Longitudinal Outcomes Truncated by Death: Causal Estimands and Bayesian Estimators

Juliette Ortholand; Marie-Abele C Bind; Young Lee

arxiv: 2604.26410 · v1 · submitted 2026-04-29 · 📊 stat.ME · stat.AP

Longitudinal Outcomes Truncated by Death: Causal Estimands and Bayesian Estimators

Juliette Ortholand , Young Lee , Marie-Abele C Bind This is my paper

Pith reviewed 2026-05-07 11:16 UTC · model grok-4.3

classification 📊 stat.ME stat.AP

keywords causal estimandstruncated by deathlongitudinal outcomesBayesian estimationrestricted mean survival timeaverage causal effectamyotrophic lateral sclerosissurvival analysis

0 comments

The pith

Stratified average causal effects combined with restricted mean survival time provide a more complete characterisation of treatment effects when death truncates longitudinal outcomes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Longitudinal studies tracking patient health over time often encounter death that renders later outcomes undefined, which complicates defining what counts as a causal treatment effect. The paper sets out a framework to spell out these definitional difficulties, reviews a range of existing estimands together with the assumptions needed to identify them from observed data, and develops Bayesian estimators for each. Simulations compare estimator performance, and an application to amyotrophic lateral sclerosis trial data illustrates the ideas. The central point is that the absence of any natural ordering or distance measure for post-death outcomes turns the problem into a multifactorial one, so a single summary number is insufficient.

Core claim

The main difficulty in defining causal estimands for longitudinal outcomes truncated by death arises from the lack of a natural notion of ordering and distance for such outcomes, which leads to an inherently multifactorial problem. Within a proposed framework that clarifies the challenges of censoring due to death, existing estimands are reviewed and the assumptions required for their identification and estimation are made explicit. Bayesian estimators are developed for each estimand and compared in a simulation study. Using data from a randomized controlled trial in amyotrophic lateral sclerosis, the stratified average causal effect combined with restricted mean survival time is shown to be

What carries the argument

A framework that makes explicit the assumptions required for identification of causal estimands in longitudinal settings with death truncation, highlighting the multifactorial character caused by absent ordering and distance for post-death outcomes and supporting the stratified average causal effect paired with restricted mean survival time.

Load-bearing premise

Outcomes truncated by death have no natural ordering or distance, turning the causal question into an inherently multifactorial problem that requires specific assumptions for any estimand to be identified.

What would settle it

A simulation or real dataset in which the combination of stratified average causal effect and restricted mean survival time fails to detect a clinically meaningful treatment difference that an alternative single estimand successfully captures under the same data-generating process.

read the original abstract

Defining a causal estimand for a longitudinal outcome truncated by death is challenging, because the outcome may be undefined at the end of follow-up. Although a range of estimands and several estimators have been proposed, guidance on the underlying causal assumptions and on the contexts in which each estimand is most appropriate remains limited. We propose a framework to clarify the challenges of defining causal estimands in a longitudinal setting with censoring due to death. Within this framework, we review existing estimands and make explicit the assumptions required for their identification and estimation. We develop Bayesian estimators for each estimand and compare their behavior in a simulation study. Finally, we illustrate the proposed approach using data from a randomized controlled trial in amyotrophic lateral sclerosis. We show that the main difficulty arises from the lack of a natural notion of ordering and distance for outcomes truncated by death. This leads to an inherently multifactorial problem. In this context, the stratified average causal effect, combined with restricted mean survival time, provides a more complete characterisation of treatment effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a clear framework for causal estimands on longitudinal outcomes truncated by death, with Bayesian estimators and concrete examples, but the advance is mostly in organization and explicit assumptions rather than new identification results.

read the letter

The paper's core move is to frame the problem around the lack of natural ordering or distance for outcomes that become undefined after death. This leads them to review the main existing estimands, state the identification assumptions up front, and supply Bayesian estimators for each. They then compare the estimators in simulation and apply the approach to data from an ALS randomized trial. The central recommendation is that the stratified average causal effect paired with restricted mean survival time gives a more complete picture than single-estimand alternatives. That framing is the part that feels fresh and practical for people who actually analyze these trials. The simulation and ALS example are straightforward and help show how the estimators behave under the stated assumptions of sequential ignorability, positivity, and consistency. The work is transparent about what each estimand requires, which is useful even if the ideas build on prior literature. The softer spot is that the multifactorial claim and the push for the combined SACE-plus-RMST approach rest on conceptual grounds and the provided illustrations rather than on a decisive comparison that would rule out simpler single-estimand strategies in many settings. The Bayesian estimators are presented without extensive sensitivity checks or head-to-head results against frequentist alternatives, so readers will still need to judge whether the computational overhead is justified for their data. This is the kind of paper that methodologists and trial statisticians working on survival and longitudinal outcomes will find worth reading. It is solid enough on the assumptions and examples to merit peer review, even though the overall novelty is incremental.

Referee Report

0 major / 3 minor

Summary. The manuscript proposes a framework for defining and estimating causal effects on longitudinal outcomes truncated by death. It reviews existing estimands, explicitly states the identification assumptions (sequential ignorability, positivity, consistency, and principal-stratum definitions), develops Bayesian estimators for each, compares their performance in a simulation study, and illustrates the approach with data from a randomized trial in amyotrophic lateral sclerosis. The central claim is that the lack of a natural ordering or distance metric for death-truncated outcomes makes the problem inherently multifactorial, so that the stratified average causal effect combined with restricted mean survival time supplies a more complete characterization of treatment effects than single-estimand alternatives.

Significance. If the framework and estimators hold, the work provides a useful clarification tool for a notoriously difficult area of causal inference. Explicitly stating assumptions for each estimand, supplying Bayesian estimators, and offering both simulation comparisons and a real-data ALS example adds practical value. The recommendation to combine SACE with RMST is grounded in the reviewed literature rather than a new identification result, and the illustrative nature of the simulation and trial analysis is appropriately scoped.

minor comments (3)

The abstract states that assumptions are made explicit, but the main text should include a dedicated table or subsection that maps each reviewed estimand to its precise identifying assumptions for quick reference.
In the simulation study, clarify the precise data-generating process and the range of sample sizes or censoring rates examined so that readers can assess how representative the reported estimator behavior is.
Notation for principal strata and the definition of the stratified average causal effect should be introduced with a small illustrative example early in the methods section to aid readers unfamiliar with the principal-stratum approach.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and constructive review of our manuscript. The recommendation for minor revision is noted, and we will prepare a revised version addressing any editorial or minor points that may arise during the process.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reviews existing estimands for longitudinal outcomes truncated by death, explicitly states standard identification assumptions (sequential ignorability, positivity, consistency, and principal-stratum definitions), develops Bayesian estimators under those assumptions, and evaluates them via simulation study plus an ALS RCT illustration. The central recommendation—that the stratified average causal effect combined with restricted mean survival time supplies a more complete characterization—follows directly from the stated challenge of lacking natural ordering/distance for death-truncated outcomes, without any derivation step reducing to a fitted parameter, self-citation chain, or input-by-construction equivalence. The framework is presented as a clarification and review tool rather than a novel identification theorem, rendering the chain self-contained against external causal-inference benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available, so ledger is minimal; relies on standard causal inference assumptions for identification which are reviewed but not detailed here.

axioms (1)

domain assumption Standard causal assumptions required for identification of estimands in settings with death truncation
Paper states it makes explicit the assumptions required for identification and estimation of reviewed estimands.

pith-pipeline@v0.9.0 · 5480 in / 1198 out tokens · 64351 ms · 2026-05-07T11:16:40.825585+00:00 · methodology

discussion (0)

Reference graph

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