Model-Based Residual Post-Processing for Residual Model Identification

The purpose of this study was to investigate if model-based post-processing of common diagnostics can be used as a diagnostic tool to quantitatively identify model misspecifications and rectifying actions. The main investigated diagnostic is conditional weighted residuals (CWRES). We have selected to showcase this principle with residual unexplained variability (RUV) models, where the new diagnostic tool is used to scan extended RUV models and assess in a fast and robust way whether, and what, extensions are expected to provide a superior description of data. The extended RUV models evaluated were autocorrelated errors, dynamic transform both sides, inter-individual variability on RUV, power error model, t-distributed errors, and time-varying error magnitude. The agreement in improvement in goodness-of-fit between implementing these extended RUV models on the original model and implementing these extended RUV models on CWRES was evaluated in real and simulated data examples. Real data exercise was applied to three other diagnostics: conditional weighted residuals with interaction (CWRESI), individual weighted residuals (IWRES), and normalized prediction distribution errors (NPDE). CWRES modeling typically predicted (i) the nature of model misspecifications, (ii) the magnitude of the expected improvement in fit in terms of difference in objective function value (ΔOFV), and (iii) the parameter estimates associated with the model extension. Alternative metrics (CWRESI, IWRES, and NPDE) also provided valuable information, but with a lower predictive performance of ΔOFV compared to CWRES. This method is a fast and easily automated diagnostic tool for RUV model development/evaluation process; it is already implemented in the software package PsN.