Longitudinal Outcomes Truncated by Death: Causal Estimands and Bayesian Estimators

Juliette Ortholand; Marie-Abele C Bind; Young Lee

REVIEW 2 major objections 6 minor 47 references

For trials where patients die before follow-up ends, the paper argues that pairing the survivor average causal effect with restricted mean survival time gives an interpretable treatment-effect picture without ranking death against disease s

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2026-08-02 15:15 UTC pith:JHUS6MZN

load-bearing objection Useful taxonomy and a defensible SACE+RMST recommendation, but the SACE estimator rests on an unstated conditional-independence assumption and the simulation priors are partly circular—still deserves refereeing. the 2 major comments →

arxiv 2604.26410 v3 pith:JHUS6MZN 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

classification stat.ME stat.AP MSC 62D2062F1562N0162P10

keywords causal estimandstruncation by deathprincipal stratificationsurvivor average causal effectrestricted mean survival timeBayesian estimationcomposite outcomesamyotrophic lateral sclerosis

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

When patients die before the end of follow-up, their longitudinal outcome is no longer a real number, and the treatment effect on that outcome is no longer well defined for everyone. The paper shows that existing estimands split into two classes: those that assume an ordering between death and the outcome scale—such as composite scores that treat death as the worst outcome—and those that avoid such an ordering, notably the survivor average causal effect (SACE) and restricted mean survival time (RMST). Because ordering assumptions encode either a biological claim or a patient preference that is rarely justified in chronic disease, the paper argues that SACE and RMST should be reported together: SACE captures the effect among patients who would survive under either treatment, and RMST captures the effect on survival itself. The authors support this by comparing Bayesian estimators in simulations and in an amyotrophic lateral sclerosis trial, finding that composite estimands can obscure an unfavorable survival effect when the treatment helps function but harms survival. If the paper is right, trials with death truncation should report these two estimands jointly rather than a single composite score.

Core claim

The paper's central claim is that estimands for longitudinal outcomes truncated by death fall into two classes: those that assume an ordering between death and the outcome scale (pairwise comparison, median of the composite outcome), and those that do not (SACE, RMST). Composite estimands encode a preference—commonly that death is worst—which is often inappropriate in chronic disease, where survival and function are driven by the same biological process and patients may value them differently. SACE avoids the ordering by restricting to always-survivors, whose longitudinal outcomes are real numbers under both treatments; RMST captures the survival effect over a fixed horizon. The paper theref

What carries the argument

The central machinery is the principal-stratification decomposition of the population by joint survival under both treatments: always-survivors (LL_t, live under either treatment), protected (DL_t), harmed (LD_t), and never-survivors (DD_t). SACE is the average treatment effect on the longitudinal outcome within LL_t; RMST is the integrated difference of survival curves. The classification of estimands turns on whether they order the post-death symbol * with the real-valued outcome scale. The Bayesian estimators combine a piecewise-constant proportional-hazards/Poisson model for survival (from which the always-survivor probability Ŝ^mis_i,t is computed) with a normal linear model for longitu

Load-bearing premise

The load-bearing premise is that, given baseline covariates, a patient's potential survival time under one treatment carries no information about their potential survival time under the other; if an unmeasured frailty drives both (so the diagonal-Poisson independence is false), the estimated always-survivor weights and the resulting SACE are systematically biased.

What would settle it

Simulate trials with a shared patient-level frailty that multiplies both potential hazards, so T(0) and T(1) are dependent given covariates; run the paper's Bayesian SACE estimator and compare it to the true always-survivor effect. If the estimated SACE shows bias that grows with the frailty variance, the conditional-independence assumption—not just finite-sample noise—is what the estimator depends on.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

If SACE and RMST are reported together, a trial can separately quantify a treatment's effect on function among always-survivors and its effect on survival, without collapsing them into one number that presupposes how death compares to disability.
Composite estimands such as pairwise comparison and median of composite outcome are only interpretable if the ordering assumption (e.g., death as worst outcome) is accepted; in chronic diseases that assumption can mask a harmful survival effect when the treatment benefits function.
The simulation shows that when treatment helps function but harms survival, composite estimands may flip from beneficial to harmful over time, while SACE alone only shows the functional benefit; RMST is needed to reveal the survival cost.
The MCO estimand can take infinite values in finite samples, limiting its practicality, whereas SACE and RMST always produce finite estimates.
Bayesian estimation with weakly informative priors gives posterior intervals for SACE and RMST, and the paper's application to the ALS trial shows credible intervals that include the null for both, suggesting no clear treatment effect on either dimension.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The ordering assumption could be relaxed by eliciting patient-specific utilities for survival-with-disability versus death, making composite estimands preference-sensitive rather than assuming a universal order; the paper's classification suggests a template for such preference-weighted estimands.
The SACE estimator's reliance on the estimated always-survivor probability Ŝ^mis_i,t inherits the survival model's assumption that potential survival times under the two treatments are conditionally independent given covariates; a sensitivity analysis introducing a shared frailty would test how robust SACE is to unmeasured common causes of death under both arms.
The two-step weighting structure suggests a diagnostic: when the estimated always-survivor probability is near zero for many observed survivors, SACE estimates will be unstable, and reporting the distribution of Ŝ^mis_i,t alongside SACE would make that fragility visible.
The estimand classification generalizes beyond ALS to any chronic disease with mortality and patient-reported or functional outcomes, providing a decision rule for choosing estimands before trial analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Useful taxonomy and a defensible SACE+RMST recommendation, but the SACE estimator rests on an unstated conditional-independence assumption and the simulation priors are partly circular—still deserves refereeing.

read the letter

The paper you ask about is a review-plus-simulation piece on estimands for longitudinal outcomes truncated by death. The thing to know: the central recommendation—report SACE and RMST together instead of a single composite score—strikes me as sensible, and the order/no-order taxonomy is a genuinely useful frame. But the paper's own evidence for SACE is weaker than the abstract suggests: the SACE estimator in §4.2.2 weights observed survivors by a model-based counterfactual survival probability that is only valid if the two potential survival times are conditionally independent, and that assumption is never flagged as load-bearing. Also, the simulation sets some priors to the true generating values, which makes the coverage results partly circular.

What it does well: it gives a clear map of the estimand landscape (ACE, RMST, SACE, PC, MCO, hypothetical estimands) and separates them by whether they need to order death against the outcome scale. The point that composite estimands implicitly encode patients' preferences is important for chronic disease. The Bayesian estimators are concretely specified, the code is public, and the simulation reports coverage and bias honestly, including the poor performance of SACE when mortality is high. That last fact actually undercuts their recommendation slightly, but they don't hide it.

Soft spots, in order. First, the independence assumption: §4.1.1 specifies a diagonal Poisson vector for (d(0), d(1)), which implies conditional independence of potential survival times given covariates. The SACE weights rely on this. If unmeasured frailty affects mortality under both arms, the always-survivor weights are wrong and SACE is biased. The paper never says "we assume conditional independence" in the identification section, and there is no sensitivity analysis. That is a real gap, and the reader's stress-test is right to flag it. Second, priors: the slope prior N(-2,3) and the hazard prior Gamma(0.035,0.1) are centered on the true simulated values. Appendix C shows slope misspecification doesn't change much, but hazard misspecification isn't tested. So the coverage results are optimistic. Third, SACE itself becomes unstable with high mortality (bias at 15 months is wide), which means the "pair with RMST" advice needs a caveat: SACE may be near-unidentifiable in the very settings where death truncation matters most.

Who benefits: biostatisticians and clinical trialists working in ALS or other fatal chronic diseases; also anyone who teaches estimands for truncation-by-death. It deserves a serious referee—the framework is coherent and the recommendation is practical, but both issues above need attention (at minimum, a stated independence assumption with sensitivity analysis). I'd engage with it.

Referee Report

2 major / 6 minor

Summary. The paper reviews causal estimands for longitudinal outcomes truncated by death, proposes a classification into estimands that require an ordering assumption placing death on the real-valued outcome scale (composite estimands such as PC and MCO) and estimands that do not (SACE and RMST). It develops Bayesian estimators for missing potential survival and longitudinal outcomes under a piecewise-constant proportional hazards model and a normal longitudinal model, evaluates them in simulations with four scenarios, and illustrates them on the olesoxime ALS RCT. The paper's central recommendation is that, in the presence of truncation by death, SACE and RMST should be reported together to give an interpretable, multidimensional characterization of treatment effects.

Significance. If the central claim holds, the paper provides a useful practical synthesis for trialists in chronic, fatal diseases: it clarifies that composite estimands encode value judgments about death versus disability that may not be clinically appropriate, while SACE and RMST avoid such ordering assumptions. The paper is commendable for its explicit finite-sample formulation, its reproducible public code, its honest tabulation of bias and coverage, and its application to a real ALS trial. However, the SACE estimator relies on a conditional independence assumption for potential survival times that is not stated, and the simulation study calibrates priors to the true generating values, so the empirical support for the recommendation is partly circular. The conceptual taxonomy is defensible, but the paper needs revision before the practical guidance can be accepted.

major comments (2)

[§4.1.1 and §4.2.2] The SACE estimator weights observed survivors by S_hat_mis_i,t, the model-based probability that the counterfactual survival time exceeds t. In §4.1.1, the joint model for (d_i,j(0), d_i,j(1)) is a diagonal bivariate Poisson, which implies T(0) ⟂ T(1) | X. This conditional independence is never stated or justified in the identification sections (§3.3.1, §4.1.1). Under unmeasured shared frailty or common genetic risk, observing T_obs > t under the assigned arm is informative about T_mis; the correct weight is Pr(T_mis > t | T_obs > t, X), not Pr(T_mis > t | X). Because the paper's central recommendation—report SACE alongside RMST—depends on SACE being reliably estimable, this missing assumption is load-bearing. Please state the assumption explicitly, justify it in the ALS context, or implement a sensitivity analysis with correlated potential survival times.
[§5.1 and Tables 8–9] The simulation sets the longitudinal slope prior β_u,0 ~ N(−2,3) to the simulated control slope and the hazard prior λ_u,j ~ Γ(0.035,0.1) to the true hazard range. These are not weakly informative priors in the usual sense; they are calibrated to the data-generating truth. Favorable coverage results (e.g., SACE 65–99%) may therefore reflect prior tuning rather than estimator performance. Appendix C checks only one alternative slope prior in the beneficial scenario and does not vary the hazard prior. Please add a systematic prior sensitivity analysis—varying both means and variances, including priors centered away from the truth—and discuss how bias and coverage change. This is load-bearing for the empirical claim that the proposed estimators are reliable.

minor comments (6)

[Table 3] The PC row appears to contain a duplicated term: the expression for τ_PC includes two identical '1/2 1(Z_i,t(1)=Z_i,t(0))' terms. Please correct.
[References] Reference [31] is incomplete: it contains placeholder text '<NOTEBOOK AUTHORS,S.A. <notebook title>'. This must be fixed.
[§5.1] In the sentence listing the estimators, 'MOC' should be 'MCO' (median of the composite outcome).
[§3.3.1] Typo: 'Conditionning' should be 'Conditioning'.
[§5.2 and Table 8] The PC estimator has 0% coverage in the beneficial and mixed scenarios, which is striking. The text notes prior sensitivity but does not interpret this coverage failure; please add a sentence explaining whether this is an artifact of the symmetric no-effect prior or a more general limitation of the PC estimator.
[§4.2.2] The formula for the RMST estimator is typeset awkwardly: the integral of S_hat_mis appears without a clear differential placement. Please reformat to avoid ambiguity.

Circularity Check

1 steps flagged

Simulation priors encode true data-generating values, making coverage validation partially circular; central SACE+RMST recommendation remains independent.

specific steps

other [Section 5.1 (Simulation Study); Supplementary A Tables 7-9]
"We assume prior knowledge on the longitudinal slope, and the priors are set to the simulated value β u,0_t ∼ N(−2,3). The simulated median survival lies between 18 and 22 months under a Weibull distribution (Supplementary A). Assuming a constant hazard over time and with equation 7, this corresponds to λ u,j ∈ [0.032,0.038]. Accordingly, we specify λ u,j ∼ Γ(0.035,0.1)."

The simulation study's validation targets—coverage and bias (Supplementary A Tables 8–9)—are evaluated using priors centered on the data-generating truth: the longitudinal slope prior N(−2,3) is centered on the true slope a0_0 = −2, and the hazard prior Γ(0.035,0.1) is centered on the true median survival range (18–22 months). Thus the reported coverage values are partly a consequence of the prior matching the truth, not an independent test of the estimators' calibration. This is a circular element in the simulation evidence, although it does not affect the paper's conceptual recommendation to pair SACE with RMST, which rests on the definitions and interpretation of the estimands rather than on these simulation results.

full rationale

The paper's central contribution is a conceptual review and recommendation: estimands for death-truncated longitudinal outcomes fall into two classes, and pairing SACE with RMST gives an interpretable characterization. This conclusion follows from the definitions of the estimands (SACE conditions on always-survivors; RMST summarizes survival) and from the stated implausibility of ordering death on the outcome scale. It is not derived by fitting a parameter and then predicting the same quantity, and there are no load-bearing self-citations: the cited works (Frangakis & Rubin, Imbens & Rubin, Mattei et al., Grossi et al.) are external, and the modeling choices are stated as assumptions, not imported as unverified author-specific results. The one genuine circular element is the simulation study: the priors for the longitudinal slope and hazard are explicitly set to the simulated truth, so the favorable coverage results are partly in-sample. The paper does include a prior-sensitivity check in Appendix C for the slope prior, which mitigates but does not eliminate this concern. The skeptical point about unstated conditional independence of potential survival times (diagonal Poisson in §4.1.1) is a substantive identification/correctness concern about bias under unmeasured frailty, not a circularity, because the model explicitly posits conditional independence and the paper acknowledges strong ignorability assumptions in the Discussion. Overall, the circularity is limited to a validation artifact and does not undermine the central argument's independence.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The central recommendation rests on standard causal assumptions that are plausible in RCTs, plus two stronger untestable assumptions: conditional independence of potential outcomes and, for composite estimands, a value judgment ordering death as worst. The simulation evaluation uses priors centered at the true generating values, which is a free-parameter concern.

free parameters (4)

Longitudinal slope prior mean β_{u,0} = N(-2,3) in simulation; N(-1,3) in ALS application
Hand-chosen: in the simulation it is set to the true simulated slope; in the application it is set to the literature progression rate. It affects SACE, PC, and MCO estimates.
Hazard prior baseline λ_{u,j} = Γ(0.035,0.1)
Chosen to match an expected median survival of 18-30 months; in the simulation this equals the true generating hazard range, making the prior unusually well calibrated.
Survival covariate effects α_u and piecewise hazards λ_{u,j} posterior = posterior samples
Estimated from data under the piecewise-constant proportional hazards model; standard model parameters.
Longitudinal intercepts/slopes β_{u,k,t} and residual SD σ_t = posterior samples
Estimated from data via the Normal linear model per treatment arm; weakly informative priors for covariates and residual SD.

axioms (8)

domain assumption SUTVA and no interference for survival and longitudinal outcomes
Stated in §4.1.1 and §4.1.2; standard and reasonable in an RCT.
domain assumption Strong ignorable treatment assignment given covariates for survival
Stated in §4.1.1; holds by randomization.
domain assumption Strong ignorable treatment assignment for longitudinal outcome conditional on principal strata
Stated in §4.1.2 and §7; acknowledged as strong and requiring substantive knowledge.
ad hoc to paper Conditional independence of potential survival times T(0) and T(1) given X
Implied by the diagonal Poisson model in §4.1.1 but never stated; load-bearing for the SACE weights.
ad hoc to paper Uncorrelated potential longitudinal outcomes given X and LL stratum
Stated in §4.1.2 as an assumption to avoid unsupported dependence; unidentifiable from data but does not affect the SACE mean parameter.
domain assumption Death as worst possible outcome ordering for PC and MCO estimands
Assumed in §3.2; a value judgment that may not reflect individual patient preferences in chronic disease.
domain assumption Missing at random for longitudinal outcomes conditional on covariates
Stated in §6.1 for the ALS application.
domain assumption Normal approximation for ALSFRS-R without floor or ceiling effects
Stated in §6.1; reasonable given baseline scores but an approximation.

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read the original abstract

In randomized controlled trials with longitudinal outcomes, death before the end of follow-up poses a fundamental challenge: after death, the outcome is no longer a real-valued measurement. This complicates the definition and interpretation of causal estimands, particularly when treatment may affect both survival and longitudinal outcomes. We review existing estimands for longitudinal outcomes truncated by death and clarify the assumptions required for their identification and estimation. We show that these estimands fall into two broad classes, distinguished by whether they require additional assumptions to compare longitudinal outcomes beyond death. Such assumptions may be inappropriate in chronic diseases, either because i) death and longitudinal outcomes are driven by the same underlying biological process or ii) the relative desirability of survival with poor function versus death may depend on individual preferences. We compare the behavior of the estimands in a simulation study using Bayesian estimators and illustrate their use with data from a randomized controlled trial in amyotrophic lateral sclerosis. We argue that, in the presence of death truncation, pairing the survivor average causal effect with the restricted mean survival time estimand provides an interpretable characterization of treatment effects on longitudinal and survival outcomes.

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Reference graph

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