Eric Novik1, Jacqueline Buros2, Juho Timonen2
1New York University, 2Generable
Recent advances in oncology have spurred the development of semi-mechanistic models to better understand tumor-size response to treatment. Traditional approaches, such as the Stein-Fojo function, model tumor dynamics using a combination of exponential decay—representing treatment response—and exponential growth—representing resistance. However, these methods often fall short when confronted with the inherent heterogeneity across patient subpopulations. Modern immune-oncology treatments yield diverse outcomes, including sustained responses, hyper-progression, and pseudo-progression. This motivates the need for a flexible Bayesian modeling approach that captures heterogeneous tumor responses. *Objectives* – Develop a Bayesian model for diverse tumor response profiles. – Create an R package for rapid model implementation in Stan. – Summarize treatment effects by simulating expected patient populations. – Evaluate the approach on a realistic simulated dataset. *Methods* To address these challenges, we introduce sfgp, a novel R package that implements a semi-mechanistic parametric Gaussian Process (GP) regression framework for longitudinal tumor response modeling. Our approach extends traditional models by decomposing the overall response into a sum of distinct components. The mean function is specified as a combination of classic nonlinear functions—exemplified by the Stein-Fojo formulation—and additional GP terms that can be shared across patients or tailored to specific subgroups. A unique aspect of our method is that the parameters of the mean function, such as the exponential decay and regrowth rates, can themselves be expressed as a sum of components, incorporating shared and group-specific GP terms. This hierarchical structure allows these parameters to vary over time in response to treatment, thereby accommodating dynamic changes such as pseudoprogression (an initial increase in tumor size due to immune infiltration) and delayed regrowth phenomena. Our framework leverages Hilbert space basis function approximations to implement the GP components efficiently. This mathematical underpinning not only reduces computational complexity but also enhances the flexibility of the model in capturing covariate effects and multimodal response patterns. By doing so, our approach is capable of discerning subtle patterns in tumor kinetics that are often obscured by noise or oversimplified by conventional models. Moreover, the incorporation of both shared and group-specific GP terms ensures that the model can account for both the common underlying trends across a patient population as well as individual deviations from these trends. We applied our method to a simulated dataset modeled after a metastatic melanoma cohort treated with an aPD-L1 drug [1] and compared the standard SF model to two SF+GP variants. For additional context, we also evaluated jmpost [2]. *Results* Preliminary analyses using sfgp have demonstrated its potential in robustly modeling complex tumor dynamics. The flexible integration of GP terms with a mechanistic baseline allows our model to accommodate significant variability between responder and non-responder groups. In simulated datasets and early-phase clinical trial data, the framework successfully characterized both the depth of tumor shrinkage and the duration of treatment effects. Notably, the ability of the model to allow decay and regrowth parameters to vary over time has proven particularly advantageous in scenarios where traditional models might fail, such as in cases of pseudoprogression or delayed rebound. These features are crucial in capturing the full spectrum of tumor behavior, which in turn is vital for improving predictions related to overall survival. Detailed comparisons with conventional models indicate that sfgp not only provides a better fit to observed data but also yields more informative post-inference summaries. The package includes functions for visualizing expected treatment effects across both observed and hypothetical patient populations, thereby offering clinicians and researchers a valuable tool for decision-making and further analysis. In addition, the framework’s capacity to quantify uncertainty through the GP terms adds an extra layer of interpretability, allowing for more nuanced assessments of treatment efficacy. Both SF+GP models outperformed the standard SF model, yielding improvements in expected log predictive density (ELPD) differences (via LOO-PSIS [3]) of -594 and -1549, with standard errors of 44 and 42, respectively. Subject-level predictive checks indicated that the SF+GP models more effectively captured response heterogeneity, especially in cases where the SF model missed hyper-progression or sustained responses. Preliminary analyses further showed that the best-performing SF+GP model improved accuracy in detecting treatment effects, particularly regarding response duration. *Conclusions* In summary, the sfgp package represents a significant advancement in the modeling of longitudinal tumor response. By integrating semi-mechanistic parametric modeling with the flexibility of Gaussian Processes, our approach overcomes key limitations of traditional methods. It balances the need to capture individual patient variability with the robustness required for population-level inference. This dual capability is essential for developing predictive models that can accurately forecast treatment outcomes and ultimately guide clinical decision-making. The extended structure of the model, with its ability to allow decay and regrowth parameters to vary dynamically over time, is particularly well-suited to address complex phenomena such as pseudoprogression and delayed regrowth. These advances promise to enhance our understanding of treatment dynamics in oncology and to improve the predictive accuracy of models related to overall survival. The sfgp package is available as an open-source tool, complete with a comprehensive codebase and detailed vignettes, which are accessible at https://github.com/generable/sfgp. Future work will focus on further validating the model in larger clinical datasets and exploring its application to other dynamic biological processes.
1. Dutta R, Mohan A, Buros-Novik J, et al. A bootstrapping method to optimize go/no-go decisions from single-arm, signal-finding studies in oncology. CPT Pharmacometrics Syst. Pharmacol. 2024; 13:1317–1326 2. Gower-Page C, Mercier F, Sabanes Bove D, et al. Jmpost: Joint models for predicting overall survival trajectories. 2025; 3. Vehtari A, Gelman A, Gabry J. Practical bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat. Comput. 2017; 27:1413–1432
Reference: PAGE 33 (2025) Abstr 11601 [www.page-meeting.org/?abstract=11601]
Poster: Drug/Disease Modelling - Oncology