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Decoupling CAR-T Expansion, Conversion, and Decay Timing: Physiologically Aligned Semi-Mechanistic Modeling With

Yiming Cheng1, Yan Li1

  • 1Clinical Pharmacology and Pharmacometrics, Bristol Myers Squibb, Summit, NJ, USA.

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This study introduces the Cauchy distribution for robust analysis of chimeric antigen receptor (CAR) T-cell therapy data, improving parameter estimation with complex kinetics. The Cauchy approach offers stable results comparable to Student’s t, enhancing CAR T-cell modeling across platforms.

Keywords:
BLQ censoring (M3)CAR‐TCauchy likelihoodStudent's tcellular kineticsrobust nonlinear mixed‐effects modeling

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Area of Science:

  • Pharmacokinetics and Pharmacodynamics
  • Immunotherapy
  • Statistical Modeling

Background:

  • Chimeric antigen receptor (CAR) T-cell therapies present complex cellular kinetics, characterized by high variability, data below quantification limits, and outliers.
  • Standard statistical methods assuming Gaussian distributions struggle with parameter estimation in CAR T-cell data, necessitating robust approaches.
  • Existing robust methods like Student's t residuals with M3 censoring face implementation challenges due to the absence of a closed-form cumulative distribution function (CDF).

Purpose of the Study:

  • To evaluate the Cauchy distribution as a robust, implementation-friendly alternative for analyzing CAR T-cell kinetics.
  • To compare the performance of Cauchy residuals against Normal and Student's t residuals in pharmacokinetic simulations and real-data applications.
  • To enhance CAR T-cell kinetic models by incorporating smooth, S-shaped rate functions for improved physiological representation.

Main Methods:

  • Pharmacokinetic simulations were conducted using terminal-phase outliers to assess parameter recovery under different residual distributions (Normal, Cauchy, Student's t).
  • A real-world CAR T-cell dataset was analyzed using full Bayesian inference, comparing Cauchy and Student's t likelihoods.
  • The semi-mechanistic CAR-T model was extended with smooth, S-shaped rate functions to replace piecewise switching, allowing for asynchronous transition modeling.

Main Results:

  • Cauchy residuals demonstrated stable parameter recovery in simulations with outliers, performing comparably to Student's t and outperforming Normal residuals.
  • In real-data analysis, Cauchy and Student's t likelihoods produced highly consistent posterior inference and subject-level predictions.
  • Bayesian analysis of the enhanced model revealed asynchronous transitions, including earlier memory conversion and delayed decay processes, supporting the physiological plausibility of smooth modeling.

Conclusions:

  • The Cauchy distribution is a viable and robust alternative for analyzing complex CAR T-cell kinetic data, offering implementation advantages over Student's t.
  • Smooth, decoupled transition modeling in CAR T-cell frameworks improves physiological realism and provides deeper insights into cellular processes.
  • This work supports the use of Cauchy likelihoods for robust, cross-platform CAR T-cell data analysis and advanced kinetic modeling.