# Confidence intervals estimator of the kinetic parameters: do its reliability depend on the assembling method of the oxygen uptakes?

## TL;DR

This study compares two methods for assembling oxygen uptake data to determine which provides more reliable confidence intervals for kinetic parameters during exercise.

## Contribution

The study evaluates the reliability of confidence intervals based on different data assembly methods for oxygen uptake kinetics.

## Key findings

- The 'stacking' method provided confidence intervals that included true values in 95% of cases.
- The '1-s-bins' method included true values in 85% of cases.
- The 'stacking' method is recommended for more statistically valid confidence intervals.

## Abstract

Gas exchange data acquired repeatedly under the same exercise conditions are assembled together to improve the kinetic parameters of breath-by-breath oxygen uptake. The latter are provided by the non-linear regression procedure, together with the corresponding estimators of the width of the Confidence Intervals (i.e., the Asymptotic Standard Errors; ASEs). We tested, for two different assembling procedures, whether the range of values identified by the ASE actually correspond to the 95% Confidence Interval. Ten O2 uptake responses were acquired on 10 healthy volunteers performing a square-wave moderate-intensity exercise. Kinetic parameters were estimated running the non-linear regression with a mono-exponential model on an increasingly greater number of responses (Nr, from 1 to 10), assembled together using the “stacking” and the “1-s-bins” procedures. Kinetic values obtained assembling together the 10 repetitions were assumed as “true” values. The time constant was not affected by Nr or by the assembling procedure (ANOVA; p>0.54 and p>0.16, respectively). The corresponding ASE decreased according to Nr (ANOVA; p=0.000), being significantly smaller for the “1-s-bins” procedure compared to the “stacking” one (ANOVA; p<0.001). Excluding 20s at the start of the fitting window, the range of values identified with the ASE provided by the “1-s-bins” and the “stacking” procedures included the “true” value in 85% and in 95% of cases, respectively. The “stacking” procedure should be preferred since it yielded ASEs for the time constant that provided a range of values satisfying the statistical meaning of the width of the Confidence Intervals, at the given degree of probability.