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Implementing the principal stratum strategy for intercurrent events with survival outcomes: a tutorial

This tutorial paper reviews and demonstrates the implementation of the principal stratum strategy for handling intercurrent events in survival analysis within the ICH E9 (R1) estimand framework, offering a detailed guide on methodology, assumptions, sensitivity analysis, and R code through a clinical oncology example and simulation studies.

Original authors: Xiaoxiao Zhou, Joyce Chen, Pallavi Mishra-Kalyani, Xiaoxue Li, Yuan Li Shen, Shu Wang, Susan Halabi, Fan Li

Published 2026-05-28

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiaoxiao Zhou, Joyce Chen, Pallavi Mishra-Kalyani, Xiaoxue Li, Yuan Li Shen, Shu Wang, Susan Halabi, Fan Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a race to see which of two running shoes (Shoe A vs. Shoe B) helps people run the longest. You randomly give half the runners Shoe A and the other half Shoe B.

But here's the problem: during the race, many runners stop wearing their assigned shoes. Maybe Shoe A hurts their feet, so they switch to Shoe B. Maybe Shoe B falls apart, so they quit the race entirely.

In a standard analysis, you would just look at who finished the race first, regardless of whether they kept wearing their assigned shoe. This is called "Intention-to-Treat." It's fair, but it doesn't tell you if Shoe A is actually better at helping people run, or if the people who stopped wearing it just happened to be slower runners to begin with.

This paper is a tutorial (a step-by-step guide) for scientists on how to answer a much harder question: "If a runner had stuck with their assigned shoe the whole time, how would they have done?"

The authors call this the "Principal Stratum Strategy." Here is how they explain it using simple concepts:

1. The "Time Travel" Problem

To know if a shoe works, you need to know what would have happened if a runner never stopped wearing it. But you can't time travel. You can only see what actually happened.

You see a runner who wore Shoe A for 10 minutes and then quit.
You don't know if they would have quit even if they had been assigned Shoe B.
You don't know if they would have kept going if they had been assigned Shoe A.

Because you can't see the "what if," these groups of runners are invisible (latent). The paper calls these invisible groups "Principal Strata."

2. The Four Invisible Teams

The authors imagine that every runner belongs to one of four invisible teams based on how they would react to the shoes, regardless of which one they actually got:

The "Always-Continuers": People who would keep wearing the shoe no matter which one they got. (These are the people we really want to study to see if the shoe works).
The "Always-Quitters": People who would quit no matter which shoe they got.
The "Switchers": People who would quit if they got the "bad" shoe but keep going if they got the "good" shoe.
The "Reverse Switchers": People who would quit if they got the "good" shoe but keep going if they got the "bad" shoe.

Since you can't see which team a person is on, you have to use math to guess.

3. Two Ways to Guess the Invisible Teams

The paper teaches two different mathematical "magic tricks" to separate these invisible teams and calculate the results:

Method 1: The Mixture Model (The "Blender" Approach)
Imagine you have a smoothie made of four different fruits (the four teams). You can taste the smoothie (the data), but you can't see the individual fruits. This method uses a computer to "un-blend" the smoothie. It makes guesses about the ingredients based on the taste and the recipe (the assumptions). It is very flexible but requires a lot of computer power and careful guessing.
Method 2: The Weighting Method (The "Scale" Approach)
This method is like putting weights on a scale. It looks at the runners who did quit and tries to find runners who didn't quit but look exactly like them (same age, same health, etc.). It then "weights" the data to pretend that the invisible teams are visible. This method is faster and often more precise, but it relies on a strict rule: that the "invisible" reasons for quitting are fully explained by the information we already have (like age or health).

4. The Real-World Test: The Cancer Trial

To prove these methods work, the authors tested them on a real medical study about kidney cancer.

The Scenario: Patients were given a new drug or a standard drug. Many stopped taking the new drug because of side effects (toxicity).
The Goal: They wanted to know: "If the patients who stopped the new drug had been able to keep taking it, would they have lived longer?"
The Result: Both methods agreed on the big picture:
- For the "Always-Continuers" (the people who could tolerate the drug), the new drug didn't seem to make a huge difference in survival time compared to the old drug.
- However, the math showed that the results were uncertain. The "confidence intervals" (the margin of error) were very wide. It's like saying, "The new shoe might help, or it might hurt, or it might do nothing—we just can't be sure yet."

5. The "What If" Safety Check (Sensitivity Analysis)

Because these methods rely on guessing about invisible people, the authors emphasize the importance of Sensitivity Analysis.
Think of this as a stress test. You ask: "What if my guess about the invisible teams was slightly wrong?"

If the answer changes drastically when you tweak the guess, the result is fragile.
If the answer stays roughly the same, the result is robust.
The paper shows that even when they changed their assumptions, the main conclusion (that the drug didn't clearly help the "always-continuers") remained the same.

Summary

This paper is a guidebook for scientists who want to look past the "noise" of people quitting treatments in clinical trials. It teaches them how to use advanced math to isolate the specific group of people who could stick with a treatment, to see if the treatment actually works for them.

The authors conclude that while this strategy is powerful and gives deeper insights than standard methods, it is complex and often results in uncertain answers because we are trying to measure things we can't directly observe. They urge scientists to use these tools carefully, check their assumptions, and use both methods (the "Blender" and the "Scale") to see if they agree.

Technical Summary: Implementing the Principal Stratum Strategy for Intercurrent Events with Survival Outcomes

Problem Statement
Clinical trials frequently encounter intercurrent events (ICEs)—post-randomization events that affect the interpretation or existence of outcome measurements. The ICH E9 (R1) addendum introduced the estimand framework to address ICEs, offering five strategies: treatment policy, hypothetical, principal stratum, while on treatment, and composite. Among these, the principal stratum strategy is the most conceptually and technically challenging because it defines treatment effects on unobserved (latent) subpopulations based on counterfactual ICE statuses. While the framework is established, practical guidance for implementing the principal stratum strategy, particularly with survival (time-to-event) outcomes, remains limited. Existing literature often focuses on general principles or non-censored outcomes, leaving a gap in regulatory and clinical practice regarding how to estimate these effects when censoring is present.

Methodology
The paper focuses on a specific, common scenario: a binary treatment and a single binary ICE (treatment discontinuation). It defines the target estimand as the survival principal causal effect (SPCE) within specific principal strata, specifically the "always-continuer" stratum ( $U=(0,0)$ ), representing patients who would continue treatment regardless of assignment.

The authors review and compare two primary estimation approaches for survival outcomes:

The Mixture Modeling Approach (Bayesian):
- Concept: Treats the observed data as a mixture of latent strata. It employs a strata model (multinomial logistic regression) to predict principal stratum membership (principal scores) and an outcome model (Weibull-Cox proportional hazards) to model survival within strata.
- Assumptions: Relies on unconfounded assignment, monotonicity (e.g., active treatment is more likely to cause discontinuation), and often the Exclusion Restriction (ER) assumption (treatment has no effect on strata where the ICE occurs regardless of assignment, e.g., "always-discontinuers").
- Implementation: Uses Bayesian inference (MCMC/HMC) to handle unobserved strata membership, implemented via the PStrata R package.
The Principal Score Weighting Approach (Frequentist):
- Concept: A "multiply robust" estimator that avoids direct modeling of latent strata by using weighting. It relies on the Principal Ignorability (PI) assumption, which posits that conditional on covariates, the potential survival functions are identical between specific strata (e.g., $U=11$ and $U=01$ ).
- Assumptions: Requires unconfounded assignment, monotonicity, and PI.
- Implementation: Involves estimating four models: propensity score, principal score (derived from observed ICE probabilities), time-to-event, and time-to-censoring. It uses inverse probability weighting to adjust for confounding. Implemented via the mrPStrata R package.

Key Contributions

Tutorial and Implementation: The paper provides a comprehensive tutorial bridging the gap between theoretical principal stratification and practical implementation for survival data.
Software and Code: It details the use of two specific R packages (PStrata and mrPStrata) and provides example R code for both synthetic and real data.
Sensitivity Analysis Framework: The authors elaborate on methods to assess the robustness of results to violations of key assumptions (monotonicity, ER, and PI) using sensitivity parameters (e.g., $\xi$ for PI, $\zeta$ for monotonicity).
Case Study: The methods are applied to the CALGB 90206 trial (metastatic renal cell carcinoma), re-analyzing the effect of bevacizumab plus interferon alfa versus interferon alfa monotherapy on overall survival, accounting for treatment discontinuation.
Simulation Study: Extensive simulations mimicking the CALGB 90206 trial were conducted to evaluate the operating characteristics (bias, coverage, precision) of both methods under various assumption violations.

Results

Case Study Findings: In the CALGB 90206 re-analysis, both methods indicated heterogeneity in treatment effects across principal strata. For the target "always-continuer" stratum, the intervention showed a null effect on survival. The "always-discontinuer" stratum showed a harmful effect, while other strata showed protective effects.
Precision and Uncertainty: The weighting method yielded significantly narrower confidence intervals (higher precision) compared to the mixture model, attributed to the stronger PI assumption. However, both methods produced wide credible/confidence intervals that included zero for the primary target stratum, leading to inconclusive results regarding the intervention's efficacy for continuers.
Sensitivity: Results were generally robust to variations in the sensitivity parameters for PI and monotonicity, though the mixture model showed greater uncertainty without restrictive assumptions like ER.
Simulation: The simulations confirmed that both methods can recover true causal effects for strata with sufficient sample sizes (e.g., 00 and 11) even with mild assumption violations. However, for strata with few units (e.g., 10 or 01), both methods produced unreliable estimates with wide intervals, highlighting the intrinsic difficulty of identifying small latent subpopulations.

Significance and Claims
The paper claims to provide a necessary resource for practitioners and regulators to implement the principal stratum strategy for survival outcomes, an area previously considered inaccessible. It emphasizes that while the strategy offers refined clinical insights beyond standard Intention-to-Treat (ITT) analysis by characterizing treatment effect heterogeneity, it is fraught with large uncertainties even in simple binary ICE scenarios.

The authors modestly conclude that:

The principal stratum strategy is conceptually and technically complex, and its adoption requires careful consideration of the plausibility of underlying causal assumptions (monotonicity, ER, PI).
There is no single "best" method; the choice depends on the clinical context and the plausibility of assumptions. They recommend analyzing data with both methods; concordant results lend credibility, while discordant results suggest assumption violations.
Sensitivity analysis is not optional but essential for interpreting results, as the assumptions required for identification are untestable from observed data alone.
The strategy is most suitable for handling a single ICE; extending it to multiple ICEs leads to an exponential increase in strata, often rendering estimation infeasible without strong, potentially unrealistic assumptions.