A nonstatistical approach to estimating confidence intervals about model parameters: application to respiratory...

Estimates of parameters obtained by fitting models to physiologic data are of little use unless accompanied by confidence intervals. The standard methods for estimating confidence intervals are statistical, and make the assumption that the fitted model accounts for all the deterministic variation in the data while the residuals between the fitted model and the data reflect only stochastic noise. In practice, this is frequently not the case, as one often finds the residuals to be systematically distributed about zero. In this paper, we develop an approach for assessing confidence in a parameter estimate when the order of the model is clearly less than that of the system being modeled. Our approach does not require a parameter to have a single value located within a region of confidence. Instead, we let the parameter value vary over the data set in such a way as to provide a good fit to the entire data set. We apply our approach to the estimation of the resistance of the respiratory system in which a simple model is fitted to measurements of tracheal pressure and flow by recursive multiple linear regression. The values of resistance required to achieve a good fit are represented as a modified histogram in which the contribution of a particular resistance value to the histogram is weighted by the amount of information used in its determination. Our approach provides parameter frequency distribution functions that convey the degree of confidence one may have in the parameter, while not being based on erroneous statistical assumptions.