Compares two tests of the same athlete (e.g. before and after a training block): the change of each threshold, whether it is larger than the noise of the method, the heart rate at each threshold, and notes on what could make the comparison unfair.
Usage
compare_tests(before, after, cv = NULL, swc = 0, level = 0.9)
# S3 method for class 'lactate_comparison'
autoplot(object, ...)Arguments
- before, after
The results of
lactate_threshold()for the two tests, with the same sport.- cv
The test-retest coefficient of variation (%) of each method: one number for all methods, or a named vector (e.g.
c("LTP2" = 3)) that adds to or replaces the defaults, or the result oflactate_reliability()for your own tests.- swc
The smallest worthwhile change, in % of the intensity before. Defaults to
0.- level
The confidence level of the interval. Defaults to
0.9.- object
The result of
compare_tests().- ...
Not used.
Value
a lactate_comparison tibble with one row per method found in both tests: method, before,
after, change, change_percent, the interval of the change (change_low, change_high), the cv (%) it
was computed with, the noise, the ratio of the change to it, the verdict,
and the heart rate at each threshold in both tests (when recorded). The notes attribute lists what differs
between the two tests (stages, step, resting sample, sample type) and a fall in peak lactate. Plot both
curves with autoplot().
Details
A threshold moves between two tests even without any change in fitness, by the day-to-day variation of
the athlete and the error of the analyzer and the method. Each change is therefore given with an
interval, change +/- z * sqrt(2) * typical error, where the typical error is the coefficient of
variation (cv) times the intensity before (Hopkins, 2000; Swinton et al., 2018). This is the model behind the
repeatability of Bland & Altman (1996), for whom two measurements of the same person differ by less than
1.96 * sqrt(2) within-subject standard deviations in 95% of pairs, a size also known as the minimal detectable
change (Sainani, 2017). With a cv from lactate_reliability(), z is the t quantile for its degrees of freedom,
because a typical error from few athletes is itself uncertain (Swinton et al., 2018): with 10 athletes tested
twice, the normal quantile would call 13% of unchanged pairs "beyond the noise" at the 90% level instead of 10%.
Three columns say how the change stands against that noise, without a probability attached to them:
noise:sqrt(2)x the typical error, the typical difference between two tests when nothing changed, in the unit of the intensity.ratio: the change divided by the noise. At 1, the change is as large as two tests usually differ by anyway.verdict:"beyond the noise"when the whole interval lies beyond the smallest worthwhile change (swc; beyond zero by default), which at the default 90% is a ratio above 1.64, and"within the noise"otherwise. A change within the noise is not a sign that nothing changed: one pair of tests cannot tell. The words describe this one comparison against thecvin the table; graded terms such as "likely" are not used, because they read a frequentist interval as a probability of the true change (Lohse et al., 2020).
Three things decide how often a verdict is wrong, so settle them before looking at the result:
The level. At the default 90%, an unchanged threshold is called "beyond the noise" in 10% of comparisons: 5% as a gain and 5% as a loss, which is a one-sided test for a gain at 5%, the test Sainani (2018) recommends in place of graded terms. No level is agreed on: 95% is the classic choice, and narrower intervals are defended for decisions in practice (Swinton et al., 2018).
The smallest worthwhile change. With
swcabove zero, the verdict asks for a change that is certainly larger thanswc, not merely larger than zero. No value is agreed on for lactate thresholds; one convention is 0.2 times the standard deviation between athletes (Swinton et al., 2018). Choosingswcorlevelafter seeing the verdict lets one pick the verdict one likes (Sainani, 2018).The threshold. Each method gets its own verdict, and with every method in the table some of them will lie beyond the noise by chance. In 157 pairs of consecutive tests of the cyclists of Heuberger et al. (2018), each method was beyond the noise in 6% to 15% of pairs, but at least one of the 18 was in 50%, and the default LT1 or LT2 in 19%. The LT1 and LT2 chosen in
lactate_threshold()are the ones to read, as the header does; a method picked because its verdict stands out proves nothing.
The default cv of each method is lactater's own calculation: lactate_reliability() on the five step tests of
each of 47 well-trained male cyclists in the open data of Heuberger et al. (2018; 204 tests, 5-min stages, venous
blood, about two weeks apart), so that it is the noise of each method as lactater computes it, on a step test. The
output gives it in the cv column.
| Method | Default cv (%) | Published (%) |
| OBLA 2.0, 2.5, 3.0, 3.5 | 7.7, 5.2, 4.6, 4.8 | |
| OBLA 4.0 | 4.4 | 3.8 (Heuberger et al., 2018) |
| Bsln + 0.5, 1.0, 1.5 | 8.2, 5.0, 4.5 | 3.7, 3.4, 3.4 (Pallares et al., 2016; ramp test) |
| Dmax | 5.9 | 3.4 (Heuberger et al., 2018) |
| ModDmax | 5.1 | 4.3 (Heuberger et al., 2018) |
| Exp-Dmax, Log-Poly-ModDmax, Log-Exp-ModDmax | 4.3, 5.5, 4.9 | |
| IAT | 4.4 | 3.6 (Heuberger et al., 2018) |
| LTP1, LTP2 | 10.6, 6.0 | |
| Log-log, LTratio | 7.8, 9.4 |
The defaults are on the careful side. Heuberger et al. computed their values on the riders who received placebo,
with their own implementation of each method; the open data do not say which riders received erythropoietin, so the
defaults use every rider and are, if anything, too high (pairs of consecutive tests gave values of the same size,
so a drift between the two groups does not explain them). Those tests have no resting sample, so Bsln+ rose from
the first stage. To use the published values instead, give them: cv = c("IAT" = 3.6, "Dmax" = 3.4).
Stegmann, Keul, Simon and your own fixed or baseline_plus values have no default: their verdict is NA
unless you give one.
The defaults come from cycling and are used for every sport, as a percentage of the intensity; the notes say so
for other sports. No open test-retest data of running step tests were found to compute running values the same way.
Published running values are of a similar size in trained runners: typical errors of about 0.3 to 0.8 km/h (2% to
6%) for 22 trained men on a treadmill with 1-min stages, from the SDs of their test-retest differences (the CVs
they report, 1.2% to 3.5%, are smaller; Cerezuela-Espejo et al., 2018), and 0.4 to 1.4 km/h for 19 healthy,
untrained people with 4-min and 8-min stages (Gavin et al., 2014).
The best cv is the one of your own athletes, measured with your protocol and analyzer. A cv assumes that the
noise grows with the intensity, which is common for such measures but should be checked where the data allow
(Atkinson & Nevill, 1998).
References
Atkinson G, Nevill AM. Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine. Sports Medicine. 1998;26(4):217-238.
Bland JM, Altman DG. Measurement error. BMJ. 1996;312(7047):1654. doi:10.1136/bmj.312.7047.1654
Cerezuela-Espejo V, Courel-Ibáñez J, Morán-Navarro R, Martínez-Cava A, Pallarés JG. The relationship between lactate and ventilatory thresholds in runners: validity and reliability of exercise test performance parameters. Frontiers in Physiology. 2018;9:1320. doi:10.3389/fphys.2018.01320
Gavin JP, Willems MET, Myers SD. Reproducibility of lactate markers during 4 and 8 min stage incremental running: a pilot study. Journal of Science and Medicine in Sport. 2014;17(6):635-639. doi:10.1016/j.jsams.2013.08.006
Heuberger JAAC, Gal P, Stuurman FE, de Muinck Keizer WAS, Mejia Miranda Y, Cohen AF. Repeatability and predictive value of lactate threshold concepts in endurance sports. PLOS ONE. 2018;13(11):e0206846.
Hopkins WG. Measures of reliability in sports medicine and science. Sports Medicine. 2000;30(1):1-15.
Lohse KR, Sainani KL, Taylor JA, Butson ML, Knight EJ, Vickers AJ. Systematic review of the use of "magnitude-based inference" in sports science and medicine. PLOS ONE. 2020;15(6):e0235318.
Pallares JG, Moran-Navarro R, Ortega JF, Fernandez-Elias VE, Mora-Rodriguez R. Validity and reliability of ventilatory and blood lactate thresholds in well-trained cyclists. PLOS ONE. 2016;11(9):e0163389.
Sainani KL. Reliability statistics. PM&R. 2017;9(6):622-628. doi:10.1016/j.pmrj.2017.05.001
Sainani KL. The problem with "magnitude-based inference". Medicine & Science in Sports & Exercise. 2018;50(10):2166-2176. doi:10.1249/MSS.0000000000001645
Swinton PA, Hemingway BS, Saunders B, Gualano B, Dolan E. A statistical framework to interpret individual response to intervention: paving the way for personalized nutrition and exercise prescription. Frontiers in Nutrition. 2018;5:41.
Examples
series <- subset(lactate_tests, athlete == "cyclist_series")
before <- lactate_threshold(subset(series, day == 0), intensity, lactate, heart_rate, plot = FALSE)
after <- lactate_threshold(subset(series, day == 58), intensity, lactate, heart_rate, plot = FALSE)
compare_tests(before, after)
#> # Tests compared: cycling, 18 methods; noise: what two tests differ by when
#> # nothing changed; verdict at 90%
#> # LT1: 257 to 268 W (+10, 0.3 x the noise of 30 W: within the
#> # noise), by Bsln + 0.5
#> # LT2: 304 to 326 W (+22, 0.9 x the noise of 24 W: within the
#> # noise), by Log-Poly-ModDmax
#> method before after change change_percent change_low change_high cv noise
#> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Log-log 239 236 -3 -1.1 -46 41 7.8 26
#> 2 OBLA 2… 282 301 19 6.8 -31 70 7.7 31
#> 3 OBLA 2… 296 316 19 6.5 -17 55 5.2 22
#> 4 OBLA 3… 308 328 20 6.4 -13 53 4.6 20
#> 5 OBLA 3… 318 338 20 6.3 -15 56 4.8 22
#> 6 OBLA 4… 327 348 21 6.3 -13 54 4.4 20
#> 7 Bsln +… 257 268 10 4 -39 59 8.2 30
#> 8 Bsln +… 279 291 12 4.4 -20 45 5 20
#> 9 Bsln +… 294 307 14 4.6 -17 44 4.5 19
#> 10 Dmax 270 291 22 8.1 -15 59 5.9 22
#> 11 ModDmax 290 327 36 12.6 2 71 5.1 21
#> 12 Exp-Dm… 277 303 26 9.3 -2 53 4.3 17
#> 13 Log-Po… 304 326 22 7.1 -17 61 5.5 24
#> 14 Log-Ex… 309 333 24 7.8 -11 59 4.9 21
#> 15 LTP1 222 257 35 15.8 -20 90 10.6 33
#> 16 LTP2 301 341 40 13.3 -2 82 6 26
#> 17 LTratio 192 180 -12 -6.1 -54 30 9.4 25
#> 18 IAT 294 304 10 3.4 -20 40 4.4 18
#> # ℹ 4 more variables: ratio <dbl>, verdict <chr>, heart_rate_before <dbl>,
#> # heart_rate_after <dbl>