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Simultaneous vs. Sequential Estimation in PK/PD Data Analysis

Liping Zhang

UCSF, San Francisico, CA

Introduction Rational drug dosing requires knowledge of the dose[– concentration] – effect relationship, which can be obtained by estimating a predictive pharmacokinetic (PK) – pharmacodynamic (PD) model to both concentration and effect observations from a population. The bivariate data can be fit to a model for both responses simultaneously, or sequentially: first estimate the PK model based on PK data alone, and then estimate the PD model conditional on the PK model estimate and the PD data. We compare the performance of a simultaneous method with that of five sequential method variants with respect to computation time and estimation precision.

Methods Using NONMEM V, PK/PD observations from different numbers of individuals and various study designs are simulated according to a one or two compartment PK model and direct Emax or sigmoid Emax model, with parameters drawn from an appropriate population distribution, and fitted to a 1 compartment PK model and Emax PD model. Performance measures include computation time, fraction of successful analyses, integrated prediction error (interpolation and extrapolation) and, for cases that the simulation and analysis models are identical, precision of PD parameter estimates.

Results Sequential approaches take less computation time and are more likely to succeed. When the analysis model is the same as the simulation model, a sequential approach that conditions on subject-specific posterior Bayes PK estimates is as precise as the “gold standard” simultaneous method using an approximate maximum likelihood method, and is considerably faster. When the analysis PK model is misspecified, the simultaneous method has greater precision than the best sequential method; when the analysis PD model is misspecified, sequential and simultaneous methods perform similarly.