Predicting individual disease progression including parameter uncertainty in rare neurodegenerative diseases: the example of Autosomal-Recessive Spastic Ataxia Charlevoix Saguenay (ARSACS)
Niels Hendrickx (1), France Mentré (1), Rebecca Schüle (3,4), Cynthia Gagnon (5), ARCA Study Group, EVIDENCE-RND consortium, Andreas Traschütz (3,4), Matthis Synofzik (3,4), Emmanuelle Comets (1,2)
(1) Université Paris Cité and Université Sorbonne Paris Nord, Inserm, IAME, 75018, Paris, France. (2) Univ Rennes, Inserm, EHESP, Irset - UMR_S 1085, 35000, Rennes, France. (3) Division Translational Genomics of Neurodegenerative Diseases, Hertie Institute for Clinical Brain Research (HIH), University of Tübingen, Tübingen, Germany; (4) German Center for Neurodegenerative Diseases (DZNE), Tübingen, Germany. (5) Centre de recherche du CHUS et du Centre de santé et des services sociaux du Saguenay–Lac-St-Jean, Faculté de médecine, Université de Sherbrooke, Québec, Canada
Objectives: Genetic cerebellar ataxias are ultra-rare progressive neurological diseases (RNDs) affecting the cerebellum, often with multisystemic damage to other neurological systems, causing debilitating impairment of gait and balance, speech, and fine motor skills. More than >100 ataxia diseases are autosomal-recessive cerebellar ataxias (ARCAs), often starting in early childhood or early adulthood. Their genetic disease cause renders them forerunners for future targeted molecular treatment trials, highlighting the urgent need to develop robust statistical methodologies that allows to predict individual progression trajectories and treatment-induced deviations (e.g., single subject customized genetic treatments [1]).
Through an application to Autosomal Recessive Spastic Ataxia of Charlevoix-Saguenay (ARSACS) - one of the more common, but still ultra-rare ataxias, we develop a paradigmatic disease progression model that allows to model individual disease progression trajectories and to quantify its uncertainty.
Methods:
This study leverages cross-sectional and longitudinal real-world data from the ARCA Registry [2] comprising 173 ARSACS patients (1-7 visits, median 2). The core dataset comprised: reported age of onset (AoO) and ataxia severity rated by the Scale for the Assessment and Rating of Ataxia (SARA). Time since onset (TSO) was computed as current age visit minus AoO. Missing AoO were imputed to 2 years of age (median), consistent with early childhood presentation in ARSACS. The following covariates were considered: body mass index (BMI) at baseline (36 missing), INAS score at baseline (Inventory for Non-Ataxia Signs, 67 missing), type of ARSACS mutation (loss-of-function/missense; 32 missing), and sex.
We modelled the SARA score as a function of TSO using non-linear mixed effect models. Several structural models with inter-individual variability on all parameters were fit and compared with the likelihood ratio test (p-value=0.05). The covariate effects were tested according to stepwise covariate model building procedure with an initial univariate exploration. Parameter estimation was performed with the SAEM algorithm (package saemix [3] in R 4.2.0 [4]).
Missing covariates were imputed with multiple imputation (MI) using the MICE algorithm [5] using the other covariates and the empirical Bayes estimates from a base model without covariates [6]. An additional voting step at each iteration of the SCM+ was implemented to select the same covariate over the 10 data sets generated.
To account for parameter uncertainty, we drew samples of the population parameters from the bootstrap distributions (with replacement) for each imputed dataset, computed the individual conditional distributions for each sample, and combined the results to obtain the distribution of the individual trajectories. We compared the width of the confidence intervals at 5 years after the last visit with and without taking into account parameter uncertainty.
Results: For the structural model, a four-parameter logistic equation was selected. All the population parameters were well estimated.
The population SARA score at onset of symptoms (S0) was estimated to be 9.2 and the maximum SARA score (Smax) was 35.7. T50 (time to reach (S0+Smax)/2) was estimated at 41.1 years since onset. Our covariate model predicted: (i) a lower T50 with higher AoO (faster progression), (ii) a lower S0 and a lower T50 in males than females, (iii) a higher sigmoidicity (slower progression when TSO< T50) and lower Smax with lower INAS score.
Preliminary results for prediction intervals for a model without missing covariates showed that the widths of the prediction intervals were not necessarily larger when including bootstrap uncertainty.
Conclusions: A four-parameter logistic equation was used to model disease progression for ARSACS patients using MI to account for missing covariates. This approach will also be compared to a full modelling approach developed in [6].
Taking into account parameter uncertainty was shown to have little effect as, in our case, parameter uncertainty was negligible compared to interindividual uncertainty. The approach will now be applied to other RNDs with fewer individuals available to our consortium.
Acknowledgements: This work was supported by the European Joint Programme on Rare Diseases (EJPRD) (Grant Agreement n°825575) WP20 Innovation Statistics project “EVIDENCE-RND” (to F.M. R.S, and M.S), the EJPRD PROSPAX consortium, Further supported by the Clinician Scientist program "PRECISE.net".
References:
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