Optimal sampling theory: effect of error in a nominal parameter value on bias and precision of parameter estimation

The authors examined the robustness of optimal sampling theory in estimating the parameter values of two different populations of patients receiving a constant rate, half-hour intravenous infusion of theophylline. One population consisted of smokers; the other included nonsmokers. The smoking population was predicted to have a serum clearance approximately 50% greater than the nonsmokers because of an induction of the cytochrome P450 system. After an initial study to provide both patient-specific and population mean parameter values, optimal sampling strategies that were derived from each population (seven sample split designs) and the patient's seven sample and four sample design were determined. A second study was performed with an overall sampling strategy that was superset of all the above strategies. The analysis of all samples served as the reference for the parameter values. Bias and precision of the values determined with each of the optimal sampling sets (seven sample sets based on the "correct" and "wrong" populations, the patient's seven and four sample sets) were determined relative to these reference values. Irrespective of the sample set used for analysis, unbiased and precise parameter estimates, particularly of hybrid parameters were provided. With the patient's four sample set, Vss was significantly biased, but the value of (2.2%) was clinically insignificant. The authors conclude that optimal sampling theory, as implemented in this study, provides robust estimates of important pharmacokinetic parameter values, even when errors of 50% are present in the clearance of the population used to calculate the optimal sampling design.