Reply

In their Letter to the Editor entitled ‘Interpreting the confidence intervals of model parameters of breath-by-breath pulmonary O2 uptake’, Francescato and colleagues correctly point out that in some instances, the use of the 95% confidence interval (CI95) may not truly reflect the precision of parameter estimation when fitting phase II pulmonary O2 uptake () data using the non-linear regression analysis technique. Specifically, they mention that artificially narrower CI95 values (associated with the parameter estimates of the non-linear model) can be generated by increasing the number of data points used in the non-linear regression procedure (e.g. by linearly interpolating on a second-by-second basis). The authors are correct that we did not make this point in our paper. However, it should be emphasized that the main focus of our study was to determine whether different data-processing techniques affected parameter estimation and confidence of phase II kinetics. Using real breath-by-breath data, our analyses showed that: (i) phase II kinetic parameter estimates were not different when modelling data using like-trials that were combined without processing of any kind, after interpolation (using two interpolation techniques) and/or after bin averaging; (ii) the ‘noise’ statistics for were highly variable both between subjects and within subject trial repeats; (iii) though variable, the amplitude of breath-by-breath ‘noise’ is not different between low or moderate exercise intensities or between young and older individuals; and (iv) the statistics of breath-by-breath ‘noise’ were normally distributed independent of age group or steady-state exercise intensity (Keir et al. 2014). In their study, Francescato and colleagues (2014) indicate that resampling responses (individual trials) to a time interval slightly longer than the average breath duration provides the best method by which to obtain an asymptotic CI95 that contains the ‘true’ parameter. A shortcoming of this recommendation is that the ‘true’ parameter values normally are not known and thus the confidence interval, as defined (‘the range of values that over a set of notional repeated samples, would contain the true parameter of interest’) cannot truly be established. Pulmonary O2 uptake kinetic analyses provide a means for quantifying the rate at which pulmonary (and muscle) O2 uptake adjusts in response to a change in metabolic demand, and the parameter used to describe the rate of this adjustment is the time constant (τ). When fitting real breath-by-breath data, the value of τ can be influenced by a number of factors, including the inclusion of data from phase I (and phase III) and the level of noise within the non-steady-state (transient) phase of the response. To circumvent these issues, it is common practice to perform and combine repeat trials (Lamarra et al. 1987) and to constrain the fitting window (at least within the moderate-intensity domain) to data that appear beyond an identified phase I–phase II transition or that appear ∼20 s after the onset of exercise (Murias et al. 2011). While these strategies do help to improve ‘confidence’ during the fitting procedure, there are always situations where the signal-to-noise ratio of the data is less than desirable (particularly in situations where the change in is small and/or the individual has a large noise amplitude). We appreciate the information presented in the study by Francescato et al. (2014) and acknowledge that this type of modelling exercise can be useful to help understand the technical aspects of characterizing dynamic physiological responses. However, when dealing with real breath-by-breath data there is considerable interbreath variability in the signal (with respect to ‘noise’ and temporal pattern), both between subjects and within subject repeats, and the ‘true’ values of the parameters are not known. It is therefore difficult to state with appropriate ‘confidence’ that the ‘true’ parameter estimates lie within a predicted range. In practice, higher ‘confidence’ in the fit can be obtained only by collecting quality data and carefully modelling the phase II response, with attention paid to the parameters and statistical outcomes (CI95, χ2) and the goodness of fit of the model as determined by visual inspection of the model best-fit relationship with the real data and the resulting residuals, especially within the non-steady-state region of interest.

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