Data sensitivity of estimated parameters in a seven-compartment model for pharmacokinetics

Abstract

A computer algorithm was developed to estimate transfer rate constants in a multicompartment model for pharmacokinetics. Given a series of measured drug concentration-time datapoints the parameters are optimized in the maximum likelihood sense from an initial estimate, using a modified Gauss-Newton method. It was studied to what extent the results are sensitive to the number and location of the measurements, and whether this might imply fewer laboratory animals required for in vivo experiments.First, a set of simulated measurements was generated in a seven-compartment model of the rat body. Assuming linear first order kinetics the concentration-time courses were calculated - for certain chosen values of the transfer rate constants - over a 48 h period after a pulse drug input into the central compartment. In each compartment 25 sample points were taken. To account for measurement errors Gaussian noise was added to the model response in these points. Next, random Gaussian deviations were added to the true parameter values. With the thus obtained initial estimates several series of optimization runs were conducted with varying numbers of observations and observed compartments. The accuracies with which the computer program determined the optimal parameter values in each case were compared. It appeared that a large reduction (upto 25%) in the number of observations, in particular the early ones (0–10h), could be allowed without unacceptable loss of accuracy, as long as all compartments remained observed. A shift from 1–5% to 5–10% accuracy in determining the true values was seen for one fifth of the parameters. In all cases the largest deviations remained the same (5% of the parameters estimated with 30% accuracy). If unobserved compartments were present a substantial loss of accuracy resulted (e.g., two fifths of the parameters showing accuracies poorer than 30%). The sensivity of the estimation procedure for deliberately introduced errors in the model structure (distribution pathways) was also investigated. Small model errors were found to go unnoticed.