The propagation of information in PK modelling: The use of IV information to support the analysis of PK data
In-Sun Nam, Leon Aarons
School of Pharmacy, University of Manchester, UK
A logical method of information transfer from IV to oral data was investigated using four data sets generated from phase I studies which differed in design, study population and sampling scheme.
Drug in question has fast absorption with nearly complete bioavailability. Its kinetics are linear and show biexponential elimination with a terminal half-life of 7.5 to 9 hours. From the analysis of IV data (Data I, Data III: bioavailability data (IV + ORAL)), it was shown that the drug has a very rapid early distribution (clearance (CL): 20.5 L/hr, distributional clearance (CLD): 171.2 L/hr, volume of compartment one (V1): 17.3 L and volume of compartment two (V2): 166.8 L).
As the fraction of dose eliminated associated with the first exponential term was less than 10 %, identifying early distribution parameters such as CLD and V1 was not easy in the oral data analysis (Data II). These parameters were correlated with absorption parameters, and even with moderate amounts of data in the early disposition phase (single dose data: SOD), the analysis might produce multiple numerical solutions (based on close simulations). In the case of a multiple oral dose study (MOD) with few data in the early phase, one compartment model was preferred, as the value of V1 approached that of VSS. Moreover, the pooled analysis for SOD and MOD produced results which overestimated V1, underestimated CLD (CL/F: 20.5 L/hr, CLD/F: 54.7 L/hr, V1/F: 67.0 L, V2/F: 151.7 L and Infusion time of 3.0 hr with a zero order model).
Two approaches were taken to resolve this problem; one was a simultaneous approach where IV data were analysed together with SOD/MOD using NLME. While the analysis of all the IV data with SOD produced reasonable results, the analysis of all the available data including MOD generated overestimated V1 as well as underestimated CLD. Moreover, the range of the individual V1 estimates for MOD was different from that for SOD or Data III.
The other approach was a sequential one using the Bayesian program PKBUGS. Here SOD or MOD were analysed separately given appropriate prior knowledge from previous analyses. The analysis of SOD was performed with an informative prior on fixed effects directly from the IV analysis results and a weak prior on random effects, which generated not only an reasonable results, but also the range of individual V1 estimates were much stabilised and the random effects for the absorption parameters were also estimable. Nonetheless, the analysis of MOD required a strong prior on random effects as well; otherwise the variation of individual V1 estimates for MOD allowed the values to be inflated unrealistically (CL/F: 20.1 L/hr, CLD/F: 185.7 L/hr, V1/F: 20.1 L, V2/F: 188.1 L, lag Time: 0.46 hr and Infusion time of 2.2 hr).
In conclusion, Bayesian approach offers a unique way to incorporate the existing knowledge, which is logical and sensible. Moreover, it provides more stability in terms of estimating random effects with limited data
 Pinheiro, J. C. and Bates, D. M. The NLME model formulation, Springer, New York, 2000.
 Lunn, D. J., Wakefield, J., Thomas, A., Best, N. and Spiegelhalter, D. PKBUGS User Guide, Epidemiology & public health at Imperial College School of Medicine, London, 1999.