Comparing heavy-tailed residual error models for outlier handling in population PK modeling

Reliable population pharmacokinetic (PopPK) estimation is often compromised by outliers under Gaussian error models. While post hoc filtering using conditional weighted residuals (CWRES) is common, this approach is often insensitive due to model "masking" from variance inflation.

We implemented a one-compartment model in Monolix using a custom likelihood workaround to benchmark four distributions: Normal, Laplace, Generalized Error Distribution (GED), and Student's t. We assessed CWRES sensitivity under extreme contamination and compared estimation performance using theoretical tail-behavior analysis, controlled simulation studies spanning multiple contamination severities, and a real-world caffeine PK case study with influential terminal-phase deviations.

Simulations revealed that CWRES-based diagnostics are unreliable; extreme outliers frequently produced |CWRES| < 6 because the Normal model inflated residual variance, masking the contamination. Exponential-tail models (Laplace, GED) improved robustness for moderate outliers but failed under extreme deviations due to insufficiently heavy tails. Conversely, the Student's t model, utilizing power-law tail behavior, maintained stable and minimally biased structural parameter estimates across the contamination settings examined. These patterns were confirmed in the caffeine case study.

Reliance on CWRES-driven residual screening alone is methodologically fragile. Among the models evaluated, exponential-tail distributions are insufficient for extreme outliers, whereas the Student's t distribution provided the most consistent stability across the contamination settings examined here and showed the most robust overall performance among the residual-error models evaluated when influential outliers were present.