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

HAL
open science

# How to improve statistical power in a trial with SCA2 patients using natural history data

Maylis Tran, Pierre-Emmanuel Poulet, Cécile Di Folco, Emilien Petit, Alexandra Durr, Thomas Klockgether, Tetsuo Ashizawa, Giulia Coarelli, Sophie Tezenas Du Montcel

► To cite this version:

Maylis Tran, Pierre-Emmanuel Poulet, Cécile Di Folco, Emilien Petit, Alexandra Durr, et al. How to improve statistical power in a trial with SCA2 patients using natural history data. ICAR 2024 - International Congress for Ataxia Research, Nov 2024, London, United Kingdom. hal-05233996

HAL Id: hal-05233996

https://hal.science/hal-05233996v1

Submitted on 1 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# How to improve statistical power in a trial with SCA2 patients using natural history data

<figure><img src="image_3.png" /></figure>

ARAMIS
LAB
BRAIN DATA SCIENCE

Maylis Tran¹, Pierre-Emmanuel Poulet¹, Cécile di Folco¹, Emilien Petit¹, Alexandra Durr¹, Thomas Klockgether², Tetsuo Ashizawa³, Giulia Coarelli¹, Sophie Tezenas du Montcel¹

¹Sorbonne Université, Paris Brain Institute, INSERM, INRIA, CNRS, APHP, Paris, France, ²German Center for Neurodegenerative Diseases (DZNE), Bonn, Germany, ³Weill Cornell Medicine at the Houston Methodist Research Institute, Houston, Texas, USA

## INTRODUCTION

### ATRIL Clinical Trial (CT)

* A population of N=45 subjects

* A treatment T = Riluzole

* An outcome Y = Change in SARA score between baseline and 1 year of CT

* An estimand : the Average Treatment Effect (ATE) $\Leftrightarrow ATE = E(Y_i|T_i = 1) - E(Y_i|T_i = 0)$

ATRIL study showed that riluzole **did not improve clinical outcomes**¹, due to non-significant results:

$$ \hat{ATE}^{\text{classic}} = -0,250 $$

$$ \text{Var}(\hat{ATE}^{\text{classic}}) = 0,407 $$

$$ CI_{95\%} = [-1,501; 1,001] $$

### Objectives

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

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

A priori

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

A posteriori

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

## METHODS

### Prediction-powered inference principle

#### A. PPI principle applied to ATRIL clinical trial and the natural history data of ataxia disease

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

Outputs: Estimator $\hat{ATE}^{\text{PPI}}$ and reduced confidence interval

#### B. Mean predicted and observed SARA score progression for treated and placebo arms

<figure><img src="image_11.png" /></figure>

1. Clinical trial dataset

<figure><img src="image_12.png" /></figure>

Pre-inclusion and CT timepoints were collected for 45 patients (22 treated and 23 placebo).

2. Longitudinal dataset

<figure><img src="image_13.png" /></figure>

218 patients were followed for 14 years maximum.

3. Disease Course Mapping to predict the prognostic score

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

3 non-linear Bayesian mixed-effects models (univariate, multivariate and ordinal) were trained on the longitudinal dataset (A) and personalized on the pre-inclusion data of the clinical trial dataset (B).

## RESULTS

<table><thead><tr><th colspan="4">Disease Course Mapping</th></tr><tr><th></th><th>Leaspy Univariate</th><th>Leaspy Multivariate</th><th>Leaspy Ordinal</th></tr></thead><tbody><tr><td colspan="4"><strong>R<sup>2</sup> on PoolSCA</strong></td></tr><tr><td>With test set simulating ATRIL</td><td>0.134±0.088</td><td><strong>0.144±0.083</strong></td><td>0.084±0.114</td></tr><tr><td colspan="4"><strong>R<sup>2</sup> on ATRIL</strong></td></tr><tr><td>With pre-inclusion &amp; baseline</td><td>0.134</td><td>0.128</td><td>-</td></tr><tr><td>With baseline only</td><td>0.002</td><td>0.001</td><td>0.130</td></tr><tr><td>With M6 included</td><td>0.380</td><td>0.398</td><td>0.375</td></tr><tr><td colspan="4"><strong>Variances</strong></td></tr><tr><td>Var(ATE<sub>PPI++</sub>)</td><td><strong>0.346</strong></td><td>0.348</td><td>0.355</td></tr><tr><td>(1 - R<sup>2</sup>) * Var(ATE<sub>classic</sub>)</td><td><strong>0.352</strong></td><td>0.355</td><td>0.354</td></tr></tbody></table>

The formula $V(ATE_{PPI++}) = (1 - R^2)V(ATE_{classic})$ seems to hold empirically, with $R^2 = \text{corr}(SARA\_diff_{pred}, SARA\_diff_{real})^2$.

As the total sample size N is proportional to the variance of the estimator, this leads to a reduction of the sample size of R²%.

<figure><img src="image_16.png" /></figure>

95% Confidence Intervals (CI) on the estimator of ATE of ATRIL trial enriched with different models computing the prognostic score.

<figure><img src="image_17.png" /></figure>

CI width reduction of **7.8%** (univariate model, without M6).

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

Sample size reduction of **6 patients** (univariate model, without M6).

<figure><img src="image_20.png" /></figure>

## References

1. Coarelli, G. et al. Safety and efficacy of riluzole in spinocerebellar ataxia type 2 in France (ATRIL): a multicentre, randomised, double-blind, placebo-controlled trial. Lancet Neurol. **21**, 225–233 (2022).

2. Angelopoulos, A. N., Bates, S., Fannjiang, C., Jordan, M. I. & Zrnic, T. Prediction-powered inference. Science **382**, 669–674 (2023).

<figure><img src="image_21.png" /></figure>

SORBONNE
UNIVERSITÉ

<figure><img src="image_22.png" /></figure>

ICM

Paris Brain
Institute

Inserm

cnrs

<figure><img src="image_23.png" /></figure>

ASSISTANCE
PUBLIQUE

<figure><img src="image_24.png" /></figure>

HÔPITAUX
DE PARIS