Predicting serum lithium concentration using Bayesian method: a comparison with other methods

Two pharmacokinetic approaches (single-point Bayesian and two fixed volume of distribution-iterative methods) for predicting serum lithium concentrations in patients treated with lithium carbonate for manic-depressive illness or cyclic neutropenia in Kyushu University Hospital were evaluated and compared retrospectively. Prior to these analyses, three methods (prediction using mean parameters reported by Mason et al., the Pepin method, and the Zetin method) without measuring serum concentrations were also compared. In the Bayesian analysis, the effect of population mean parameters (reported by Mason et al. and Pepin et al.), which were used as initial estimates in a fitting process, on predictive performance was also studied. Forty five patients (21 male, 24 female) were included in this study. The average number of determinations per patient was 6.3, and the sampling times ranged from 2 to 18 h after the last dose. Serum lithium concentrations were measured by atomic absorption spectrometer. The Bayesian method used a computer program (PEDA) developed previously by one of us. The prediction using the population mean values from Mason's report gave the least root mean squared error (RMSE; a composite measure for bias and precision of prediction), and was considered to be the most precise among the methods without measuring serum concentrations. Among the methods using a single measured concentration, the Bayesian prediction was less biased and more precise than that by the two fixed volume of distribution-iterative methods. The Bayesian method reduced prediction error in serum concentration prediction compared with those obtained from population mean parameters in both cases: A high reduction of RMSE was observed when the values from Pepin method were used as initial estimates (from 0.320 to 0.219 meq/l), while, Mason's values gave less reduction (from 0.219 to 0.213 meq/l). In the Bayesian prediction of serum lithium concentration, the selection of population-based initial estimates gave no effect on predictive ability of the Bayesian method in terms of RMSE. In conclusion, the Bayesian method was robust and flexible with regard to dosing schedule, sampling time and number of blood samples, and gave the most clinically acceptable precision among the methods evaluated.