How many patients and blood levels are necessary for population pharmacokinetic analysis? A study of a one compartment model applied to cyclosporine

Objective: This paper describes a method to determine the number of patients and the number of blood levels which are appropriate for a pharmacokinetic population analysis. Methods: We studied this question by performing 203 runs of population analysis, using the NPEM algorithm with a one compartment model, starting with only one patient and only one blood level, then 2 patients with one blood level each, until reaching 38 patients each with 5 blood levels. Data were obtained from liver transplant patients treated with cyclosporine. Results: For 2, 3, 4 or 5 blood levels, the values of median clearance (CL) converged and became almost equal after about 10 patients were studied. The value then remained stable and the variation was fairly small. With only one blood level per patient, the variation was greater. In contrast, with one blood level, median CL became similar to groups having 2, 3, and 4 blood levels only after about 35 patients had been studied, versus about 10. Similar results were found for the median values of the volume of distribution (V). For a one compartment model with parameters of V and CL, from 15 to 20 patients with 2 blood levels may be enough to perform a reasonable population pharmacokinetic analysis; the values of the pharmacokinetic parameters were very similar to those obtained with to 5 blood levels and with more patients. However, a subpopulation probably requires more patients and at least 4 or 5 blood levels per patient to be recognised. Conclusion: Examination of converging pharmacokinetic parameter values by stepwise increases in the number of patients and blood levels appears to be a pragmatic and empirical approach to determine the possible number of patients and blood levels required for population pharmacokinetic analysis.