Misspecification and Violation of the Model Assumptions

Box (1976), in one of the most famous quotes reported in the pharmacokinetic literature, stated all models are wrong, some are useful. This adage is well accepted. The question then becomes how precise or of what value are the parameter estimates if the model or the model assumptions are wrong. A variety of simulation studies have indicated that population parameter estimates are surprisingly robust to all kinds of misspe-cifications, but that the variance components are far more sensitive and are often very biased when misspeci-fication of the model or when violations of the model assumptions occur. Some of the more conclusive studies examining the effect of model misspecification or model assumption violations on parameter estimation will now be discussed. 

Wade et al. (1993) simulated concentration data for 100 subjects under a one-compartment steady-state model using either first-or zero-order absorption. Simulated data were then fit using FO-approximation with a first-order absorption model having ka fixed to 0.25-, 0.5-, 1-, 2-, 3-, and 4 times the true ka value. Whatever value ka was fixed equal to, clearance was consistently biased, but was relatively robust with underpredictions of the true value by less than 5% on average. In contrast, volume of distribution was very sensitive to absorption misspecification, but only when there were samples collected in the absorption phase. When there were no concentration data in the absorption phase, significant parameter bias was not observed for any parameter. The variance components were far more sensitive to model misspecification than the parameter estimates with some 

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