REVIEW 7 minor 2 references
Dealing with multiple intercurrent events using hypothetical and treatment policy strategies simultaneously
T0 review · 0 major / 7 minor · reviewed 2026-08-09 · deepseek-v4-flash
Pith's one-line read The causal ordering of rescue and discontinuation determines whether and how discontinuation enters the analysis of a hypothetical estimand.
desk verdict Careful, useful paper: it separates two estimands that ICH E9 language conflates and shows the causal ordering of intercurrent events dictates the adjustment set; the main caveat is the known-ordering assumption, which the authors acknowledge. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The carrying tools are DAGs and single-world intervention graphs (SWIGs). DAGs encode the assumed causal ordering of treatment, the two intercurrent events, covariates, and outcome; a SWIG represents the post-intervention world after setting $A=a$ and $R=0$, and it shows which paths remain open from $R$ to the potential outcome $Y^{a,r=0}$. That determines whether $D$ is ignored, included as a time-varying confounder at visit $k$, or included at visit $k+1$. The cross-world estimand cannot be drawn in a single SWIG, which is why it requires an extra cross-world independence assumption that does not follow from the intervention graphs alone.
What would settle it
Generate data under the DAG where rescue use $R$ precedes discontinuation $D$ and analyse it with the inverse-probability-weighting variant that assumes no $D$--$R$ effect; the paper's claim predicts bias and confidence intervals that miss the true effect, so observing nominal coverage in a correctly specified simulation would directly refute the claim that the ordering must enter the analysis.
Extended reading notes
Core claim
The central claim is that the EMA-style choice of handling rescue medication $R$ hypothetically and treatment discontinuation $D$ by treatment policy can be formalised in two genuinely different ways. The hypothetical estimand $E[Y^{a=1,r=0} - Y^{a=0,r=0}]$ lets $D$ take whatever value it would take once $R$ is intervened on; $D$ is then a post-intervention variable, and it must be adjusted for as a time-varying confounder exactly when it is a common cause of $R$ and $Y$. The cross-world hypothetical estimand $E[Y^{a=1,r=0,D^{a=1,R^{a=1}}} - Y^{a=0,r=0,D^{a=0,R^{a=0}}}]$ keeps $D$ at its natural value in the unset world; this mixture of worlds cannot be drawn in a single single-world intervention graph, has no possible trial interpretation, and is identifiable only under a cross-world assumption. For the first estimand, identification uses standard consistency, conditional exchangeability, and positivity; for the second, the paper shows that an imputation-style estimator identifies the quantity when a cross-world independence holds. The simulations show that, of three inverse-probability-weighting variants, only the one respecting the true causal ordering of $D$ and $R$ is unbiased.
Load-bearing premise
The load-bearing premise is that the causal ordering of the two intercurrent events is known, fixed for all patients, and fully captured by the assumed DAG; if the true ordering varies or is mis-specified, the analysis targets a different quantity, and if an unmeasured common cause directly affects the outcome, no adjustment set fixes it.
Editorial extensions
If this is right
- Trial teams that follow the EMA-style choice must decide, and state in the statistical analysis plan, whether discontinuation precedes or follows rescue use; the wrong choice biases the estimate of the treatment effect.
- If discontinuation and rescue use do not affect each other, $D$ can be ignored in the imputation and weighting models; if $D$ precedes $R$, $D$ belongs in that visit's time-varying confounder set; if $R$ precedes $D$, $D$ enters the next visit's confounder set.
- The cross-world version of the estimand, in which discontinuation keeps its natural value, is identifiable only under a cross-world assumption, but no conceivable trial realizes it; the paper advises that stakeholders generally should not use it.
- With more than two intercurrent events handled by the treatment policy strategy, each additional event becomes part of the appropriate time-varying confounding set, so the same ordering logic generalizes.
- The hypothetical estimand itself is identified by standard time-varying confounding assumptions; an unmeasured common cause of $D$ and $Y$ with a direct effect on $Y$ breaks identification even when the ordering is correctly specified.
Reading between the lines
- Beyond the paper: when true orderings vary across patients, the DAG-based target becomes a mixture over orderings; a practical step the paper leaves implicit is a sensitivity analysis that repeats the analysis under plausible orderings and reports the spread of estimates.
- Beyond the paper: the same two-interpretation ambiguity should reappear when two intercurrent events are both handled by the hypothetical strategy but one causes the other; the paper does not work out that case, but its SWIG logic suggests the estimand would again split into a single-world and a cross-world version.
- Beyond the paper: in trials where event times are recorded, comparing estimates under different assumed orderings can serve as a diagnostic check on whether the protocol's ordering assumption is consistent with the data.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper addresses the definition, identification, and estimation of clinical-trial estimands when two intercurrent events are handled by different strategies: one by the treatment policy strategy and the other by the hypothetical strategy. Using potential outcomes and single-world intervention graphs, the authors define a primary 'hypothetical estimand' E[Y^{a=1,r=0} - Y^{a=0,r=0}] (Eq. 3) and a contrasting 'cross-world hypothetical estimand' (Eq. 4), and they show that the estimand and the required adjustment set depend on the assumed causal ordering of the two intercurrent events, D and R. The paper extends the discussion to a longitudinal setting with two time points, gives multiple imputation and inverse probability weighting algorithms under three causal structures, and demonstrates via simulation that only the IPW estimator whose adjustment set matches the true causal structure is unbiased. The motivating diabetes trial is revisited to illustrate the practical choice of ordering, and the paper concludes by recommending that trial protocols state the causal ordering of intercurrent events.
Significance. If the paper's claims hold, it makes a useful and practically important contribution to the implementation of the ICH E9(R1) estimand framework. The central conceptual point—that the phrase 'one ICE handled by treatment policy and another by the hypothetical strategy' does not define a unique causal estimand—is clearly made and is supported by formal graphical arguments. Strengths of the paper include the explicit statement of consistency, conditional exchangeability, and positivity assumptions in Section 4; the transparent treatment of the cross-world estimand, whose strong cross-world assumption (23) is stated explicitly and whose usefulness is appropriately questioned; the extension to longitudinal settings with concrete algorithms in Section 5; and the simulation study in Section 6, which is calibrated against a known generative model and whose R code is publicly available. The paper's limitation that the causal ordering of D and R may be unknown or vary across individuals is acknowledged by the authors and does not undermine the theoretical contribution, though it does constrain direct application.
minor comments (7)
- [§3, Eq. (3)] The statement that the estimands in Figure 1 j), k), and l) 'both reduce to' E[Y^{a=1,r=0} - Y^{a=0,r=0}] is concise to the point of being potentially misleading: in the column where R affects D, the D appearing in Y^{a,r=0} is D^{a,r=0}, not D^a. A sentence making this explicit would prevent misreading.
- [§5, first paragraph] The text says the estimation algorithms are described 'under the three causal structures depicted in Figure 5 a), b) and c)', but the relevant panels appear to be a), c), and e). Please correct the panel references.
- [Table 1] The first row, 'The ICEs do not affect each other. The treatment policy ICE can be ignored', should be read together with the Section 4 discussion of an unmeasured common cause U of D and R; as the text correctly notes, if a shared cause exists, D must still be accounted for even when there is no direct arrow between D and R. The table could state this qualification explicitly to avoid a misleading shortcut.
- [§6, Figure 6] The simulation results are presented only as box plots. Reporting numerical summaries such as Monte Carlo mean bias, empirical standard error, and coverage of confidence intervals would strengthen the reproducibility and allow readers to assess the magnitude of the biases shown.
- [§7 and References] There are minor consistency issues in naming: the text refers to 'EMEA guidelines' in Section 7 while earlier sections and the abstract use EMA, and the reference list gives 'European Medicines Society' where the intended body is the European Medicines Agency. These should be harmonized.
- [Figure 2 caption] The caption says 'unmeasured variables affecting D and U' but the figure and text indicate that U affects D and R. This typo should be corrected.
- [Title page] The affiliation contains typographical errors: 'Enviromental Medicine' should be 'Environmental Medicine', and 'Karolinska Universitet' should be 'Karolinska Institutet'.
Circularity Check
No significant circularity: the estimands, identification assumptions, and simulation are self-contained, with self-citations supplying tools rather than load-bearing conclusions.
full rationale
The paper's central claims are not circular. Section 3 defines the estimands as explicit potential-outcome expressions (Eqs. 1-4), where the distinction between the hypothetical estimand (3) and the cross-world hypothetical estimand (4) follows from how D is indexed under the intervention on R, not from a fitted parameter. Section 4 derives identification via stated consistency, exchangeability, and positivity assumptions using SWIGs, and Section 5 spells out the resulting MI and IPW algorithms for each causal ordering. The simulation in Section 6 generates data from a known mechanistic model, computes the true effect by simulating potential outcomes under R=0, and then compares the estimators; no fitted value is renamed as a prediction. The supplementary material's identification of the cross-world estimand is an explicit proof from assumptions (5)-(23), including the plainly labeled cross-world assumption (23), rather than an imported uniqueness claim. Self-citations to Olarte Parra et al. (2023, 2025) and Ocampo & Bather (2023) are used for the SWIG framework and for prior estimation approaches, but the paper's key conclusion—that the assumed causal relationship between D and R determines whether and how D enters the analysis—is established in the text and demonstrated by simulation, not derived from those citations. The acknowledged uncertainty about the temporal ordering of intercurrent events is a stated practical limitation of applying the framework, not a circular step in its derivation.
Assumptions & free parameters
free parameters (1)
- Simulation coefficients alpha, beta, gamma =
alpha=-1, beta=0.25, gamma=1
assumptions (6)
- domain assumption Consistency: observed outcome equals the potential outcome under the assigned treatment and observed intercurrent event values.
- domain assumption Conditional exchangeability for the hypothetical ICE R: Y^{a,r=0} is independent of R given A, L0, L1 (and D where D is a common cause).
- domain assumption Positivity for the hypothetical ICE R: P(R=0|A,L0,L1)>0 for all strata.
- domain assumption The causal ordering of D and R is known and identical across individuals.
- domain assumption No unmeasured common cause of D and R that also directly affects Y (for Figure 2b identifiability).
- domain assumption Non-parametric structural equation model interpretation of the DAG (for the cross-world estimand).
Cite this review
Pith. "Pith review of Dealing with multiple intercurrent events using hypothetical and treatment policy strategies simultaneously." pith.science (2026). https://pith.science/paper/P2L5D2KS
@misc{pith2026250203329,
author = {Pith},
title = {Pith review of: Dealing with multiple intercurrent events using hypothetical and treatment policy strategies simultaneously},
year = {2026},
howpublished = {\url{https://pith.science/paper/P2L5D2KS}},
note = {Machine review of arXiv:2502.03329}
}
read the original abstract
To precisely define the treatment effect of interest in a clinical trial, the ICH E9 estimand addendum describes that relevant so-called intercurrent events should be identified and strategies specified to deal with them. Handling intercurrent events with different strategies leads to different estimands. In this paper, we focus on estimands that involve addressing one intercurrent event with the treatment policy strategy and another with the hypothetical strategy. We define these estimands using potential outcomes and causal diagrams, considering the possible causal relationships between the two intercurrent events and other variables. We show that there are different causal estimand definitions and assumptions one could adopt, each having different implications for estimation, which is demonstrated in a simulation study. The different considerations are illustrated conceptually using a diabetes trial as an example.
Figures
Figures from the paper (3 more)
Reference graph
Works this paper leans on
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[1]
Committee for Medicinal Products for Human Use (2023), ‘Guideline on clinical investiga- tion of medicinal products in the treatment or prevention of diabetes mellitus’, European Medicines Society. Hernán, M. A. (2004), ‘A definition of causal effect for epidemiological research’,Journal of Epidemiology & Community Health 58(4), 265–271. Hernan, M. A. & R...
work page 2023
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[2]
Consistency and Composition Assumptions We make use of the following consistency and composition assumptions. In fact these fol- low from DAG 4a) when this DAG is interpreted as a non-parametric structural equation model(Pearl 2010). La 1 = L1 when A = a (5) Ra = R when A = a (6) Da,r = D when A = a and R = r (7) Y a,r = Y when A = a and R = r (8) Y a,r,d...
work page 2010
Reviewed August 9, 2026 · model on record in the stance chip above.
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