[Paper Review] Semiparametric estimation of structural failure time model in continuous-time processes

Shu Yang, Karen S. Pieper+1 more|arXiv (Cornell University)|Aug 20, 2018

Advanced Causal Inference Techniques4 citations

TL;DR

This paper proposes a semiparametric doubly robust estimator for structural failure time models in continuous-time observational studies, addressing time-varying confounding and dependent censoring without requiring artificial data discretization. By leveraging martingale-based identification and inverse probability of censoring weighting, the method ensures consistent estimation if either the treatment process or failure time model is correctly specified, enabling valid inference via resampling.

ABSTRACT

Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed to estimate the model parameters in the presence of time-dependent confounding and administrative censoring. However, most of existing methods require manually preprocessing data into regularly spaced data, which may invalidate the subsequent causal analysis. Moreover, the computation and inference are challenging due to the non-smoothness of artificial censoring. We propose a class of continuous-time structural failure time models, which respects the continuous time nature of the underlying data processes. Under a martingale condition of no unmeasured confounding, we show that the model parameters are identifiable from potentially infinite estimating equations. Using the semiparametric efficiency theory, we derive the first semiparametric doubly robust estimators, in the sense that the estimators are consistent if either the treatment process model or the failure time model is correctly specified, but not necessarily both. Moreover, we propose using inverse probability of censoring weighting to deal with dependent censoring. In contrast to artificial censoring, our weighting strategy does not introduce non-smoothness in estimation and ensures that the resampling methods can be used to make inference.

Motivation & Objective

• To develop a continuous-time structural failure time model that respects the natural timing of longitudinal data, avoiding artificial discretization.
• To address time-varying confounding in observational survival studies where treatment and confounders evolve over continuous time.
• To construct a semiparametric estimator that is doubly robust, ensuring consistency if either the treatment process or failure time model is correctly specified.
• To handle dependent censoring using inverse probability of censoring weighting, avoiding non-smoothness issues from artificial censoring methods.
• To enable valid inference through resampling techniques by ensuring smooth estimating equations.

Proposed method

• Formalizes a continuous-time structural failure time model using a distributional relationship between treatment and potential baseline failure time, relaxing the rank-preserving assumption.
• Imposes a martingale condition for no unmeasured confounding, enabling identification of model parameters from potentially infinite estimating equations.
• Derives a class of regular asymptotically linear semiparametric estimators using efficient score theory, including semiparametric efficient estimators.
• Proposes an optimal estimator within this class that is computationally tractable and maintains double robustness.
• Uses inverse probability of censoring weighting (IPCW) to adjust for dependent censoring, avoiding non-smoothness and enabling bootstrap-based inference.
• Applies l1-penalized regression to fit nuisance models for censoring and treatment processes, ensuring sparsity and stability in high-dimensional settings.

Experimental results

Research questions

• RQ1 Can a continuous-time structural failure time model be developed that avoids the need for data discretization in longitudinal observational studies?
• RQ2 Does the proposed estimator maintain double robustness in the presence of time-varying confounding and dependent censoring?
• RQ3 Can inverse probability of censoring weighting replace artificial censoring to preserve smoothness and enable resampling-based inference?
• RQ4 How does the performance of the proposed estimator compare to existing discrete-time methods under model misspecification?
• RQ5 What is the impact of misspecifying either the treatment process or failure time model on estimator bias and coverage in finite samples?

Key findings

• The proposed doubly robust estimator maintains consistent estimation when either the treatment process model or the failure time model is correctly specified, even if the other is misspecified.
• Under correct censoring model specification, the proposed IPCW-based estimator achieves coverage rates close to the nominal 95% level in simulations.
• When the censoring model is misspecified, coverage drops significantly (e.g., 61.6% to 81.4%), but the doubly robust estimator still shows reduced bias compared to naive or IPCW-only approaches.
• The estimator based on the optimal nuisance model (c^opt) achieves the lowest bias and mean squared error among all estimators in simulation settings.
• The discrete-time g-estimator (ψ_disc) performs poorly under continuous-time data, showing extreme bias (e.g., -1.09 for ψ* = 0.5), highlighting the need for continuous-time methods.
• In applications, l1-penalized Cox models are successfully used to estimate baseline and time-dependent hazard functions for censoring and treatment processes, enabling high-dimensional adjustment.