Statistical Measures of Parameter Estimates from Models Fit to Respiratory Impedance Data: Emphasis on Joint Vanabilities

To describe respiratory mechanical impedance data, many investigators have proposed electromechanical models and then fit them to data using formal parameter estimation techniques. This approach has resulted in confusion as to how to interpret the resulting estimated values, and hence as to which model is most appropriate. A key cause of this confusion is that most studies rely on the quality of fit between the model and the data as the only measure of model validity rather than performing adequate statistical analysis of the parameter estimates themselves. This paper describes several statistical measures that should be applied to parameter estimates obtained from forced oscillation data. Specifically, we describe standard errors of the parameter estimates, confidence intervals for each parameter estimate, and the joint confidence region for the parameters. Much emphasis is placed on the joint confidence region which, unlike the interval, allows for simultaneous variations in parameters. The measures are applied to an often used six-element model for respiratory impedance data of dogs from 4 to 64 Hz. This application indicated that even when fitting data over this frequency range, parameter estimates are not well defined and the parameter estimated with least accuracy is airway resistance.