Modelling the slow component: the effect of starting values in the resulting parameter estimates

Activity: Talk or presentation typesOral presentation at Conference


Breath-by-breath VO2 data are a composite of the underlying response and the breath-to-breath fluctuations that constitute ‘noise’ on this signal. Despite the majority of studies investigating exercise intensities above the gas exchange threshold (where the slow component is present), the bi-exponential model used has not been examined to ensure it is sensitive enough to adequately estimate parameters. Such an analysis has only occurred in moderate (1, 2) and severe intensity exercise (3), where a single exponential function was used. All iterative models require starting (estimate) values to be entered, and it is possible these affect the derived parameter estimates. Until this possible effect is understood it is impossible to the properly evaluate the quality of the model being used. Therefore the purpose of the present study was to investigate the effect of altering these starting values on the derived parameter estimates.
Six male participants each completed six transitions (8 minutes) at 25% of the difference between gas exchange threshold and maximal oxygen uptake. Data were interpolated, and modelled for each person and the average for each parameter was used as the underlying response to test the bi-exponential model. Studies typically use two transitions to model slow component data (4) and so the typical SD of residuals from two transitions was superimposed onto the underlying response to perform a Monte-Carlo analysis. Starting values were manipulated ranging from -50% to +50% of the actual underlying curves. Ninety five percent confidence limits were calculated as the 1.96 x SD of residuals. All data were analysed using SPSS (IBM, Portsmouth) (nonlinear regression) and were unconstrained.
Results demonstrated that both the returned parameter estimates and the variability of these values (95% confidence limits) were affected by starting values. The mean values from each simulation showed that starting values would need to be within 10% of the actual value to return values with 5% of the actual for all parameter estimates. The 95% confidence limits were wide for the key slow component parameter estimates (amplitude and time constant) even when starting values were at or close to the actual values.
These results show that that bi-exponential modelling of oxygen uptake kinetics is heavily influenced by the starting values used in the iterative methods for model fitting. Authors in this area should make more explicit how data were modelled and report all parameter estimates. Furthermore these results suggest that the confidence intervals for slow component parameters are wide and we should be cautious how these are interpreted.
PeriodJul 2019
Event titleEuropean College of Sport Sciences Annual Conference 2019
Event typeConference
LocationPrague, Czech RepublicShow on map