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# Non-parametric modeling for dopaminergic treatment effect in Parkinson's disease

Pierre-Emmanuel Poulet, Bruno Jedynak, Zoltan Mari, Stanley Durrleman

► To cite this version:

Pierre-Emmanuel Poulet, Bruno Jedynak, Zoltan Mari, Stanley Durrleman. Non-parametric modeling for dopaminergic treatment effect in Parkinson's disease. AD/PD 2023 - 17th International Conference on Alzheimer's & Parkinson's Diseases, Mar 2023, Goteborg, Sweden. hal-04158200

HAL Id: hal-04158200

https://inria.hal.science/hal-04158200

Submitted on 11 Jul 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# Non-parametric modeling for dopaminergic treatment effect in Parkinson's disease

Pierre-Emmanuel Poulet¹, Bruno Jedynak², Zoltan Mari³, Stanley Durrleman¹

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pierre-emmanuel.poulet@inria.fr

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https://gitlab.com/icm-institute/aramislab/leaspy

¹ Aramis project Team, Inria, Paris Brain Institute, Sorbonne Université, INSERM, CNRS

²Portland State University 3. Cleveland Clinic Lou Ruvo Center for Brain Health, For the Parkinson's Progression Markers Initiative

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## Introduction

Disease progression models have been shown to successfully recover the natural history of the disease at a population level and also at an individual level, thus providing reliable predictions for the future disease progression. However these models usually do not account for the effect of a treatment. We propose a method to combine a disease progression model with a non-parametric conditional average treatment effect (CATE) model. We apply it to dopaminergic treatment in Parkinson's disease (PD). Our treatment model also allows for the analysis of the influence of covariates over treatment efficiency.

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## Method

* Observations: $y_{ij}^{ON}$ of patient i at age $t_{ij}$ after taking drug (ON state), $y_{ij}^{OFF}$ when treatment effect wears off (OFF state)

* Disease course mapping (DCM) model: a Bayesian mixed-effect model predicts natural progression of the disease

* Treatment effect: difference between OFF and ON states

$$y_{ij}^{OFF} - y_{ij}^{ON} = \Delta_{ij}$$

* In the absence of observed $y_{ij}^{OFF}$ we use DCM predictions :

$$\Delta_{ij} \approx \text{DCM}(t_{ij}; z_i) - y_{ij}^{ON}$$

* CATE model: $\Delta_{ij} = f(X_{ij})$ with time-dependent variables $X_{ij}$

* Covariate importance $X_{ij}$ is computed as percentage of total variance explained

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## Data (from PPMI*)

Outcome: MDS-UPDRS parts 2 and 3 (OFF only available for part 3).
Treatment variables: Levodopa equivalent daily dose (LEDD) and category (Levodopa, dopamin agonist...)

<table><thead><tr><th># Patients</th><th># Visits/patient</th><th>Mean age</th><th>Follow-up (years)</th><th>Sex</th></tr></thead><tbody><tr><td>900</td><td>8.8±5.6</td><td>64.6±10.0</td><td>4.0±2.8</td><td>W:36%, M:64%</td></tr><tr><td>MDS-UPDRS 1</td><td>MDS-UPDRS 2</td><td>MDS-UPDRS 4</td><td>Dose (LEDD mg)</td><td>Weight</td></tr><tr><td>8.0±5.6</td><td>8.7±6.4</td><td>1.2±2.5</td><td>565±904</td><td>78.5±16.8</td></tr><tr><td>State</td><td># observations</td><td>MDS-UPDRS 3</td><td>Time since dose (h)</td><td>PIGD score TD score</td></tr><tr><td>ON</td><td>2285</td><td>21.3±12.0</td><td>2.1±1.3</td><td>2.1±2.2</td></tr><tr><td>OFF</td><td>7519</td><td>25.5±12.4</td><td>14.9±9.3</td><td>5.4±4.5</td></tr></tbody></table>

### Model scheme for one patient

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### Patient samples

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## Results

### Treatment effect on part 3 (motor)

* R²: 0.82

* Variable importance: Current motor state (MDS-UPDRS 3 OFF) explains most of the variance because it is proportional to treatment effect. Dopaminergic treatment improves this score by 35% approximately. Otherwise treatment dose is most impactful.

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* Covariates interaction on treatment effect: Our model allows to understand how several covariates interact. The next figure shows how we can optimize the dose based on current motor score.

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* Covariates impact on mean treatment effect: Secondary effects (MDS-UPDRS 4) are correlated to better motor outcome. Treatment effect increases with dose but plateaus at high LEDD. Patients with higher tremor (TD score) are more treatment responsive.

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### Treatment effect on part 2 (Quality of life)

* R²: 0.83

* Variable importance: most notable is PIGD score, high PIGD patients experience less treatment effect.

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The two variables which influence the most the treatment effect on motor outcome are the dose and the current disease state. Our model is able to learn treatment effect even in the absence of placebo or control arm.

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## Conclusion

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