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A Causal Framework for Quantile Residual Lifetime

Taekwon Hong, Woojung Bae, Sang Kyu Lee, Dongrak Choi, Jong-Hyeon Jeong

TL;DR

A formal causal framework for estimating quantiles of residual lifetime among individuals surviving to a landmark time and introducing a reweighting-based supplementary estimator for the Principal Survivor Quantile Contrast to disentangle mechanisms under stronger assumptions is proposed.

Abstract

Estimating prognosis conditional on surviving an initial high-risk period is crucial in clinical research. Yet, standard metrics such as hazard ratios are often difficult to interpret, while mean-based summaries are sensitive to outliers and censoring. We propose a formal causal framework for estimating quantiles of residual lifetime among individuals surviving to a landmark time $t_0$. Our primary estimand, the "Observed Survivor Quantile Contrast" (OSQC), targets pragmatic prognostic differences within the observed survivor population. To estimate the OSQC, we develop a doubly robust estimator that combines propensity scores, outcome regression, and inverse probability of censoring weights, ensuring consistency under confounding and informative censoring provided that the censoring model is correctly specified and at least one additional nuisance model is correctly specified. Recognizing that the OSQC conflates causal efficacy and compositional selection, we also introduce a reweighting-based supplementary estimator for the "Principal Survivor Quantile Contrast" (PSQC) to disentangle these mechanisms under stronger assumptions. Extensive simulations demonstrate the robustness of the proposed estimators and clarify the role of post-treatment selection. We illustrate the framework using data from the SUPPORT study to assess the impact of right heart catheterization on residual lifetime among intensive care unit survivors, and from the NSABP B-14 trial to examine post-surgical prognosis under adjuvant tamoxifen therapy across multiple landmark times.

A Causal Framework for Quantile Residual Lifetime

TL;DR

A formal causal framework for estimating quantiles of residual lifetime among individuals surviving to a landmark time and introducing a reweighting-based supplementary estimator for the Principal Survivor Quantile Contrast to disentangle mechanisms under stronger assumptions is proposed.

Abstract

Estimating prognosis conditional on surviving an initial high-risk period is crucial in clinical research. Yet, standard metrics such as hazard ratios are often difficult to interpret, while mean-based summaries are sensitive to outliers and censoring. We propose a formal causal framework for estimating quantiles of residual lifetime among individuals surviving to a landmark time . Our primary estimand, the "Observed Survivor Quantile Contrast" (OSQC), targets pragmatic prognostic differences within the observed survivor population. To estimate the OSQC, we develop a doubly robust estimator that combines propensity scores, outcome regression, and inverse probability of censoring weights, ensuring consistency under confounding and informative censoring provided that the censoring model is correctly specified and at least one additional nuisance model is correctly specified. Recognizing that the OSQC conflates causal efficacy and compositional selection, we also introduce a reweighting-based supplementary estimator for the "Principal Survivor Quantile Contrast" (PSQC) to disentangle these mechanisms under stronger assumptions. Extensive simulations demonstrate the robustness of the proposed estimators and clarify the role of post-treatment selection. We illustrate the framework using data from the SUPPORT study to assess the impact of right heart catheterization on residual lifetime among intensive care unit survivors, and from the NSABP B-14 trial to examine post-surgical prognosis under adjuvant tamoxifen therapy across multiple landmark times.
Paper Structure (42 sections, 3 theorems, 74 equations, 1 figure, 5 tables)

This paper contains 42 sections, 3 theorems, 74 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Causal framework for quantile residual lifetime
  3. Setup and target estimand
  4. Assumptions
  5. Identification of the Causal Residual Lifetime Distribution
  6. Estimation and Inference
  7. IW Estimator
  8. Proposed DR Estimator
  9. Inference
  10. Supplementary Analysis: Decomposing Prognostic and Compositional Effects
  11. Principal Stratification and Reweighting
  12. Implementation
  13. Simulation Study
  14. Simulation Setup
  15. Simulation Results
  16. ...and 27 more sections

Key Result

Theorem 1

Suppose Assumptions ass:consistency--ass:censoring hold. Then, for each $a\in\{0,1\}$, $t_0>0$ and $r\ge 0$, the causal distribution $F_{R_a}(r;t_0)$ in eq:FR_def is identified and satisfies In particular, the quantile $q_a(\tau;t_0)$ defined in eq:qa_def is identified for all $0<\tau<1$.

Figures (1)

  • Figure 1: Causal DAG representing the data structure. $X$: baseline covariates; $A$: baseline treatment; $T$: event time; $C$: censoring time. Identification assumes no unmeasured confounding of $(A,T)$ given $X$, and independent censoring given $(A,X)$.

Theorems & Definitions (5)

  • Theorem 1: Identification of the residual-lifetime CDF
  • Theorem 2: Double Robustness
  • Theorem 3: Identification of PSQC Quantile
  • Remark : Assumption Burden and the Role of Supplementary Analysis
  • Remark : Why the PSQC Quantile is Identified via IW