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Robust evaluation of treatment effects in longitudinal studies with truncation by death or other intercurrent events

Georgi Baklicharov, Kelly Van Lancker, Stijn Vansteelandt

TL;DR

The key idea is to compare treated and untreated individuals, matched on baseline covariates, at the most recent time point before either experiences an intercurrent event, and develop asymptotically efficient, model-free tests and treatment effect estimators using data-adaptive nuisance parameter estimation.

Abstract

Intercurrent events, such as treatment switching, rescue medication, dropout, or truncation by death, frequently complicate intention-to-treat analyses in randomized clinical trials. Existing causal inference frameworks typically target hypothetical or principal stratum estimands (e.g., survivor average causal effects), which rely on unverifiable assumptions and can be sensitive to unmeasured confounders or positivity violations. We propose a novel approach that mitigates this sensitivity by using only information measured prior to the intercurrent event. Our key idea is to compare treated and untreated individuals, matched on baseline covariates, at the most recent time point before either experiences an intercurrent event. We call these contrasts Pairwise Last Observation Time (PLOT) estimands. PLOT estimands are identified in randomized trials without structural assumptions, even under severe positivity violations. Although PLOT-based tests may theoretically be susceptible to residual selection bias, we show this bias vanishes under standard conditions and remains negligible in extensive simulations. We develop asymptotically efficient, model-free tests and treatment effect estimators using data-adaptive nuisance parameter estimation. We evaluate performance via simulation and apply the method to re-analyze the DEVOTE trial, affected by truncation by death. PLOT offers a robust, data-driven alternative for evaluating treatment efficacy in the presence of complex intercurrent events.

Robust evaluation of treatment effects in longitudinal studies with truncation by death or other intercurrent events

TL;DR

The key idea is to compare treated and untreated individuals, matched on baseline covariates, at the most recent time point before either experiences an intercurrent event, and develop asymptotically efficient, model-free tests and treatment effect estimators using data-adaptive nuisance parameter estimation.

Abstract

Intercurrent events, such as treatment switching, rescue medication, dropout, or truncation by death, frequently complicate intention-to-treat analyses in randomized clinical trials. Existing causal inference frameworks typically target hypothetical or principal stratum estimands (e.g., survivor average causal effects), which rely on unverifiable assumptions and can be sensitive to unmeasured confounders or positivity violations. We propose a novel approach that mitigates this sensitivity by using only information measured prior to the intercurrent event. Our key idea is to compare treated and untreated individuals, matched on baseline covariates, at the most recent time point before either experiences an intercurrent event. We call these contrasts Pairwise Last Observation Time (PLOT) estimands. PLOT estimands are identified in randomized trials without structural assumptions, even under severe positivity violations. Although PLOT-based tests may theoretically be susceptible to residual selection bias, we show this bias vanishes under standard conditions and remains negligible in extensive simulations. We develop asymptotically efficient, model-free tests and treatment effect estimators using data-adaptive nuisance parameter estimation. We evaluate performance via simulation and apply the method to re-analyze the DEVOTE trial, affected by truncation by death. PLOT offers a robust, data-driven alternative for evaluating treatment efficacy in the presence of complex intercurrent events.

Paper Structure

This paper contains 14 sections, 7 theorems, 99 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Estimand
  3. Identification and estimation
  4. PLOT estimand: simple estimator
  5. CPLOT estimand
  6. Simulation experiments
  7. Assumptions for valid treatment effect testing
  8. Estimation of hypothetical estimands
  9. Additive Treatment Effects
  10. General Time-Varying Effects
  11. Application to the DEVOTE trial
  12. Discussion
  13. Proofs
  14. Estimation and inference

Key Result

Proposition 1

Under (conditional) randomization (or $A \hbox{$\perp\!\!\!\perp$} (Y^a(t), T^a)|L$ for $a=0,1$) and the consistency assumption, $E\left[ E\left\{Y^1(\min(T^1, T^{*0}, t))|L=L^*\right\}\right]$ can be identified as

Figures (4)

  • Figure 1: Pointwise Treatment Contrasts $\psi_s$ and Estimated Density of First ICE Time in a Matched Pair. Left axis: estimated contrasts $\psi_s$ (black points) with 95% Wald CIs (grey bars), admitting a hypothetical (Assumption \ref{['ass1']}) or SACE (Assumption \ref{['ass: sace']}) interpretation; see Section \ref{['sec: connection']}. Right axis: estimated density of $E[P\{\min(T^1, T^{*0}, t) = s \mid L=L^*\}]$ (shaded). Dashed line: null effect. Panel (b) y-axis restricted to $[0,3]$; later CIs truncated. Time $s$ in weeks from baseline.
  • Figure 2: Comparison of RMSE for different methods for $\gamma_1\in\{-2,-1.5,-1,-0.5,0,0.5,1,1.5,2\}$.
  • Figure 3: Comparison of mean estimate (left) and mean standard error (right) for different methods for $\gamma_1\in\{-2,-1.5,-1,-0.5,0,0.5,1,1.5,2\}$.
  • Figure 4: Counterfactual Survival. This figure displays the estimated counterfactual survival probabilities for insulin degludec (IDeg OD) and insulin glargine (IGlar OD) over a period of 132 weeks.

Theorems & Definitions (10)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Proposition 3
  • proof
  • Proposition 4
  • Proposition 5
  • proof
  • Theorem 2
  • proof