The accuracy and stability of Bayesian theophylline predictions

Pharmacokinetic parameters for theophylline were determined in 33 patients (3 women), mean age 61.2 years and weight 74.6 kg using the following three methods: (a) standard one-compartmental model calculations, assuming 100% bioavailability, after a single dose of theophylline syrup (mean dose 413 mg); (b) drug nomogram; and (c) Bayesian analysis. Patients entered a randomised study of three two-monthly dosage regimens using low, medium, and high theophylline twice daily doses. These doses produced mean (+/- SE) steady-state serum theophylline concentrations of 6.3 (+/- 0.4), 12.1 (+/- 0.3) and 18.3 (+/- 0.5) mg/L, respectively. A fourth period of placebo (2-month duration) was also included. At the end of each treatment period the measured serum theophylline concentration of each patient was compared with those predicted by each of the above three methods. The revised estimates derived from Bayesian analysis produced the least biased [mean prediction error (ME)] and most precise (mean squared prediction error) predictions for all three dosage periods. Statistical analysis of relative performance demonstrated that the difference in precision between the revised estimates and those of the other two methods was significant (p less than 0.05) with the magnitude of the difference increasing with dose. The revised estimates were also found to be less biased (p less than 0.05) than those of the nomogram. The ME (+/- SE) of the revised estimates for the low, medium, and high dosage periods was 0.34 (+/- 0.30), -0.02 (+/- 0.22) and -0.48 (+/- 0.31) mg/L, respectively.