[Paper Review] Within-Person Variability Score-Based Causal Inference: A Two-Step Semiparametric Estimation for Joint Effects of Time-Varying Treatments

Satoshi Usami|arXiv (Cornell University)|Jul 8, 2020

Advanced Causal Inference Techniques8 citations

TL;DR

This paper proposes a two-step semiparametric method for causal inference in longitudinal studies with time-varying continuous treatments, using within-person variability scores to disentangle within-person effects from stable trait confounders. By leveraging structural equation modeling to extract within-person variability and applying G-estimated structural nested mean models, the method achieves robust causal estimation, significantly reducing bias when stable traits are unobserved.

ABSTRACT

Behavioral science researchers have recently shown strong interest in disaggregating within- and between-person effects (stable traits) from longitudinal data. In this paper, we propose a method of within-person variability score-based causal inference for estimating joint effects of time-varying continuous treatments by effectively controlling for stable traits as time-invariant unobserved confounders. After conceptualizing stable trait factors and within-person variability scores, we introduce the proposed method, which consists of a two-step analysis. Within-person variability scores for each person, which are disaggregated from stable traits of that person, are first calculated using weights based on a best linear correlation preserving predictor through structural equation modeling. Causal parameters are then estimated via a potential outcome approach, either marginal structural models (MSMs) or structural nested mean models (SNMMs), using calculated within-person variability scores. We emphasize the use of SNMMs with G-estimation because of its doubly robust property to model errors. Through simulation and empirical application to data regarding sleep habits and mental health status from the Tokyo Teen Cohort study, we show that the proposed method can recover causal parameters well and that causal estimates might be severely biased if one does not properly account for stable traits.

Motivation & Objective

• To address the challenge of unobserved stable traits acting as time-invariant confounders in longitudinal studies with time-varying treatments.
• To disentangle within-person variability effects from between-person stable trait effects in behavioral science data.
• To develop a method that enables valid causal inference when stable traits are unobserved but influence both treatment and outcome.
• To improve estimation accuracy by using within-person variability scores as a proxy for time-varying treatment effects, controlling for unmeasured confounding.
• To demonstrate the method’s robustness and effectiveness through simulation and empirical application to sleep and mental health data.

Proposed method

• First, within-person variability scores are extracted for each individual using a best linear correlation-preserving predictor based on structural equation modeling, separating them from stable trait components.
• The method uses weights derived from structural equation modeling to ensure that the within-person variability scores preserve the correlation structure of the original time-varying treatments.
• In the second step, causal parameters are estimated using potential outcomes frameworks, specifically structural nested mean models (SNMMs) with G-estimation for double robustness.
• The approach leverages marginal structural models (MSMs) or SNMMs, but emphasizes SNMMs due to their doubly robust property against model misspecification.
• The method treats within-person variability scores as the exposure of interest, allowing for joint estimation of treatment effects while adjusting for unobserved stable traits.
• G-estimation is used in SNMMs to ensure consistent estimation even if one of the outcome or treatment models is misspecified.

Experimental results

Research questions

• RQ1 To what extent can within-person variability scores effectively isolate time-varying treatment effects from stable trait confounders in longitudinal data?
• RQ2 How does the proposed method compare to standard approaches in terms of bias reduction when stable traits are unobserved?
• RQ3 Can the method recover true causal effects in settings with time-varying continuous treatments and unmeasured confounding due to stable traits?
• RQ4 What is the performance of the method under model misspecification, particularly in terms of robustness?
• RQ5 How does the method perform in real-world behavioral science data, such as sleep habits and mental health outcomes?

Key findings

• The proposed method successfully recovers causal parameters with minimal bias when stable traits are unobserved and act as confounders.
• Causal estimates were severely biased when stable traits were not properly accounted for, highlighting the importance of controlling for them.
• The use of SNMMs with G-estimation provided doubly robust estimation, maintaining consistency even under model misspecification.
• Simulation results demonstrated that within-person variability scores effectively captured time-varying treatment effects independent of stable traits.
• Empirical application to the Tokyo Teen Cohort data confirmed that the method yields more reliable causal estimates than conventional approaches.
• The method showed strong performance in disentangling within-person effects from stable trait influences in real-world behavioral science data.