Decoupling CAR-T Expansion, Conversion, and Decay Timing: Physiologically Aligned Semi-Mechanistic Modeling With Smooth Gating and a Cauchy Likelihood Residual Model.

Chimeric antigen receptor (CAR) T-cell therapies exhibit complex cellular kinetics with high variability, frequent observations below the limit of quantification (BLQ), and influential outliers. These features can destabilize parameter estimation under Gaussian assumptions, motivating robust likelihood-based approaches. While Student's t residuals with M3 censoring improve robustness, the lack of a closed-form cumulative distribution function (CDF) complicates implementation across platforms like Monolix. We evaluated the Cauchy distribution as an implementation-friendly, heavy-tailed alternative providing closed-form probability density and CDF expressions. In pharmacokinetic simulations with terminal-phase outliers, Cauchy residuals preserved stable parameter recovery comparable to Student's t while Normal residuals exhibited significant bias. In a real-data integrated CAR-T application using full Bayesian inference, Cauchy and Student's t likelihoods yielded highly concordant posterior inference and subject-level predictions. Furthermore, we extended the semi-mechanistic CAR-T framework by replacing piecewise switching with smooth, S-shaped rate functions and process-specific transition times. Full Bayesian summaries supported asynchronous transitions, revealing earlier memory conversion relative to expansion and delayed decay-related transitions. These results support Cauchy likelihoods for robust cross-platform implementation and demonstrate that smooth, decoupled transition modeling enhances the physiological plausibility of CAR-T kinetics.