ± 2.3	21.76 ± 5.8	22.27 ± 7.3	0.911
PO_peak Wingate (W/kg)	13.05 ± 1.30	12.35 ± 1.78	13.28 ± 2.12	12.72 ± 2.72	0.825
V̇O_2max (mL/kg/min)	51.3 ± 8.3	52.2 ± 7.6	53.6 ± 6.9	53.5 ± 10.0	0.949
PO_mean,TT (W/kg)	3.96 ± 0.81	4.06 ± 0.59	4.19 ± 0.71	4.13 ± 0.98	0.957

MIE: moderate-intensity exercise group, POL: polarised training group, CT _CON concurrent polarised and traditional strength training group, CT_ECC: concurrent polarised and eccentric strength training group, TT: time trial, PO: power output.

3.2 Individual adaptations following training interventions

Changes in time-trial performance were not different between the four training groups (+ 1.7 ± 3.9% for MIE, + 3.0 ± 6.8% for POL, + 0.8 ± 2.9% for CT_CON and + 2.3 ± 4.6% for CT_ECC, P > 0.05). However, individual changes in time-trial performance varied substantially, ranging from − 7.9% to + 17.8%. Twenty-one participants had a training compliance > 85%. Subsequently, we built ML models to predict both time-trial performance before and after the training intervention, as well as training-induced changes in performance.

--- Please insert Fig. 2 here ----

3.3 Predicting time-trial performance at baseline

To predict performance before the training intervention, ML models were created based on physiological profiles at baseline using the training set, which were evaluated based on unseen data in the test set. Generalized linear models (glm), random forest (rf) and principal component regression (pcr) models were built either after applying hyperparameter tuning and/or feature reduction using filtering. Model performances are shown in Table 2. In machine learning, the best model is typically selected based on model performance on the training set (validation), which in our case was the glm model with hyperparameter tuning (R² = 0.992, MAE = 0.053 W/kg). Model performance on the independent test set was also excellent for this model (R² = 0.923, MAE = 0.183 W/kg), indicating high generalizability of this ML model to other datasets. Predicted values closely matched the actual time-trial performance, as illustrated by the low MAE considering the range in 4-km time-trial performance from 2.75 to 5.40 W/kg.

Table 2

ML model performance for predicting average power during the 4-km time trial at baseline.
Algorithm	Tuning	Filter	Train R²	Train MAE	Test R²	Test MAE
glm			0.978	0.084	0.929	0.190
glm	x		0.992	0.053	0.923	0.183
glm	x	x	0.859	0.242	0.867	0.309
rf			0.971	0.179	0.933	0.460
rf	x		0.983	0.197	0.920	0.476
rf	x	x	0.969	0.214	0.956	0.471
pcr			0.172	0.476	0.190	0.671
pcr	x		0.773	0.239	0.789	0.332
pcr	x	x	0.677	0.313	0.849	0.273

Best models were highlighted for model performance on both the training set and test set based on the lowest MAE. Abbreviations: MAE: mean absolute error, R2: R squared, glm: generalized linear model, rf: random forest, pcr: principal component regression.

3.4 Predicting time-trial performance after training

ML models were created to predict post-intervention performance based on baseline physiological profiles and monitored training load and well-being during the intervention. Model performance is shown in Table 3. The highest model performance on the training set was achieved for the glm model with hyperparameter tuning (R² = 0.998, MAE = 0.029 W/kg). This model also demonstrated the best performance on the independent test set (R² = 0.758, MAE = 0.338 W/kg), indicating good predictions on unseen data. Predicted values did not differ much from actual time-trial performance, as shown by the MAE. The most important features from the best performing model are displayed in Fig. 3.

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Table 3

ML model performance for predicting average power during the 4-km time trial after the training intervention.
Algorithm	Tuning	Filter	Train R²	Train MAE	Test R²	Test MAE
glm			0.995	0.054	0.752	0.342
glm	x		0.998	0.029	0.758	0.338
glm	x	x	0.850	0.276	0.594	0.422
rf			0.973	0.179	0.747	0.429
rf	x		0.968	0.177	0.653	0.417
rf	x	x	0.969	0.206	0.686	0.505
pcr			0.230	0.521	0.188	0.572
pcr	x		0.915	0.171	0.720	0.367
pcr	x	x	0.873	0.209	0.686	0.378

3.5 Predicting changes in time-trial performance after training

Last, we built ML models to predict changes in 4-km time-trial performance based on physiological profiles and changes therein with training as well as monitored training load and well-being during the intervention. Model performance is shown in Table 4. High overfitting and poor generalizability were shown for the best model on the training set, which was the glm model with hyperparameter tuning (R² = 1.00, MAE = 0.005 on training set vs. R² = 0.033, MAE = 0.241 on test set). However, best performance on the independent test set was provided by the rf model using hyperparameter tuning and filtering (R² = 0.483, MAE = 0.191). Explained variance was lower than for the time-trial performance at baseline and after training, and mean absolute error was relatively high considering the range of changes in performance from − 0.32 to + 0.61 W/kg, illustrating that individual changes were more difficult to predict.

Table 4

ML model performance for predicting changes in average power during the 4-km time trial after the training intervention.
Algorithm	Tuning	Filter	Train R²	Train MAE	Test R²	Test MAE
glm			0.999	0.012	0.004	0.225
glm	x		1.000	0.005	0.033	0.241
glm	x	x	0.989	0.024	0.064	0.242
rf			0.981	0.067	0.388	0.199
rf	x		0.972	0.097	0.288	0.192
rf	x	x	0.986	0.095	0.483	0.191
pcr			0.021	0.157	0.156	0.183
pcr	x		0.021	0.157	0.156	0.183
pcr	x	x	0.288	0.147	0.061	0.217

The aim of this study was to develop ML models for the prediction of individual time-trial performance and changes therein following training in recreational cyclists, and to obtain the most important predictors. Because of the small sample size, we applied techniques to reduce overfitting. Time-trial performance could be predicted very accurately using the ML models with high internal validity, illustrating that predictions of time-trial performance are highly generalizable to unseen data, both at baseline (R² = 0.923, MAE = 0.183 W/kg) and after training (R² = 0.758, MAE = 0.338 W/kg). However, changes in time-trial performance were more difficult to predict, also for unseen data (R² = 0.483, MAE = 0.191 W/kg). The most important predictors were identified based on feature importance, demonstrating contributions from physiological profiles, individual training load and well-being during the intervention.

4.1 Predictions of time-trial performance

Machine learning models in the present study allowed for very accurate predictions of time-trial performance at baseline and after training. Differences in individual 4-km time-trial performance at baseline were largely explained by the best ML model (R² = 0.99) in the training set used to create the ML model. Similarly, previous cross-sectional studies have explained cycling time-trial performance using multiple linear regression models [11, 57–59]. In those prior studies, differences in 15-km to 1-h time-trial performance were also largely explained by physiological determinants in trained, well-trained and elite athletes (R² ≥ 0.78). The main difference with these previous studies is that those models were explanatory and have not been tested for their predictive performance, either using internal validation (testing the model on a subset of the collected data not used to build the model) or external validation (testing the model on newly gathered data from another cohort). In this study, we assessed predictive performance using internal validation, and also demonstrated high generalizability and good predictive performance of our ML model for cycling performance at baseline (R² = 0.92, MAE = 0.18 W/kg).

To the best of our knowledge, this is the first study to predicted time-trial performance after a prescribed training intervention using predictors from physiological profiles at baseline and individually monitored training load and well-being during the intervention. Our findings show that 4-km time-trial performance after a 12-week training intervention could be predicted with high accuracy and high predictive performance on unseen data (R² = 0.76, MAE = 0.34 W/kg).

Individual changes in time-trial performance, however, were more difficult to predict. When quantifying inter-individual differences in the response to training, researchers typically visualize the inter-individual responses in a bar plot ranking responses from low to high (similar to Fig. 2). However, one should be careful not to consider that all variability reflects true inter-individual differences in trainability [60]. In fact, part of the inter-individual differences are due to measurement error, (random) within-subject variability and regression to the mean [60–64]. Regression to the mean is the phenomenon whereby participants with relatively high or low values at baseline are naturally expected to regress towards the mean at follow-up [60]. As for within-subject variability, this could be partly explained by behavioural or environmental factors, such as sleep, stress, nutrition and circadian rhythm [64]. Not recognizing these three factors confounds interpretation of the differences in trainability as well as of responders and non-responders to a training intervention [62].

In this study, we demonstrated how ML analyses can help to gain more insights into these inter-individual differences in responses to training. Approximately 50% of the changes in time-trial performance in the test set could be explained by our ML model using predictors from physiological profiling and monitored training load and well-being. We are aware of only one other study that used ML analyses to predict individual changes in time-trial performance in elite short track speed skaters following 3 months of training [22]. Here, the best model explained ± 20% of differences in time-trial performance. The higher explained variance in the present study could be related to the fact that we also included predictors on comprehensive physiological profiles and on wellbeing, such as sleep and stress, that accounted for (part of the) within-subject variability in our ML model [61, 64]. In summary, using a ML approach to predict performance after training provides novel insights into performance optimization and inter-individual differences in the response to training.

4.2 Most important predictors of time-trial performance

It is well known that endurance performance can be largely explained by V̇O_2max, V̇O₂ at the lactate threshold, performance V̇O₂ and efficiency [65–67] as well as by underlying skeletal muscle determinants [65]. Accordingly, previous studies have identified key predictors of time-trial performance across different (longer) distances: ventilatory or lactate thresholds for 40-km performance [68]; performance V̇O₂ and gross efficiency for 1-h performance [58]; V̇O_2max, first ventilatory threshold, cycling economy and NIRS-derived recovery kinetics for 25-km performance [57]; performance V̇O₂, blood oxygen carrying capacity and leg oxygenation for 15-km performance [11] and mitochondrial oxidative capacity, submaximal blood lactate and leg oxygenation for 26-km performance [59]. Contrary to these longer time trials, 4-km time-trial performance has a greater anaerobic energy contribution [69], which may translate into other involved key predictors.

To the best of our knowledge, this is the first study to reveal predictors of time-trial performance before and after a 12-week training intervention based on ML modelling. Based on the feature importance of our ML models, we found predictors similar to those in literature on endurance performance, such as performance V̇O₂, ventilatory thresholds, power at V̇O_2max, gross efficiency and leg oxygenation. However, we also observed other important predictors including lean body mass, body fat percentage, skinfolds, leg circumferences as well as predictors related to Wingate power output or jump height, reflecting higher importance of sprint-related capacities. Additionally, we demonstrated important predictors derived from training impulse scores, resting heart rate, and sleep duration during the intervention. Interestingly, the ML model for changes in time-trial performance also indicated other predictors related to training and well-being, illustrating how sickness and psychological well-being may impact training adaptations, as well as compliance during the intervention. It should be noted that these predictors should be interpreted with caution, as the prior feature selection ensured that not all predictors were included in the best model. Still, these findings support the notion that key predictors of endurance performance may differ with the distance/duration of the time trial and that within-subject variability related to sleep, stress and health also contribute to the prediction of training adaptations [61,64]. In summary, ML modelling can provide new insights into key predictors of endurance performance.

4.3 Machine learning using small sample size: how to avoid overfitting?

ML is typically performed with large datasets and can be more challenging with small sample sizes, as there is a risk of overfitting. Robust evaluation of ML models is imperative for assessing generalizability of models, and is even more important when training and test samples are small [70, 71]. To obtain unbiased performance estimates on unseen data, regardless of sample size, researchers are advised to perform nested cross-validation and train-test split validation [72]. Cross-validation has also been recommended with hyperparameter tuning to avoid overfitting and improve generalizability [73]. It is important to note that k-fold cross-validation techniques may lead to biased results and should be avoided with small sample size [74]. Correspondingly, we completely separated training and test data sets using train-test splits for evaluation of model performance and applied nested leave-one-out cross-validation to obtain the best hyperparameter settings for each model. Another important factor to consider is the feature-to-sample ratio [72]. To reduce this ratio, one could perform feature selection prior to modelling or apply ML algorithms that reduce the number of features (e.g. by regularization with glm and principal components with pcr). In this study, we did both.

With overfitting, ML models are developed with a high complexity and as a result models fit random noise in the training data, which make their predictions on unseen test data less accurate. Overfitting can be reflected by a large increase in error from the training to the test set together with poor model performance on the test set. We did not observe this for modelling time-trial performance at baseline or after training. However, we did observe overfitting for the changes in cycling performance, especially for the glm algorithm. For changes in time-trial performance, best out-of-sample performance was obtained by the rf algorithm using hyperparameter tuning and feature selection, reducing the feature-to-sample ratio by ~ 50%. Another way to look at overfitting is to compare the prediction errors observed for the test set with the typical error that can be expected for the target. In our case, this typical error can be calculated from the coefficient of variation for time-trial performances (3.3% [75]) and the standard deviation in baseline performance of our participants [64], which was 0.135 W/kg. Interestingly, the MAE of our best ML models at baseline (0.183), after training (0.338) and for changes in time-trial performance (0.191) were only slightly higher than this typical error. This supports the idea that unbiased performance estimates can be obtained with ML regardless of sample size, when applying techniques to reduce overfitting.

4.4 Perspectives and limitations

On average, changes in time-trial performance were small and not different between the four types of training interventions. This may be explained by the relatively low sample size combined with the large inter-individual variability in responses to training. As mentioned, variability could be partly due to measurement error, within subject variability and regression to the mean [60, 62–64]. Moreover, training supervision, compliance and prior training volume could have influenced inter-individual variability in training responses. Many training sessions were supervised, but moderate-intensity endurance sessions were not (although heart rate was monitored throughout all cycling sessions). Compliance was used as a predictor in the ML modelling rather than as a cut-off to exclude participants that completed fewer training sessions. Finally, the training volume that cyclists were accustomed to prior to the study could have influenced their subsequent responses to training. Therefore, selecting a homogenous group of athletes in terms of training history and strict training supervision are advised for future studies.

Absence of group differences for changes in time-trial performance could also be due to the chosen outcome measure, the 4-km time-trial performance. Previous studies have reported 8% improvements in 40-km cycling time trial [43] and 10% improvements in 10-km running performance [44] based on a similar training impulse following 6 and 10 weeks of polarised endurance training, respectively. Whereas these studies focus solely on endurance training, we investigated effects of concurrent strength and endurance training and for this reason assessed a 4-km time trial, which requires a significant anaerobic energy contribution compared to longer time trials [69]. Concurrent plyometric and polarised training resulted in + 1.8% increase in 5-km running time-trial performance in well-trained runners after 8 weeks of training [12], which is comparable to the + 2.3% increase in our concurrent eccentric /plyometric and polarised training group. Notably, the magnitude of adaptations in these shorter time trials is much closer to the random error for measuring time-trial performance (i.e. typically 2–3%, although lower in athletes [75, 76]), making it more difficult to detect group differences in the changes in performance.

Performing ML with small sample size, such as with training studies, can benefit from techniques to increase sample size. Rather than upsampling records by duplication, one could generate synthetic datasets that contain more observations but with similar variable distributions and correlation structure, which improves existing AI algorithms through data augmentation [77, 78].

Predictive performance of all ML models was reported for both training and test sets. Typically, the best model is selected based on the training set (or validation dataset for model development). For predictions at baseline and after training, the best models based on the training set also performed best on the test set. However, this was not the case for changes in time-trial performance, as models were overfitting. Therefore, it may be better to investigate model performance on the test set as well, taking into account the internal validity of the model, especially when sample size is too limited to create a sufficiently large validation set during model development (this was only one sample using the leave-one-out cross validation in our case). Subsequently, these best models can be externally validated as additional proof of their generalizability.

4.5 Practical applications

This study shows that predictive modelling using machine learning may aid coaches, athletes and sport scientist in their pursuit of performance optimization. New insights can be obtained when athletes assess their comprehensive physiological profiles before and after specific training blocks, as well as when they monitoring their training load, and well-being (including sleep and stress) during these blocks. Not only can ML models provide individual predictions of performance after training, but also give new insights into the predictors that play an important role in establishing these predictions. Ultimately, such a ML approach could help coaches to determine the most promising training strategies for their individual athletes, which guides coaches in giving personalized advice for talent development and performance optimization.

Machine learning models enabled accurate predictions of time-trial performance in recreational cyclists, even though changes in performance were more difficult to predict. Accurate predictions could be obtained even with a small sample size, when applying techniques to reduce overfitting. In addition, key predictors of time-trial performance were derived from feature importance scores, highlighting contributions from expected physiological determinants of endurance performance, as well as parameters related to body composition, training impulse, sleep, sickness and well-being. In summary, machine learning helps to predict individual sports performance based on physiological profiling and individual training characteristics, which aids coaches and athletes in their pursuit of optimizing their training strategies and physical performance.

1RM one repetition maximum

3D three dimensional

$\:{\text{A}}_{\text{p}}$ Amplitude for V̇O₂-kinetics

ANOVA analysis of variance

CT_CON concurrent polarised training and traditional strength training

CT_ECC concurrent polarised training and strength training consisting of eccentric and

plyometric exercises

deoxy[heme] deoxygenated haemoglobin and myoglobin

glm generalised linear model

Lf fascicle length

MIE moderate-intensity endurance training

MAE mean absolute error

ML Machine learning

NIRS near-infrared spectroscopy

oxy[heme] oxygenated haemoglobin and myoglobin

PA pennation angle

pcr principal component regression

PO Power output

POL polarised endurance training

PO_peak peak power output

PO_VT1 Power output at the first ventilator threshold

PO_VT2 Power output at the second ventilator threshold

p$\:\dot{V}$O₂ pulmonary rate of oxygen uptake

$\:\dot{\text{p}\text{V}}{\text{O}}_{2\:\text{B}\text{L}}$ baseline pulmonary rate of oxygen uptake

R² explained variance

rf random forest

$\:{{\tau\:}}_{\text{p}}$ time constant

$\:{\text{T}\text{D}}_{\text{p}}$ Time delay for V̇O₂-kinetics

TID Training intensity distribution

TRIMP Training impulse

VL m. vastus lateralis

V̇O₂ rate of oxygen uptake

V̇O_2max maximal rate of oxygen uptake

VT1 first ventilatory threshold

VT2 second ventilatory threshold

7. Ethics approval and consent to participate

This study was approved by the ethics committee of the Faculty of Behavioral and Human Movement Sciences, Vrije Universiteit Amsterdam, The Netherlands (approval number: VCWE-2022-081). The study was conducted in accordance with the 1964 Declaration of Helsinki and written informed consent was obtained from all participants.

8. Consent for publication

Not applicable

9. Availability of data and material

The datasets generated and/or analysed during the current study are available in a Github repository (https://github.com/Luukings/Train2Adapt/).

10. Competing interests

Luuk Vos, Renske Vergeer, Richie Goulding, Guido Weide, Jos de Koning, Richard Jaspers and Stephan van der Zwaard declare that they have no competing interests.

11. Funding

This work was supported by a personal grant from the Musculoskeletal Health program of the Amsterdam Movement Sciences, The Netherlands (obtained by SZ).

12. Authors' contributions

Study design: LV, RV, RG, GW, JK, RJ and SZ.

Data collection: LV and RV.

Analysis: LV, RV, RG, GW, JK, SZ.

Creation of software: LV, RV, GW and SZ

Data interpretation: LV, RV RJ and SZ.

Writing - original draft: LV, RV and SZ

Writing - Review and Editing: LV, RV, RG, GW, JK, RJ and SZ

Supervision: RJ and SZ

13. Acknowledgements

The authors would like to express our gratitude to the participants for their investment in joining our study, Fondo for their help in the recruitment of participants and the Sport Center of the Vrije Universiteit for providing the required training facilities. We would like to thank Arie Koops and Jolanda Seijger for their flexibility and assistance in planning the training sessions. Furthermore, we are thankful to Milo Zech Wallebroek, Kjeld Kemperman and Maurice Figureredo Kariembacks for their help with the data collection, Frans-Josef Halkes for his technical support and Moritz Eggelbusch and Michel de Haan their contribution to the 3D ultrasound analysis. Moreover, we would like to thank Richard Louman from NOC*NSF to provide us with expert feedback on the training program and study design, and Jo de Ruiter for his help with the study design and jumping tests and analysis, as well as SportDataValley for allowing us to use their platform for gathering the training load and well-being data throughout the study.

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Predicting physical performance after training: insights from machine learning using small samples

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Abstract

Figures

Key Points

1. Background

2. Methods

2.1 Participants

2.2 Experimental design

2.3. Performance and physiological profiles

2.3.1 Cycling time-trial performance

2.3.2 Incremental exercise test

2.3.3 Wingate test

2.3.4 Vertical jump test

2.3.5 Anthropometry

2.3.6 Muscle morphology

2.3.7 Muscle oxygenation

2.3.8 V̇O2-kinetics

2.4 Training intervention and monitoring

2.5 Data analysis

2.5.1 Feature engineering

2.5.2 Predictive modelling using machine learning

2.6 Statistics

3. Results

3.1 No group differences at baseline

3.2 Individual adaptations following training interventions

3.3 Predicting time-trial performance at baseline

3.4 Predicting time-trial performance after training

3.5 Predicting changes in time-trial performance after training

4. Discussion

4.1 Predictions of time-trial performance

4.2 Most important predictors of time-trial performance

4.3 Machine learning using small sample size: how to avoid overfitting?

4.4 Perspectives and limitations

4.5 Practical applications

5. Conclusion

Abbreviations

Declarations

References

Supplementary Files

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2.3.8 V̇O₂-kinetics