Simulation studies of errors of parameter estimates in pharmacokinetics.

Pharmacokinetic parameters are indispensable for the development and evaluation of drugs. Therefore, they are required by international drug agencies and may influence relevant decisions. Their determination from experimental results is only possible with statistical errors. For the estimation of these errors only approximative procedures are available. A widespread approximation (information inequality) is based on specific assumptions which are invalid in practice. Erroneous estimations of unknown amount may consequently result. Alternative methods more adaptable to reality are simulation techniques with random numbers. This technique was used to calculate the statistical variability of parameter estimates for the usual compartment models. The results were compared with the variation of the parameter estimates from a descriptive model function recently developed. Adequate curves were predefined by appropriate parameter sets. Around these curves, a random generator simulated 500 data sequences. Fitting with the appertaining model function resulted in 500 sets of estimated parameters. The statistical behavior of the parameter estimates was investigated. The parameters computed by the fitting procedure--in the compartment models the rate constants--showed a large variation so that an estimate from a single data sequence does barely reproduce the "true" value of the parameter. In contrast, the parameters derived from the geometric properties of the fitted curves (e.g., area under curve, time and height of maximum) showed considerable less variation. As far as these investigations allow a conclusion, the latter parameters seem to be sufficiently reliable for practical purposes.