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TV-SurvCaus: Dynamic Representation Balancing for Causal Survival Analysis

Ayoub Abraich

TL;DR

TV-SurvCaus addresses the challenging problem of estimating causal effects of time-varying treatments on survival by marrying sequence modeling with explicit representation balancing. The framework learns history-dependent latent representations that are balanced across treatment sequences via integral probability metrics, enabling robust counterfactual survival predictions in the presence of censoring and treatment-confounder feedback. The authors provide a rigorous theoretical foundation, including generalization bounds, variance control, consistency, convergence rates, and bias analysis, and validate the approach on synthetic, semi-synthetic, and real-world MIMIC-III data, where it outperforms strong baselines across multiple metrics. Practically, TV-SurvCaus offers a principled, end-to-end method for estimating individualized effects of dynamic treatment sequences, with potential to inform adaptive treatment strategies in medicine and beyond.

Abstract

Estimating the causal effect of time-varying treatments on survival outcomes is a challenging task in many domains, particularly in medicine where treatment protocols adapt over time. While recent advances in representation learning have improved causal inference for static treatments, extending these methods to dynamic treatment regimes with survival outcomes remains under-explored. In this paper, we introduce TV-SurvCaus, a novel framework that extends representation balancing techniques to the time-varying treatment setting for survival analysis. We provide theoretical guarantees through (1) a generalized bound for time-varying precision in estimation of heterogeneous effects, (2) variance control via sequential balancing weights, (3) consistency results for dynamic treatment regimes, (4) convergence rates for representation learning with temporal dependencies, and (5) a formal bound on the bias due to treatment-confounder feedback. Our neural architecture incorporates sequence modeling to handle temporal dependencies while balancing time-dependent representations. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that TV-SurvCaus outperforms existing methods in estimating individualized treatment effects with time-varying covariates and treatments. Our framework advances the field of causal inference by enabling more accurate estimation of treatment effects in dynamic, longitudinal settings with survival outcomes.

TV-SurvCaus: Dynamic Representation Balancing for Causal Survival Analysis

TL;DR

TV-SurvCaus addresses the challenging problem of estimating causal effects of time-varying treatments on survival by marrying sequence modeling with explicit representation balancing. The framework learns history-dependent latent representations that are balanced across treatment sequences via integral probability metrics, enabling robust counterfactual survival predictions in the presence of censoring and treatment-confounder feedback. The authors provide a rigorous theoretical foundation, including generalization bounds, variance control, consistency, convergence rates, and bias analysis, and validate the approach on synthetic, semi-synthetic, and real-world MIMIC-III data, where it outperforms strong baselines across multiple metrics. Practically, TV-SurvCaus offers a principled, end-to-end method for estimating individualized effects of dynamic treatment sequences, with potential to inform adaptive treatment strategies in medicine and beyond.

Abstract

Estimating the causal effect of time-varying treatments on survival outcomes is a challenging task in many domains, particularly in medicine where treatment protocols adapt over time. While recent advances in representation learning have improved causal inference for static treatments, extending these methods to dynamic treatment regimes with survival outcomes remains under-explored. In this paper, we introduce TV-SurvCaus, a novel framework that extends representation balancing techniques to the time-varying treatment setting for survival analysis. We provide theoretical guarantees through (1) a generalized bound for time-varying precision in estimation of heterogeneous effects, (2) variance control via sequential balancing weights, (3) consistency results for dynamic treatment regimes, (4) convergence rates for representation learning with temporal dependencies, and (5) a formal bound on the bias due to treatment-confounder feedback. Our neural architecture incorporates sequence modeling to handle temporal dependencies while balancing time-dependent representations. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that TV-SurvCaus outperforms existing methods in estimating individualized treatment effects with time-varying covariates and treatments. Our framework advances the field of causal inference by enabling more accurate estimation of treatment effects in dynamic, longitudinal settings with survival outcomes.
Paper Structure (41 sections, 7 theorems, 17 equations, 1 figure, 11 tables)

This paper contains 41 sections, 7 theorems, 17 equations, 1 figure, 11 tables.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. Causal Inference with Time-Varying Treatments.
  5. Deep Learning for Causal Inference.
  6. Survival Analysis in Causal Inference.
  7. Sequential Decision Making and DTRs.
  8. Problem Statement and Background
  9. Notations and Setup
  10. Causal Assumptions for Time-Varying Treatments
  11. Causal Estimands of Interest
  12. Theoretical Framework and Guarantees
  13. Generalization Bound via Representation Balancing
  14. Variance Control via Sequential Balancing Weights
  15. Consistency for Dynamic Treatment Regimes
  16. ...and 26 more sections

Key Result

Theorem 4.1

Let $\phi$ be the representation function and $h \in \mathcal{H}$ be the survival predictor. Under Assumptions ass:seq_exch-ass:no_anticip, for any two treatment sequences $\overline{a}$ (source) and $\overline{a}'$ (target), the expected risk of predicting the potential outcome under $\overline{a}' where $\lambda^*$ represents the combined error of the ideal hypothesis that minimizes risk on both

Figures (1)

  • Figure 1: TV-SurvCaus Architecture: A sequence encoder $\psi$ (e.g., LSTM) processes history $(X(k), T(k-1))$ into summary $\bm{s}$. The representation network $\phi$ maps $\bm{s}$ to latent $\bm{z}$. The balancing loss $\mathcal{L}_{bal}$ minimizes IPM distance between $p(\bm{z}|\overline{T}=\overline{a})$ and $p(\bm{z}|\overline{T}=\overline{a}')$. The prediction network $h$ estimates survival $\hat{\overline{F}}_{\overline{a}}(\tau|\bm{z})$ based on $\bm{z}$ and target sequence $\overline{a}$.

Theorems & Definitions (17)

  • Remark 3.1: Assumption Plausibility
  • Definition 3.2: Conditional Potential Survival Function
  • Definition 3.3: Time-Varying Conditional Average Treatment Effect (TV-CATE)
  • Definition 3.4: Time-Varying Precision in Estimation of Heterogeneous Effects (TV-PEHE)
  • Theorem 4.1: Bound on Counterfactual Risk via Representation Discrepancy
  • proof : Proof Sketch
  • Corollary 4.2: Implication for TV-PEHE
  • Theorem 4.3: Sequential Stabilized Weights Definition
  • Proposition 4.4: IPTW Estimator Variance
  • Remark 4.5: Weight Management
  • ...and 7 more