The application of repeated testing and monoexponential regressions to classify individual cardiorespiratory fitness responses to exercise training

  • Jacob T. Bonafiglia
  • Robert Ross
  • Brendon J. GurdEmail author
Original Article



We tested the hypothesis that monoexponential regressions will increase the certainty in response estimates and confidence in classification of cardiorespiratory fitness (CRF) responses compared to a recently proposed linear regression approach.


We used data from a previously published RCT that involved 24 weeks of training at high amount–high intensity (HAHI; N = 28), high amount–low intensity (HALI; N = 48), or low amount–low intensity (LALI; N = 33). CRF was measured at 0, 4, 8, 16, and 24 weeks. We fit the repeated CRF measures with monoexponential and linear regressions, and calculated individual response estimates, the error in these estimates (TEMONOEXP and TESLOPE, respectively), and 95% confidence intervals (CIs). Individuals were classified as responders, uncertain, or non-responders based on where their CI lay relative to a minimum clinically important difference. Additionally, responses were classified using observed pre–post-changes and the typical error of measurement.


Comparing the error in response estimates revealed that monoexponential regressions were a better fit than linear regressions for the majority of individual responses (N = 81/109) and mean CRF data (mean TEMONOEXP:TESLOPE; HAHI = 2.00:2.58, HALI = 1.91:2.46, LALI = 1.63:2.18; all p < 0.01). Fewer individuals were confidently classified as responders with linear regressions (N = 29/109) compared to monoexponential (N = 55/109). Additionally, response estimates were highly correlated across all three approaches (all r > 0.92).


Future studies should determine the type of regression that best fits their data prior to classifying responses. The similarity in response estimates and classification from regressions and observed pre–post-changes questions the purported benefit of using repeated measures to characterize CRF responses to training.


Cardiorespiratory fitness Repeated measures Individual response Individual regressions Typical error Non-responder 



Analysis of variance


Body mass index


Confidence interval


Cardiorespiratory fitness


High amount and high intensity


High amount and low intensity


Low amount and low intensity


Minimum clinically important difference


Metabolic equivalent task


Randomized controlled trial


Standard error of measurement


Typical error


Error in monoexponential regression


Error in linear regression


Author contributions

Conceptualization: JB, RR, BG. Data curation: JB, RR, BG. Formal analysis: JB, RR, BG. Funding acquisition: RR. Methodology: JB, RR, BG. Writing—original draft: JB, BG. Writing—review and editing: JB, RR, BG.


This work was supported by the Canadian Institutes of Health Research [Grant OHN-63277;]. RR received this funding. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Research involving human participants

All procedures performed in studies involving human participants were in accordance with ethical standards of the Health Sciences Human Research Ethics Board at Queen’s University, verbal and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study. Verbal and written explanation of the experimental protocol and associated risks were provided to all participants prior to obtaining written informed consent.

Supplementary material

421_2019_4078_MOESM1_ESM.tif (151 kb)
Supplemental Fig. 1. Representative individual monoexponential regression without (A) and with (B) a constraint on the time constant value (K). K was constrained in panel B to equal the K value associated with the monoexponential regression of the mean CRF data of this participant’s group. Plateaus represent the highest predicted CRF value at infinite time and the plateau and K values are presented in CRF units (mL/kg/min). (TIF 151 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Kinesiology and Health StudiesQueen’s UniversityKingstonCanada

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