MULTIPLE SOLUTIONS, ILLEGAL PARAMETER VALUES, LOCAL MINIMA OF THE SUMOF SQUARES, AND ANOMALOUS PARAMETER ESTIMATES IN LEAST-SQUARES FITTING OF THE 2-COMPARTMENT PHARMACOKINETIC MODEL WITH ABSORPTION

When the two-compartment model with absorption is fitted to data by no nlinear least squares, in general six different outcomes can be obtain ed, arising from permutation of the three exponential rate constants. The existence of multiple solutions in this sense is analogous to the flip-flop phenomenon in the one-compartment model. It is possible for parameter estimates to be inconsistent with the underlying physical mo del. Methods for recognizing such illegal estimates are described. Oth er common difficulties are that estimated values for two of the rate c onstants are almost identical with very large standard deviations, or that the parameter estimation algorithm converges poorly. Such unwante d outcomes usually signal a local (false) minimum of the sum of square s. They can be recognized from the ratio of largest to smallest singul ar value of the Jacobian matrix, and are, in principle, avoidable by s tarting the estimation algorithm with different initial values. There also exists a class of data sets for which all outcomes of fitting the usual equations are anomalous. A better fit fit to these data sets (s maller sum of squares) is obtained if two of the relevant rate constan ts are allowed to take complex conjugate values. Such data sets have u sually been described as having ''equal rate constants.'' A special fo rm of the model equation is available for parameter estimation in this case. Precautions relating to its use are discussed.