Methodology for generating continuous prediction equations for pulmonary function measures

A mathematical procedure is described for fitting piecewise linear equations constrained to join at estimable multiple junctions or breakpoints. The model parameters, a combination of both linear and nonlinear, are estimated using a "Separable Least Squares" algorithm. In this algorithm the linear parameters, estimated using the General Linear Model, are nested within the iterations of a nonlinear optimization routine. This formulation allows additional covariates to be included in the model and can be easily expanded to include any number of line segments, both linear and nonlinear. The procedure is demonstrated by estimating continuous lung function reference equations for healthy normal subjects. Comparison of these reference equations with previously published equations derived for the same subjects, illustrates the advantages of having continuous equations throughout the age range of the data.