Measures of uncertainty of pharmacokinetic and pharmacodynamic parameter estimates: a new computerized algorithm

Numerous algorithms exist to fit data to nonlinear models of the type used in chemistry, pharmacology, physiology, etc. Most include modules that provide some measure of the reliability of the estimated model parameters. The variance-covariance matrix (VCM) is the common tabulation of information that is used to quantify the parameter uncertainty as well as correlations between parameters. The VCM has its mathematical foundation in the linear regression world, where the dependent variable is a linear function of the parameters. However, when the model is not linear in its parameters, then the VCM is no longer an absolute quantitative measure of reliability of the parameter estimates and should be interpreted with caution. If the goal is to obtain a realistic and quantitative rather than a qualitative measurement of the parameter reliability, then it is necessary to have an alternative approach to describe the parameter likelihood region. We present a computerized algorithm that fills that need, and we compare its performance with the traditional VCM approach for different data sets. We also discuss criteria that may be used to determine when the VCM approach should and should not be used.