# Modelling for Principal Stratification: Analyzing Stroke Events in CADASIL Patients Across NOTCH3 Variant

Léa Aguilhon, Sophie Tezenas Du Montcel, Juliette Ortholand

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Léa Aguilhon, Sophie Tezenas Du Montcel, Juliette Ortholand. Modelling for Principal Stratification: Analyzing Stroke Events in CADASIL Patients Across NOTCH3 Variant. ISCB 2025 - 46th Annual Conference of the International Society for Clinical Biostatistics, Aug 2025, Basel, Switzerland. hal-05285233

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Submitted on 26 Sep 2025

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# Modelling for Principal Stratification: Analyzing Stroke Events in CADASIL Patients Across NOTCH3 Variant

L. AGUILHON¹, S. TEZENAS DU MONTCEL¹, J. ORTHOLAND¹

1 - Inria, centre of Paris, ARAMIS team, Sorbonne Université, Institut du Cerveau / Paris Brain Institute AP-HP, INSERM, CNRS, University Hospital, Paris, France

ARAMIS
LAB
BRAIN DATA SCIENCE

<figure><img src="image_1.png" /></figure>

lea.aguilhon@icm-institute.org

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http://www.aramislab.fr/

## Background & Objectives

Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL), a cerebral small vessel disease caused by **NOTCH3 mutations**, shows heterogeneity in age of onset, symptom severity, and stroke recurrence. Variants in **EGFr domains 1-6** may worsen disease progression, but post-stroke trajectories remain unclear. Traditional studies face bias from competing risks (death truncating stroke observation). To address this, we propose a **causal inference approach**: first **comparing mutation types** and **first stroke incidence**, then analyzing **second strokes** using **Principal Stratification**, a method that accounts for immortal time bias by modeling latent survival outcomes. Finally, we assess **mortality** differences between variant groups. This framework enables unbiased estimation of variant-specific stroke risks, improving disease trajectory understanding for clinical trials.

## Methods

### Population

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- 326 CERVCO's CADASIL patients
- First visit between 2005 and 2021
- Have done at least one stroke before or after inclusion (165 had a 2nd stroke)

<figure><img src="image_4.png" /></figure>

Reference time = Age first stroke

<figure><img src="image_5.png" /><figcaption>Figure 1: Schema inclusion criteria with first stroke</figcaption></figure>

### Covariates

- Sex
- Education level

- EGF domain mutation
- Age first stroke

- Cardiovascular risk factors

- Alcohol

- Hypertension

- Hypercholesterolemia

- Smoking

### Events outcomes

- Death

- Second stroke

<table><caption>Table 1: Classification of strata for principal stratification based on predicted survival status from a Cox model, based on mutation status</caption><thead><tr><th>Stratas</th><th>Y(0)<br>7-34 mutation</th><th>Y(1)<br>1-6 mutation</th></tr></thead><tbody><tr><td>Always-survivors</td><td>Alive</td><td>Alive</td></tr><tr><td>Protected</td><td>Dead</td><td>Alive</td></tr><tr><td>Harmed</td><td>Alive</td><td>Dead</td></tr><tr><td>Never-survivors</td><td>Dead</td><td>Dead</td></tr></tbody></table>

### Statistical Method

1. **Propensity score matching** for covariates balancing to create a pseudo-randomized and population groups (1-6 vs 7-34 mutations).
   → Avoid observational bias

2. **Survival model adjusted (Cox model) to predict principal stratification**
   → Neutralizes competing influences on survival, so the principal stratification reflects mutation-specific effects

3. **Selection of Always-survivors**
   → Avoids immortal time bias and competing risk from death, isolating the pure effect on stroke recurrence

4. **RMST (Restricted Mean Survival Time)** comparison between EGFr 1-6 and 7-34 groups
   → Provides an interpretable estimand, robust to censoring and model assumptions

## Results

1

<figure><img src="image_6.png" /><figcaption>Figure 2: Love plot assessing covariate balance before and after matching</figcaption></figure>

<figure><img src="image_7.png" /></figure>

Propensity score permits to have more equilibrated groups (1-6 vs 7-34 EGFr mutation)

2

<figure><img src="image_8.png" /><figcaption>Figure 3: Stratification of population at 5 years after the first stroke</figcaption></figure>

<table><thead><tr><th>Years to predict</th><th>Nb always survivors</th><th>RMST 1-6 mutation</th><th>RMST 7-34 mutation</th><th>Difference</th><th>p.value</th></tr></thead><tbody><tr><td>2 years</td><td>232</td><td>1.70 [1.59-1.82]</td><td>1.74 [1.62-1.83]</td><td>0.020</td><td>0.797</td></tr><tr><td>5 years</td><td>216</td><td>3.83 [1.48-2.17]</td><td>3.88 [2.74-4.22]</td><td>0.057</td><td>0.814</td></tr><tr><td>10 years</td><td>195</td><td>6.43 [5.74-7.22]</td><td>6.52 [5.67-7.38]</td><td>0.127</td><td>0.830</td></tr><tr><td>15 years</td><td>154</td><td>8.64 [7.30-9.98]</td><td>8.57 [7.03-10.11]</td><td>0.110</td><td>0.916</td></tr></tbody></table>

3

<figure><img src="image_9.png" /><figcaption>Figure 4: Adjusted Kaplan-Meier curve estimating second stroke risk within 5 years following initial stroke</figcaption></figure>

<figure><img src="image_10.png" /></figure>

No significant difference are observed between 1-6 and 7-34 mutation groups when studying their second stroke.

<caption>Table 2: RMST estimand for 1-6 and 7-34 EGFr mutation type at 2,5,10 and 15 years after the first stroke</caption>

## Conclusion

There were no significant differences in second stroke study between groups (1-6 and 7-34 EGFr mutation). Further confirmation analysis could lead to a reference time point for this heterogeneous disease, to develop future trials.

**References:**
* Frangakis CE, Rubin DB. Principal stratification in causal inference. Biometrics. 2002 Mar;58(1):21-9. doi: 10.1111/j.0006-341x.2002.00021.x. PMID: 11890317; PMCID: PMC4137767
* Han K, Jung I. Restricted Mean Survival Time for Survival Analysis: A Quick Guide for Clinical Researchers. Korean J Radiol. 2022 May;23(5):495-499. doi: 10.3348/kjr.2022.0061. PMID: 35506526; PMCID: PMC9081686.