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Stabilized Neural Prediction of Potential Outcomes in Continuous Time

Konstantin Hess, Stefan Feuerriegel

TL;DR

This paper tackles estimating conditional average potential outcomes for time-varying treatments in continuous time with irregular timestamps. It introduces SCIP-Net, a neural framework that combines a tractable continuous-time inverse propensity weighting objective with stabilized weights and neural controlled differential equations to properly adjust for time-varying confounding. The authors derive a tractable product-integral formulation, define stabilized weights, and demonstrate superior performance over continuous- and discrete-time baselines on synthetic and semi-synthetic healthcare data. The work has practical implications for personalized medicine, enabling accurate CAPO estimation when measurements and treatments occur at arbitrary times.

Abstract

Patient trajectories from electronic health records are widely used to estimate conditional average potential outcomes (CAPOs) of treatments over time, which then allows to personalize care. Yet, existing neural methods for this purpose have a key limitation: while some adjust for time-varying confounding, these methods assume that the time series are recorded in discrete time. In other words, they are constrained to settings where measurements and treatments are conducted at fixed time steps, even though this is unrealistic in medical practice. In this work, we aim to estimate CAPOs in continuous time. The latter is of direct practical relevance because it allows for modeling patient trajectories where measurements and treatments take place at arbitrary, irregular timestamps. We thus propose a new method called stabilized continuous time inverse propensity network (SCIP-Net). For this, we further derive stabilized inverse propensity weights for robust estimation of the CAPOs. To the best of our knowledge, our SCIP-Net is the first neural method that performs proper adjustments for time-varying confounding in continuous time.

Stabilized Neural Prediction of Potential Outcomes in Continuous Time

TL;DR

This paper tackles estimating conditional average potential outcomes for time-varying treatments in continuous time with irregular timestamps. It introduces SCIP-Net, a neural framework that combines a tractable continuous-time inverse propensity weighting objective with stabilized weights and neural controlled differential equations to properly adjust for time-varying confounding. The authors derive a tractable product-integral formulation, define stabilized weights, and demonstrate superior performance over continuous- and discrete-time baselines on synthetic and semi-synthetic healthcare data. The work has practical implications for personalized medicine, enabling accurate CAPO estimation when measurements and treatments occur at arbitrary times.

Abstract

Patient trajectories from electronic health records are widely used to estimate conditional average potential outcomes (CAPOs) of treatments over time, which then allows to personalize care. Yet, existing neural methods for this purpose have a key limitation: while some adjust for time-varying confounding, these methods assume that the time series are recorded in discrete time. In other words, they are constrained to settings where measurements and treatments are conducted at fixed time steps, even though this is unrealistic in medical practice. In this work, we aim to estimate CAPOs in continuous time. The latter is of direct practical relevance because it allows for modeling patient trajectories where measurements and treatments take place at arbitrary, irregular timestamps. We thus propose a new method called stabilized continuous time inverse propensity network (SCIP-Net). For this, we further derive stabilized inverse propensity weights for robust estimation of the CAPOs. To the best of our knowledge, our SCIP-Net is the first neural method that performs proper adjustments for time-varying confounding in continuous time.
Paper Structure (20 sections, 8 theorems, 85 equations, 3 figures, 7 tables)

This paper contains 20 sections, 8 theorems, 85 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. SCIP-Net
  5. Rewriting the objective for computational tractability
  6. Stabilized weights
  7. Neural architecture
  8. Inference
  9. Numerical Experiments
  10. Extended related work
  11. Product integration
  12. Neural Differential Equations
  13. Proofs of propositions
  14. Data generation
  15. Tumor growth data
  16. ...and 5 more sections

Key Result

Proposition 1

Under assumptions (i)--(iii), we can estimate the CAPO from observational data (i.e., from data sampled under $\mathop{}\!\mathrm{d} \mathbb{P}_0$) via inverse propensity weighting, that is, where the inverse propensity weights for $s\geq t$ are defined as

Figures (3)

  • Figure 1: Setup. Shown are treatment and covariate trajectories in continuous time. Observational treatment assignments are confounded by covariates and, hence, estimating CAPOs requires adjustments.
  • Figure 2: Neural architecture of our SCIP-Net.
  • Figure 3: Performance for the tumor growth model. We compare different forecast horizons and different confound strengths. Shown is the average RMSE of the potential outcomes under hard interventions over five seeds. Our proposed SCIP-Net performs best, followed by our CIP-Net.

Theorems & Definitions (18)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Definition 1
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Proposition 1
  • ...and 8 more