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CAST: Time-Varying Treatment Effects with Application to Chemotherapy and Radiotherapy on Head and Neck Squamous Cell Carcinoma

Everest Yang, Ria Vasishtha, Luqman K. Dad, Lisa A. Kachnic, Andrew Hope, Eric Wang, Xiao Wu, Yading Yuan, David J. Brenner, Igor Shuryak

TL;DR

This paper introduces CAST, a framework for estimating time-varying causal treatment effects in survival data by modeling $\tau(x,t)$ as a continuous function of time. CAST combines a parametric quadratic form and a non-parametric smoothing spline to produce continuous treatment-effect trajectories for RMST and survival probability, addressing the limitations of discrete-time causal forests. Validated on the RADCURE HNSCC dataset, CAST reveals a non-monotonic chemotherapy benefit with a peak in mid-term follow-up and substantial patient heterogeneity driven by factors like HPV status and smoking. The approach yields clinically interpretable metrics such as peak time, maximum benefit, and half-life, enabling adaptive, personalized decision-making in cancer care and offering a generalizable framework for temporal causal inference in other diseases.

Abstract

Causal machine learning (CML) enables individualized estimation of treatment effects, offering critical advantages over traditional correlation-based methods. However, existing approaches for medical survival data with censoring such as causal survival forests estimate effects at fixed time points, limiting their ability to capture dynamic changes over time. We introduce Causal Analysis for Survival Trajectories (CAST), a novel framework that models treatment effects as continuous functions of time following treatment. By combining parametric and non-parametric methods, CAST overcomes the limitations of discrete time-point analysis to estimate continuous effect trajectories. Using the RADCURE dataset [1] of 2,651 patients with head and neck squamous cell carcinoma (HNSCC) as a clinically relevant example, CAST models how chemotherapy and radiotherapy effects evolve over time at the population and individual levels. By capturing the temporal dynamics of treatment response, CAST reveals how treatment effects rise, peak, and decline over the follow-up period, helping clinicians determine when and for whom treatment benefits are maximized. This framework advances the application of CML to personalized care in HNSCC and other life-threatening medical conditions. Source code/data available at: https://github.com/CAST-FW/HNSCC

CAST: Time-Varying Treatment Effects with Application to Chemotherapy and Radiotherapy on Head and Neck Squamous Cell Carcinoma

TL;DR

This paper introduces CAST, a framework for estimating time-varying causal treatment effects in survival data by modeling as a continuous function of time. CAST combines a parametric quadratic form and a non-parametric smoothing spline to produce continuous treatment-effect trajectories for RMST and survival probability, addressing the limitations of discrete-time causal forests. Validated on the RADCURE HNSCC dataset, CAST reveals a non-monotonic chemotherapy benefit with a peak in mid-term follow-up and substantial patient heterogeneity driven by factors like HPV status and smoking. The approach yields clinically interpretable metrics such as peak time, maximum benefit, and half-life, enabling adaptive, personalized decision-making in cancer care and offering a generalizable framework for temporal causal inference in other diseases.

Abstract

Causal machine learning (CML) enables individualized estimation of treatment effects, offering critical advantages over traditional correlation-based methods. However, existing approaches for medical survival data with censoring such as causal survival forests estimate effects at fixed time points, limiting their ability to capture dynamic changes over time. We introduce Causal Analysis for Survival Trajectories (CAST), a novel framework that models treatment effects as continuous functions of time following treatment. By combining parametric and non-parametric methods, CAST overcomes the limitations of discrete time-point analysis to estimate continuous effect trajectories. Using the RADCURE dataset [1] of 2,651 patients with head and neck squamous cell carcinoma (HNSCC) as a clinically relevant example, CAST models how chemotherapy and radiotherapy effects evolve over time at the population and individual levels. By capturing the temporal dynamics of treatment response, CAST reveals how treatment effects rise, peak, and decline over the follow-up period, helping clinicians determine when and for whom treatment benefits are maximized. This framework advances the application of CML to personalized care in HNSCC and other life-threatening medical conditions. Source code/data available at: https://github.com/CAST-FW/HNSCC
Paper Structure (15 sections, 3 theorems, 9 equations, 14 figures, 2 tables, 2 algorithms)

This paper contains 15 sections, 3 theorems, 9 equations, 14 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Our contributions are as follows:
  3. Related Work
  4. Methodology
  5. Causal Machine Learning Framework
  6. CAST: Causal Analysis for Survival Trajectories
  7. Parametric Modeling Component
  8. Non-parametric Modeling Component
  9. Experiments
  10. Propensity Score Modeling
  11. Implementation & Heterogeneity Analysis
  12. Validation Methods
  13. Results
  14. Discussion
  15. Conclusion

Key Result

Theorem 1

Under assumptions (A1)--(A5), for each fixed $t$: as $n \to \infty$, where $\hat{S}_w(t \mid X)$ is the estimated conditional survival function under treatment $w$ from causal survival forests.

Figures (14)

  • Figure 1: Overview of the CAST framework
  • Figure 2: Comparison of time-varying treatment effect models using CAST. The red curve shows the parametric estimate with 95% CIs; the blue curve shows the non-parametric spline. Black dots denote average treatment effects $\pm$ standard errors on the survival probability scale.
  • Figure 3: Correlation matrices between covariates, SHAP values, and treatment effects
  • Figure 4: SHAP analysis of covariates driving treatment effect heterogeneity. (a) Older age is linked to greater chemotherapy benefit. (b) HPV-negative patients consistently show higher contributions. (c) Smoking history is positively associated with the chemotherapy benefit treatment.
  • Figure 5: SHAP values for primary tumor site. These anatomical subgroups exhibited low or diffuse contributions to treatment effect heterogeneity, though subtle site-specific trends may still hold clinical value.
  • ...and 9 more figures

Theorems & Definitions (6)

  • Theorem 1: Pointwise Consistency
  • proof
  • Theorem 2: Identifiability
  • proof
  • Theorem 3: Consistency of Estimated Peak Time
  • proof