Estimation problem due to multiple solutions in pharmacokinetic curve fitting to two-compartment model and its avoidance.

A size of error in observed data for fitting curves and an estimation problem due to multiple solutions in a two-compartment model were studied by using two different non-linear least-squares regression programs, SALS and NONLIN. It was found that bolus intravenous data have generally 5-10 per cent errors and oral data contain 10-25 per cent errors against the fitted data with respect to total 151 data sets of 11 different drugs. Parameters of five drugs reported in references were used to obtain simulated concentrations at the sampling times, and five different data sets containing 25 per cent normally distributed random errors as a coefficient of variation were generated using each data set of these simulated concentration. In the two-compartment model with tri-exponential equations, unreasonable estimates were occasionally observed, resulting in reversed relative values to the theoretical ones of L/M, L/N, M/N or Ka/alpha, which are analogous to the well-known flip-flop phenomenon in the one-compartment model, when number of parameters to be estimated is not less than five or errors of data exceed about 10 per cent. In an attempt to avoid such unreasonable values, initial estimates for curve fitting was successfully obtained by using a microcomputer program SIMPLEX based on a simplex method. On the basis of these results, some problems in curve fitting of plasma drug concentration data are discussed.