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Prediction of Functional Threshold Power from Graded Exercise Test Data in Highly-Trained Individuals

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Abstract

International Journal of Exercise Science 15(4): 747-759, 2022. The purpose of the current investigation was to derive an equation that could predict Functional Threshold Power (FTP) from Graded Exercise Test (GxT) data. The FTP test has been demonstrated to represent the highest cycling power output that can be maintained in a quasi-steady state for 60-min. Previous investigations to determine a comparable marker derived from a Graded Exercise test have had limited success to date. Consequently, the current study aimed to predict FTP from GxT data to provide an additional index of cycling performance. FTP has been reported to provide an insight not provided by a GxT and, in addition, does not require a formal exercise testing facility. The study design facilitated a deliberate and transparent sequence of statistical decisions, resolved in part from the perspective of exercise physiology. Seventy triathletes (male n=50, female n=20) completed cycling GxT and FTP tests in sequential order. Collected data (power output, blood lactate indices, VO2peak, body mass) were analysed using stepwise regression to identify the key parameters for predicting FTP, and confirmed using a Leave One Out (LOO) cross-validation. As a consequence of wittingly including some likely transiently highly correlated parameters on the basis of a physiological argument, the model's function is limited to predicting FTP. This investigation concluded the model (FTP =-6.62 + 0.32 FBLC-4 + 0.42 BM + 0.46 Pmax) was the prediction model of choice.
Original Research
Prediction of Functional Threshold Power from Graded Exercise Test Data in
Highly-Trained Individuals
EANNA McGRATH†1, NICK MAHONY‡1, NEIL FLEMING‡1, ALESSIO BENAVOLI‡2, and
BERNARD DONNE‡1
1Human Performance Laboratory, Disciplines of Anatomy and Physiology, School of Medicine,
Trinity College Dublin, IRL; 2School of Computer Science and Statistics, Trinity College Dublin,
IRL
Denotes graduate student author, Denotes professional author
ABSTRACT
International Journal of Exercise Science 15(4): 747-759, 2022. The purpose of the current investigation was
to derive an equation that could predict Functional Threshold Power (FTP) from Graded Exercise Test (GxT) data.
The FTP test has been demonstrated to represent the highest cycling power output that can be maintained in a
quasi-steady state for 60-min. Previous investigations to determine a comparable marker derived from a Graded
Exercise test have had limited success to date. Consequently, the current study aimed to predict FTP from GxT
data to provide an additional index of cycling performance. FTP has been reported to provide an insight not
provided by a GxT and, in addition, does not require a formal exercise testing facility. The study design facilitated
a deliberate and transparent sequence of statistical decisions, resolved in part from the perspective of exercise
physiology. Seventy triathletes (male n=50, female n=20) completed cycling GxT and FTP tests in sequential order.
Collected data (power output, blood lactate indices, VO2peak, body mass) were analysed using stepwise regression
to identify the key parameters for predicting FTP, and confirmed using a Leave One Out (LOO) cross-validation.
As a consequence of wittingly including some likely transiently highly correlated parameters on the basis of a
physiological argument, the model’s function is limited to predicting FTP. This investigation concluded the model
(FTP = -6.62 + 0.32 FBLC-4 + 0.42 BM + 0.46 Pmax) was the prediction model of choice.
KEY WORDS: Triathlon, lactate profile, modelling, stepwise regression, cross-validation
INTRODUCTION
The Graded Exercise Test (GxT) has been used both to assess clinical issues relating to health,
and evaluate exercise performance (4). The measured responses to each step-increase in exercise
intensity typically include; heart rate, fuel utilization, oxygen cost, and during the final stage
measurement of peak oxygen consumption, and frequently in an exercise setting an athlete’s
blood lactate profile. A key characteristic of the GxT is that it appraises contributions from
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multiple individual physiological indices concurrently at each intensification. Moreover, as the
derived step-data is interpolated using all of the performance markers listed above, exact cycling
intensities can be identified between the predefined GxT step-increases. Commonly used
indices of physical conditioning derived from a GxT such as lactate threshold (TLac), load
associated with 2 mmol.L-1 blood lactate concentration (FBLC-2), load associated with 4 mmol.L-
1 blood lactate concentration (FBLC-4), workload preceding a fixed rise of 1 mmol.L-1 in blood
lactate concentration (FRBL) and the maximum distance from a curve representing ventilatory
and metabolic variables (Dmax), reflect specific “micro-occurrences”, which infer the capacity
of a subset of actual performance. Conversely, the FTP test is a 20-min maximum effort,
reflecting the sum total of whole-body energetics. The FTP test format can be viewed in Table
1. The computation of FTP is calculated by simply reducing the average power sustained over
a 20-min time-trial period by 5 %. Allen and Coggan (1) suggested that the minor reduction of
the 20-min power equated to an output that could be sustained for 60-min. This proposition has
been demonstrated both valid and reliable (21), without these measurement qualities, a
prediction equation would not be warranted. The basis of the small (5%) reduction in power
between the 20- and 60-min cycling intervals is conjectured to be a consequence of the respective
time periods being positioned close to the lowest point of the hyperbolic curve and therefore the
40-min differential (20-min test versus 60-min limits of tolerance) being associated with only a
minor (5%) reduction in load (22).
Table 1. Test protocol for assessing FTP (1).
Duration
Description
% FTP
Warm-up
20-min
Endurance pace
65
3 by 1-min
Fast pedalling
Not applicable
with 1-min recoveries
100 revˑmin-1
5-min
Easy riding
65
5-min
Time-trial
Maximum effort
10-min
Easy riding
65
FTP test
20-min
Time-trial
Maximum effort
Cooldown
10 to 15-min
Easy riding
65
(FTP) Functional Threshold Power, (min) minute, (revˑmin-1) revolutions per minute
The goal of the current investigation was to derive an empirical equation to predict FTP from
the gold standard GxT. In some respects, the strengths and weaknesses of the GxT and FTP tests
appear to compliment one-another. The FTP test requires a power meter but does not require
the more elaborate equipment commonly associated with a GxT; namely, a metabolic cart and
lactate analyzer. The FTP test does not provide any physiological data, rather power output
alone. The proponents of the FTP test highlight the advantage of using power output to pace
time-trial efforts as this constant analogue is unaffected by time (1). Conversely, the multiple
physiological variables derived from a GxT can be influenced by a multitude of variables, for
example if heart rate is used for pacing, the associated power is likely to reduce over time (9).
Given that the two tests (GxT and FTP) in their current guise provide mutually exclusive
information; there is a rationale for predicting FTP from GxT derived data. The purpose of the
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current study was to identify an effective prediction model for FTP from GxT data from a
combination of both robust statistical analyses and using established physiological principles.
Published articles demonstrate variations in the GxT increments and durations can affect the
gleaned data (4, 17). These differences may have benefited a particular circumstance but limit
inter-investigation comparisons (4). The derivation of a model from the current research would
be limited to the same test protocols, ancillary calculations and highly-trained populations. The
hypothesis of the current investigation was that a prediction model could be trained to predict
FTP for highly-trained athletes using GxT data.
METHODS
Participants
The current study obtained ethical approval from the Faculty of Health Sciences Research Ethics
Committee in Trinity College Dublin and was performed in accordance with the ethics
standards of the International Journal of Exercise Science (24). An a priori linear multiple
regression power test was conducted with a Type 1 error probability of 0.05, a power of 0.85 and
a projected effect size 0.1. This analysis indicated that n = 74 would provide a statistical power
of 85% for 2, 3 and 4 parameter models (G*Power v3.0.10 free software; Institute of Experimental
Psychology, Heinrich Heine University, Dusseldorf, Germany). Inclusion criteria were that
participants were; aged 18-35 years; healthy and injury free as assessed by medical questionnaire
and medical assessment; competing in triathlon or cycling for a minimum of 2-years. Exclusion
criteria included the following: outside the age range of 18-35 years old; high blood pressure or
found to have high blood pressure during pre-screening assessment; a bleeding or clotting
disorder; any previous history of cardiopulmonary disease; respiratory difficulties (based on
spirometry data) or symptoms of colds/influenza on the day of testing; acute or chronic
musculoskeletal injury limiting exercise capacity; disease that would prevent participation in an
maximal exercise test; deemed unfit to participate on completion of a medical questionnaire and
medical examination due to an on-going illness, or having any of the following; diabetes,
hypertension, heart defects, metabolic disorders or other contraindications to maximal exercise
testing.
Protocol
Participants VO2peak, mass, height, BMI and age can be viewed in Table 2. Participants completed
an informed consent form prior to beginning any trials. All enlisted participants attended the
laboratory on two occasions, in a rested, carbohydrate loaded state to control for dietary induced
elevations or reductions in BLa data (19) and consequently maintain the power versus BLa
relationship (19). Athletes were requested to arrive hydrated, having abstained from alcohol
and caffeine in the 24-h prior to testing. Hydration status was assessed as urine specific gravity
(USG) using a mid-stream urine sample and an optical refractometry (Eclipse Professional,
Bellingham & Stanley, Kent, UK). A 24-h food diary completed prior to the first trial identified
that enlisted participants were consuming a training load adjusted isocaloric diet (macronutrient
breakdown; ≥ 60% carbohydrate, ≤ 20% fat and ≤ 20% protein). Each participant was requested
to replicate their food intake prior to both tests, or if different, to consume comparable
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carbohydrate quantities. When necessary, participants were assisted in planning their pre-test
meals. The two trials were performed within a two-week period, at least 7-days apart. Training
loads were agreed with both athletes and coaches prior to commencing the current study, with
weekly training load remaining as constant as possible preceding both tests. Exercise was
limited to aerobic work for 48-h prior to each test.
Table 2. Mean (± SD) VO2peak, mass, height, BMI and age data for participants.
Mass
Height
BMI
Age
(kg)
(m)
(kgˑm-2)
(yr)
Female (n = 20)
57.8 ± 7.6
1.69 ± 0.07
20.1 ± 1.9
29.1 ± 5.0
Male (n = 50)
77.0 ± 10.0
1.79 ± 0.06
23.8 ± 2.5
27.4 ± 5.7
(SD) standard deviation, (BMI) Body mass index, (VO2peak) Peak maximum oxygen uptake, (mLˑkg-1ˑmin-1) - millilitres of
Oxygen consumed per kilogram body mass per minute, (kg) kilogram, (kgˑm-2) kilogram divided by metre squared, (yr)
year.
The FTP test was performed on the athlete’s own bicycle using Garmin pedals (Garmin, KA,
USA) to measure cycling power output, with the bicycle mounted on an indoor trainer (LeMond
Revolution, WA, USA). The Lode Excalibur Sport ergometer facilitates self-paced time-trial
efforts in “Linear Mode”. However, this requires the practitioner to predetermine a specific
power and associated cadence prior to testing. We considered the risk of bias to supersede the
benefits of performing both the GxT and FTP on one ergometer, particularly given that the
Garmin power pedals could be used on both ergometers and cross-referenced. Garmin pedals
were calibrated prior to each trial as per the manufacturer’s instructions to zero offset. Having
completed the FTP test, the Garmin pedals were subsequently placed on the Lode cycle
ergometer and calibrated at their ascertained FTP to mitigate against any differences in the
respective devices (22). The corrected FTP (namely, that corrected to the Lode ergometer) was
subsequently used for all proceeding analyses throughout the current investigation.
All participants had completed an FTP test prior to enlistment into the current study. The 20-
min FTP test protocol can be viewed in Table 1. The order of the two cycle tests was not
randomized as the GxT data were used to identify the appropriate warm-up intensity for the
FTP test. The warm- up intensity was set at 65% of the alternate threshold index “Dmax”
(derived from the GxT data) in keeping with previous research (21) and utilising the recent
fitness test (< 2-weeks between tests). The line of best fit for the Dmax computation was
determined using a third order curvilinear regression using VO2 and BLa data at each workload
during the GxT test. Thereafter, the maximum perpendicular distance to the straight line
between the lowest and highest exercise BLa data identified load at Dmax (8). The instruction
given to participants for the 20-min FTP time-trial was “a strong, steady effort for the entire 20
min. Do not start out too hard! Get up to speed (power) and then try to hold that speed (power).
Your goal is to produce the highest average wattage over the entire period” (1). Subsequently,
FTP was determined by reducing the mean power output across the 20-min time-trial by 5% (1).
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Statistical Analysis
A list of potential FTP prediction variables from GxT data was compiled. The workloads (Watt)
at the following indices were included; load at TLac, Dmax, FBLC-2, FBLC-4 and Pmax.
Additionally, body mass (BM in kg) and absolute VO2peak (mL.min.-1) were included in the
initial data gathering phase, as these data were deemed relevant to both the GxT and cycling
performance. The relationship between each of these potential independent variables (IV)
versus FTP was first checked using scatter plots to visualize each relationship. Correlation
coefficients (r) and the corresponding coefficients of determination (r2) were calculated using
Prism 9 (Graph Pad, CA, USA). Two iterations of all of these initial plots and calculations were
prepared. The first used absolute data and the second used data scaled to body mass.
Computed correlation coefficients of 0.84, and accompanying coefficients of determination
0.70 were determined as a minimum inclusion requirement (6). The interpretation of r2 was also
considered from the context of the specific field of application (14). In elite sport, meaningful
improvements are relatively small (18), and, therefore any prospective model would need to be
sensitive to small biological changes.
Each of the independent variable (IV) were then correlated with one another, the rationale here
was to avoid any potential distortion of the line of best fit that could not be explained because
two or more parameters were measuring the same quantity within one equation. The
researchers were alert specifically to the risk of collinearity between; TLac, Dmax, FBLC-2, FBLC-
4 and FRBL versus Pmax or VO2peak. For physiological reasons explained in the discussion
below, the combinations of either TLac, Dmax, FBLC-2, FBLC-4 versus Pmax or VO2peak was
permitted. This caveat was not afforded to statistical evidence of collinearity between TLac,
Dmax, FBLC-2 and FBLC-4. In respect to collinearity, the following responses were considered
indicators; high variation inflation factor (VIF), a sizeable drop-off between r2 and r2 adjusted
(r2adj) to the number of parameters included, and an increase in the p-value to > 0.05.
A stepwise regression, using an entry and exit of p < 0.05 and 0.1, respectively, was applied to
all of the non-redundant IV correlates versus FTP using JMP 16 (SAS Institute, NC, USA). Every
permutation of the non-redundant IV correlates that passed this initial cull was further assessed
as a potential parameter of a single or multi-parameter predictive equation. The following
indicators were used to evaluate each equation; namely, relationship of the -coefficient to FTP;
VIF; r2; r2adj; the root mean square of the error with the number of parameters inserted into the
equation (sy.x); Akaike Information Criterion (AIC); and an estimation of the prediction error
using a Leave One Out (LOO) cross-validation technique. The iterative process of stepwise
regression facilitated the combined interpretation of statistical results with physiological tenets.
The objective of this phase of the analysis was solely to identify the apparently most suitable
parameters for estimating FTP. LOO cross-validation was included in the model selection
criteria to validate the ability of the model to predict to unseen data (athlete). The mean-squared-
error (MSE) was used as the evaluation criterion. In LOO cross-validation, for each observation
(athlete) in the dataset, say the ith observation, the same model is fitted keeping aside the ith
observation and using the remaining observations (athletes) to train the model. The MSE is then
calculated from the model prediction for the ith observation. Finally the average of the individual
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MSE is calculated, which corresponds to the LOO cross-validation metric. For linear regression,
we do not need to refit the model N-times, where N is the number of observations (16). The
predictive capacity of gender on the predictive model for FTP was assessed using comparisons
of the AIC and LOO cross-validation technique.
RESULTS
As only 70 participants met the strict inclusion criteria a subsequent post-hoc power analysis
indicated that the current study achieved an overall statistical power of 83.5%. The calculated
mean and standard deviation of power output data at TLac, Dmax, FBLC-2, FBLC-4, FRBL and
Pmax can be viewed in Table 3. The scatter plots representing FTP versus each IV are presented
in Figure 1. The correlation matrix of all IV that were used to give insight as to potential
collinearity is documented in Table 4. The results of the initial regression analyses of FTP versus
each IV are documented in Table 5, the four strongest correlates of FTP with the smallest sy.x
and most favourable 95%CI were; Dmax, Pmax, FRBL and FBLC-4. These indices remained
topmost when rescaled to body mass: Dmax (sy.x = 0.28 W.kg-1, r = 0.87, 95%CI of 0.78 to 0.93);
Pmax (sy.x = 0.26 W.kg-1, r = 0.89, 95%CI of 0.81 to 0.94); FRBL (sy.x = 0.32 W.kg-1, r = 0.74, 95%CI
of 0.76 to 1.03) and FBLC-4 (sy.x = 0.33 W.kg-1, r = 0.88, 95%CI of 0.9 to 1.2) albeit slightly inferior
to their un-scaled equivalents. The results for the same analyses versus FTP for TLac, FBLC-2,
VO2peak and BM are also presented in Table 5. Four prospective model parameter options were
extricated using stepwise regression. The formulae and associated sy.x, r2, r2adj, VIF and AIC are
presented in Table 6. The reported VIF and AIC for Model 4, see Table 6, without and with
gender as a parameter were AIC 399 versus 596 and VIF 288 versus 296, respectively.
Table 3. Mean power (in W and Wˑkg-1) associated with load at FTP, TLac, Dmax, FBLC-2, FBLC-4, FRBL and Pmax.
FTP
TLac
Dmax
FBLC-2
FBLC-4
FRBL
Pmax
Male
Mean power (W)
298 ± 34
297 ± 41
277 ± 32
265 ± 39
314 ± 35
274 ± 32
371 ± 40
Female
Mean power (W)
215 ± 22
222 ± 34
207 ± 27
200 ± 33
232 ± 29
205 ± 29
267 ± 30
Male
Mean power (Wˑkg-1)
4.0 ± 0.6
4.0 ± 0.8
3.7 ± 0.7
3.5 ± 0.7
4.2 ± 0.7
3.6 ± 0.6
4.9 ± 0.8
Female
Mean power (Wˑkg-1)
3.8 ± 0.4
3.9 ± 0.6
3.7 ± 0.5
3.6 ± 0.7
4.1 ± 0.7
3.6 ± 0.7
4.7 ± 0.7
(W) - Watt, (Wˑkg-1) Watt per kilogram of body mass, (FTP) Functional Threshold Power, (TLac)- Lactate
threshold, (Dmax) Load at maximum displacement, (FBLC-2) - load associated with 2 mmol.L-1 blood lactate
concentration, (FBLC-4) - load associated with 4 mmol.L-1 blood lactate concentration, (FRBL) - workload preceding
a fixed rise of 1 mmol.L-1 in blood lactate concentration, (Pmax) - maximum workload completed on the final stage
of the GxT, (GxT) graded incremental test.
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Table 4. Correlation matrix of IV.
TLac
(W)
Dmax
(W)
FBLC-2
(W)
FBLC-4
(W)
FRBL
(W)
VO2peak
(mL.min.-1)
Pmax
(W)
BM
(kg)
TLac (W)
-
0.97
0.78
0.84
0.85
0.67
0.90
0.50
Dmax (W)
-
0.81
0.89
0.90
0.74
0.94
0.56
FBLC-2 (W)
-
0.94
0.94
0.64
0.79
0.40
FBLC-4 (W)
-
0.97
0.75
0.90
0.55
FRBL (W)
-
0.71
0.89
0.54
VO2peak (mL.min.-1)
-
0.76
0.75
Pmax (W)
-
0.60
BM (kg)
-
Figure 1: Scatter plots of FTP versus each individual IV.
Table 5: Regression analyses of FTP versus each individual IV.
R
r2
sy.x (W)
95%CI of r
p
FTP vs. TLac (W)
0.87
0.76
25
0.78 to 0.92
<0.0001
FTP vs. Dmax (W)
0.91
0.83
18
0.85 to 0.95
<0.0001
FTP vs.FBLC-2 (W)
0.83
0.68
26
0.71 to 0.90
<0.0001
FTP vs. FBLC-4 (W)
0.93
0.86
19
0.83 to 0.94
<0.0001
FTP vs. FRBL (W)
0.90
0.81
19
0.83 to 0.94
<0.0001
FTP vs. Pmax (W)
0.92
0.85
22
0.87 to 0.96
<0.0001
FTP vs. VO2peak (mL.min.-1)
0.78
0.61
30
0.64 to 0.87
<0.0001
FTP vs. BM (kg)
0.63
0.40
37
0.43 to 0.77
<0.0001
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Table 6: Prospective parameters derived from a stepwise multiple regression analyses of non-redundant IV
FTP prediction equation
sy.x
(W)
r2
r2adj
VIF
AIC
LOO
p
Model-1
13.4 + 0.64 Pmax + 0.16 Dmax
18
0.87
0.87
8.6
8.6
410
345
0.0004
0.0300
Model-2
16.7 + 0.75 Pmax
18
0.86
0.86
-
409
501
0.0001
Model-3
21.6 + 0.98 Dmax
22
0.80
0.79
-
438
334
0.0001
Model-4
-6.6 + 0.32 FBLC-4 + 0.42 BM + 0.46
Pmax
15
0.89
0.89
-
399
288
0.0001
DISCUSSION
This investigation concluded that Model-4 (-6.6 + 0.32 FBLC-4 + 0.42 BM + 0.46 Pmax) was the
prediction model of choice. This assertion was borne from multiple statistical decisions coupled
with actualities of exercise physiology. As might be expected, the study design commenced by
identifying potential correlates to be used to predict FTP, whilst remaining alert to the potential
of collinearity in the instance that more than one prediction variable could be included in a final
equation. As mentioned in the methods section, scope for potential collinearity was afforded to
the combinations of TLac, Dmax, FBLC-2 or FBLC-4 versus Pmax or VO2peak. This exemption
was on the basis that the power output associated with these four indices changes with aerobic
fitness without an obligatory concomitant change in Pmax or VO2peak (26). Figure 2 illustrates
this scenario whereby a lower power output at FBLC-4 may be observed when an athlete is in a
deconditioned versus well-conditioned state, pivotally all the while Pmax conceivably
remaining constant (26). In this scenario, if for example Pmax alone were used to prescribe
training, the athlete would be required to train at the same intensity whether they were well-
conditioned or deconditioned. Alternatively, if FBLC-4 (or TLac, Dmax, FBLC-2) were used in
conjunction with Pmax (or VO2peak), the training load would be proportionately lower for the
deconditioned athlete. As the study population were highly-trained and all in competition-
phase at the time of testing; TLac, Dmax, FBLC-2 and FBLC-4 were likely to equate to a similarly
high fraction of Pmax or VO2peak (21). Without variation in this fraction, these four prospective
IV will exhibit a statistically linear relationship with Pmax. Importantly however, these indices
still provide unique insight not afforded by Pmax alone. Similarly, it was anticipated that gender
would likely enhance the predictive model given findings in the literature that female athletes
have lower relative VO2max data but higher thresholds relative to their VO2max (27). However,
the addition of gender did not significantly improve the error associated with future predictions.
Notably, the number of females was limited as compared to the male group (n=20 versus 50,
respectively), this may have had an impact on our results.
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100 200 300 400 500
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Conditioned
Deconditioned
FBLC-4 = 357 W
FBLC-4 = 318 W
BLa = 4.0 mmol.L-1
Load (W)
BLa (mmol.L-1)
Figure 2. Illustrative data recorded in our laboratory depicting a change in power output at FBLC-4 whilst
maintaining the same absolute Pmax load.
The study design used stepwise regression to identify the best predictor variables for FTP. The
findings derived from each regression analysis were considered from the purview of physiology
prior to being accepted or rejected as being the best prediction equation. A purely statistical
comparison of Model-1 versus Model-2, would likely favor the latter equation as a consequence
of the apparently similar predicative capacity and parsimony, see Table 6. However, the two
parameters of Model-1 engaged two principle demarcations of physical conditioning; namely,
aerobic fitness by using load at Dmax (8) and aerobic capacity vis-à-vis Pmax (5). Conversely,
the single parameter Model-2 is limited to peak power, not necessarily an indicator of training
status and not convergent with the quintessence of a GxT.
The single-parameter Model-3 was expected to reflect trained state in the guise of Dmax, a kernel
marker for current training status associated with a GxT (8). However, the statistical findings
herein are less favourable as the sy.x and AIC are higher than the other prospective models, see
Table 5. Although the bivariate Model-1 contains succinct measures of training status, the
results of the stepwise regression (Table 5) favor the alternative Model-4 parameters; FBLC-4,
BM and Pmax. This Model-4 yielded the lowest sy.x and AIC (Table 5). Model-4 demonstrated
the lowest LOO, indicating the best equation for predicting the performance of an athlete not
included within a data set.
From a statistical perspective, caution should be taken when analysing these findings. Firstly,
the -coefficients cannot be used for explanatory purposes, as a consequence of some
collinearity, although not enough to diminish the principles of the regression equation. Notably,
the three explanatory parameters in Model-4 were still found to be significant, see Table 5,
irrespective of the likely inflated p-value associated with co-variance. The IV of Model-4 can be
partitioned to illustrate the redundant explanatory function of Model-4. If FBLC-4 and the Y-
intercept are held constant, FTP will only increase by 0.46 W (the slope coefficient for Pmax) for
every 1 W increase in Pmax. This is proportionately at odds with the relative intensity of power
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output at FTP versus Pmax. This can be seen in Model-2 where FTP equates to more than 75%
of Pmax (the sample slope coefficient of 0.75 plus the constant of 17 W) and has been
demonstrated elsewhere to occur at approximately 80% of the peak power reached during the
same GxT protocol in a similarly trained athletic cohort (21). That stated, the main purpose of
this regression model was to predict FTP rather than to explain the relationships of the already
well-established and reliable equation parameters.
There were some decisions that were taken from the perspective of exercise science that are
worth highlighting. Firstly, the GxT derived measurements of TLac, Dmax, FRBL-2 and FRBL-4
each serve similar functions physiologically; namely, to track lactate kinetics. Without any
unique predictive capacity, only one of these measures was anticipated to be included in any
single equation. This point did not preclude the inclusion of all four indices prior to data
reduction as the purpose was to commence the regression analyses with the strongest predictors
of FTP, rather than cherry-picking any particular marker. The merits of each of these four
measurements (TLac, Dmax, FRPB-2 and FRBL-4) has polarised opinions (8, 15), and we
acknowledged that some researchers may have a preference for one particular BLa calculation,
hence the initial inclusion of each of them. Secondly, cycling data is frequently normalized to
body mass as a way of making intra- and inter-individual comparisons. FTP is reported by its
originators in W.kg-1 facilitating the tabulation of categorizations of cyclist’s performance
capacity (1). Herein, normalized data were also assessed with the view that a relationship
between variables may have existed that may not have been evident when expressed in absolute
terms. However, this conjecture was not reflected in our current findings. Scaling data to body
mass did not appear to have any additional predictive capacity for FTP in this cohort of well-
trained triathletes. This may have been impacted by the participants having similarly low BMI
data and might differ if cyclists / triathletes with a wider range of BMI data were evaluated.
Previous investigations have sought to associate GxT derived indices with FTP, apparently
unsuccessfully (20), and, therefore, supporting the notion that a prediction equation is necessary.
One previous investigation, by Denham et al. (10), generated two relevant prediction equations,
one to predict FTP from GxT data and the second to predict VO2max from FTP (scaled to BM)
and age data. The models were trained using twenty-one inactive non-cyclists and nineteen self-
reported recreational cyclists collectively. The age profile ranged from 19 to 55 years and
included just three female participants. The model to predict FTP from GxT data was (FTP = -
56.5 + 0.86 Pmax). Their computed Y-intercept will likely have a sizeable proportional effect on
the data given that the reported mean FTP in their investigation was 200 ± 58.2 W (2.62 ± 0.75
W.kg-1). This relationship might be explained in some way by the untrained group having their
FTP occurring at a very low percentage of their Pmax, however, this is difficult to generalize to
trained athletes. The equation stipulates that FTP has a set position in excess of 57 W lower than
Pmax (the constant 56.5 W plus the 0.86 W coefficient of Pmax using the lowest possible Pmax
value of 1 W).
In respect to predicting VO2max from FTP, Denham et al. (10) suggested that, although the
bivariate model (using FTP and age) to predict VO2max was trained on a combination of
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recreational cyclists and sedentary individuals, the model appeared to “provide robust
estimates of VO2max even for those at the upper end of the fitness spectrum”. This claim was
based on Denham et al. (10) applying their predicative equation to a single elite athlete from
another researchers findings (3). Therein, Denham et al. (10) used the reported power at FBLC-
4 as a proxy for the individual athlete’s FTP (as FTP was not actually reported). The premise of
this proxy calculation was that an alternate investigation by Gavin et al. (13) had reported that
FTP and FBLC-4 were interchangeable. Again, confoundingly, the FTP reported in the Gavin et
al. (13) study was computed using an uncontrolled 8-min field test for FTP and the FBLC-4 data
were derived from altogether different GxT protocols. Specifically, Gavin et al. (13) commenced
their test at 150 W and increased power output at a rate of 25 W every 3-min, whereas Denham
et al. (10) commenced at 100-W and increased power output at a rate of 20 W every minute.
Given that modelling already has inherent error, consistent discrepancies can only compound
model inadequacies. In our investigation one particular female triathlete (swimming, cycling
running) competed in the recent Olympics in Tokyo and this investigation in the same year.
This provides a useful comparison with Denham et al. (10) proposition of using a single elite-
athlete case study to test an algorithm. This female triathlete had a body mass of 45.4 kg, a
measured Pmax of 270 W (5.9 W.kg-1) and a FTP of 229 W (5 W.kg-1), Model 4 predicted FTP.
This paradigm cannot be accommodated in the proposed Denham et al. (10) model for FTP as
the difference between Pmax and FTP is less than 56.5 W and of course the magnitude of the
delta value will only increase as the coefficient of Pmax in their predictive model is 0.865. This
scenario is usual where highly-trained endurance athletes have FTP data that occur at high FTP
fractions of VO2peak (21).
The approach taken herein is unusual insofar as each statistical and physiological step is
described and each decision explained. A wide variety of GxT indices were included so as to
create a model that was not biased to any particular GxT metric, a contentious topic ever-present
in exercise science literature (8, 15). Stepwise regression afforded the combination of science
and statistics. The heuristic LOO cross-validation approach permitted better usage of the
limited number of high-performance athletes available, a population sample that can be more
difficult to recruit for scientific research studies.
There is nothing startling in the statement that models are imperfect (14, 23) and that
physiological tests of physical fitness have limitations (8). The approach of the current
investigation was in the words of Anscombe (2) “weighing of evidence in the light of
circumstances, available knowledge and theory”. To quote Anscombe (2) a second time, “The
word 'valid' should be better dropped from the statistical vocabulary. The only real validation
of a statistical analysis, or of any scientific enquiry, is confirmation by independent
observations." The development of this model would likely benefit from an increased number
of female athletes to ensure the current analysis is accurate and gender does not enhance a
model’s predictive capacity. The application of the predictive model to an alternate sport such
as rowing, which uses power as an analogue and does not require the athlete to carry their entire
weight (25) may prove beneficial to rowers and would provide a measure of external validity of
the FTP model.
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758
ACKNOWLEDGMENTS
The authors disclose no conflicts of interest or financial arrangements related to the current
research. We would like to thank all enlisted triathletes for their gracious participation in the
current research.
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... Recently, an equation to predict FTP (m-FTP) from GxT data was constructed and reported consequently (15), furnishing another GxT-derived metric. The m-FTP equation was trained and tested on highly-trained cyclists, and reported: favorable root mean square of the error (sy.x) of 15 W, a strong r 2 (0.89), and r 2 adj remaining unchanged to two decimal places. ...
... The MSE is then calculated from the model prediction for the ith observation. Finally the average of the individual MSE is calculated, which corresponds to the LOO cross-validation metric (15). The m-FTP variables were: power output (W) at an affixed blood lactate concentration of 4 mmol.L -1 BLa (FBLC-4), maximum power output (W) achieved during the GxT (Pmax), and body mass (BM in kg), as seen Equation 1 below (15). ...
... Finally the average of the individual MSE is calculated, which corresponds to the LOO cross-validation metric (15). The m-FTP variables were: power output (W) at an affixed blood lactate concentration of 4 mmol.L -1 BLa (FBLC-4), maximum power output (W) achieved during the GxT (Pmax), and body mass (BM in kg), as seen Equation 1 below (15). The m-FTP equation was derived from cycling data in highly-trained cohort of cyclists and triathletes. ...
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