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 characterized by rapid expansion, contraction, and long-term persistence, often with substantial inter-individual variability, frequent below-quantification (BLQ) observations, and occasional influential data points. These features can destabilize inference under Gaussian residual assumptions and motivate robust, likelihood-based approaches that can jointly accommodate outliers and censoring. In prior work, we showed that combining Students t residuals with likelihood-based BLQ handling (M3 censoring) improves robustness in CAR-T cellular kinetics modeling; however, implementing Students t censoring likelihoods is not straightforward in all modeling platforms because the Students t cumulative distribution function (CDF) lacks a simple elementary closed-form. Here, we evaluated the Cauchy residual likelihood as a practical, heavy-tailed alternative to Students t that provides closed-form expressions for both the probability density function (PDF) and CDF. In a two-compartment IV pharmacokinetic simulation with terminal-phase outlier contamination, Cauchy residuals preserved stable parameter recovery comparable to Students t while avoiding the bias and instability observed under Normal residuals. In a real-data integrated CAR-T cellular kinetics application fitted with full Bayesian inference and likelihood-based BLQ handling, replacing Students t with Cauchy yielded highly concordant posterior inference and similar subject-level predictions. We further extended a semi-mechanistic CAR-T cellular kinetics framework by replacing piecewise switching with smooth S-shaped time-varying rate functions and allowing process-specific transition times. Full Bayesian posterior summaries supported asynchronous transition timing, including earlier conversion relative to expansion and later decay-related transitions. Collectively, these results support Cauchy likelihoods as an implementation-friendly robust option and demonstrate that smooth, process-specific transition modeling can enhance physiological plausibility for CAR-T kinetics.