Application of non parametric methods to pharmacokinetic models of the Michaelis-Menten type

Non linear parametric regression methods for data fitting as applied to complex pharmacokinetic models give rise to convergence difficulties which have not been completely solved. The Cornich-Bowden non parametric method was applied by Shelver to the one compartment open model with first order absorption to simulated data with different error structures. The application of his procedure was extended to a pharmacokinetic model with Michaelis-Menten elimination. Simulated concentration/time data were generated by a microcomputer program which imposed the appropriate error structure:constant and proportional standard deviation with or without one outlier of different magnitude. Parameter optimization was performed using either a Newton-Raphson algorithm based on the integrated form of the Michaelis-Menten equation and a standard non linear regression program: NONLIN. In the case of the non parametric method, the median of the parameter values obtained for each combination of data points was used as best estimate of the parameters. One hundred data sets were used and performance of the two methods was assessed by comparing bias and standard deviation of the mean parameter value thus obtained, given the true values of the parameters used to generate the data. The non parametric performed well with homoscedastic data and was less sensitive to the presence of outliers than the non linear regression technique. In the case of heterosocedastic data both methods performed poorly but the non parametric method was more sensitive to the presence of outliers.