Three new residual error models for population PK/PD analyses

Abstract

Residual error models, traditionally used in population pharmacokinetic analyses, have been developed as if all sources of error have properties similar to those of assay error. Since assay error often is only a minor part of the difference between predicted and observed concentrations, other sources, with potentially other properties, should be considered. We have simulated three complex error structures. The first model acknowledges two separate sources of residual error, replication error plus pure residual (assay) error. Simulation results for this case suggest that ignoring these separate sources of error does not adversely affect parameter estimates. The second model allows serially correlated errors, as may occur with structural model misspecification. Ignoring this error structure leads to biased random-effect parameter estimates. A simple autocorrelation model, where the correlation between two errors is assumed to decrease exponentially with the time between them, provides more accurate estimates of the variability parameters in this case. The third model allows time-dependent error magnitude. This may be caused, for example, by inaccurate sample timing. A time-constant error model fit to time-varying error data can lead to bias in all population parameter estimates. A simple two-step time-dependent error model is sufficient to improve parameter estimates, even when the true time dependence is more complex. Using a real data set, we also illustrate the use of the different error models to facilitate the model building process, to provide information about error sources, and to provide more accurate parameter estimates.