Beyond Student's t: A Systematic Exploration of Heavy-Tailed Residual Densities for Outlier Handling in Population PK Modeling

Abstract

BackgroundReliable population pharmacokinetic (PopPK) parameter estimation can be compromised by outliers under Gaussian residual error models. A common mitigation strategy is post hoc filtering based on conditional weighted residuals (CWRES); however, this approach can be insensitive due to model "masking" driven by variance inflation. Practical barriers to implementing robust likelihoods in standard software have motivated interest in computationally simpler exponential-tail alternatives such as the Laplace and exponential power distribution (EPD). MethodsWe implemented a one-compartment PopPK model using a custom likelihood workaround in Monolix to benchmark four residual error distributions: Normal, Laplace, Generalized Error Distribution (GED), and Students 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. ResultsSimulations showed that CWRES-based diagnostics can be unreliable: extreme outliers frequently produced |CWRES| < 6 because the Normal model inflated residual variance, thereby masking contamination. Exponential-tail models (Laplace, GED) improved robustness for mild to moderate outliers but failed under extreme deviations due to insufficiently heavy tails compared to power-law decay. In contrast, the Students t model, via power-law tail behavior, maintained stable and minimally biased structural parameter estimates across contamination scenarios. Consistent patterns were observed in the caffeine case study, where the Students t model provided improved fit and physiologically plausible parameter estimates. ConclusionsCWRES-driven outlier handling is methodologically fragile because influential contamination can be masked by variance inflation and induce biased inference. Among robust residual error models, exponential-tail distributions may be insufficient for extreme outliers, whereas the Students t distribution provides more stable inference across contamination severities. These findings support adopting Students t residual modeling as a default robust option in routine PopPK workflows when outlier contamination is plausible.