Simultaneous vs. sequential analysis for population PK/PD data II: robustness of methods.

A model can be fit to joint PK/PD data (concentration and effect) either simultaneously or sequentially. The results of a companion paper suggested that when the data-analytic and true models agree, a particular sequential approach is computationally faster than the simultaneous one, yet produces hardly less precise PD parameter estimates, and for suitable designs, about as accurate PD standard error estimates. In this paper, we compare the performance of various methods for the case that the data-analytic model is misspecified. We illustrate these methods by applying them to a set of real data. Using NONMEM, population PK/PD observations were simulated under various study designs according to a one- or two-compartment PK model and direct Emax or sigmoid Emax model. A one-compartment PK model and Emax PD model were fit to the simulated observations by simultaneous and sequential methods. Predictive performance (interpolation and extrapolation) of PD and the type-I error rate of a likelihood ratio test are compared. The real data set consists of PK and (more frequent) PD observations after administration of the muscle relaxant vecuronium. When only the PK data-analytic model is misspecified, the simultaneous method has greater precision than the sequential methods. However a sequential method that uses a non-parametric PK model performs better than both other methods when PK model misspecification is severe. When the PD data-analytic model is misspecified, sequential and simultaneous methods perform similarly. The analysis of the real data shows that the PK fitted with the simultaneous method can be quite sensitive to PD model misspecification, yielding a possible diagnostic for this type of misspecification.