An integrated Bayesian normative and outcome model for brain reserve in MS

1855 

Abstract Submission 

Bernd Taschler¹, Samantha Pendleton¹, Stephen Gardiner¹, Piet Aarden², Thomas Nichols¹, Dieter Haering², Laura Gaetano², Habib Ganjgahi¹

¹University of Oxford, Oxford, United Kingdom, ²Novartis Pharma AG, Basel, Switzerland

Bernd Taschler  
University of Oxford
Oxford, United Kingdom

Samantha Pendleton  
University of Oxford
Oxford, United Kingdom

Stephen Gardiner  
University of Oxford
Oxford, United Kingdom

Piet Aarden  
Novartis Pharma AG
Basel, Switzerland

Thomas Nichols  
University of Oxford
Oxford, United Kingdom

Dieter Haering  
Novartis Pharma AG
Basel, Switzerland

Laura Gaetano  
Novartis Pharma AG
Basel, Switzerland

Habib Ganjgahi  
University of Oxford
Oxford, United Kingdom

Normative modelling is a standard method to define subject-specific deviations from a reference population. These deviations can then be used as outcomes for prediction, classification, clustering or other tasks. Traditionally, this is done in two steps with separate models for i) the normative component to create deviation scores, and ii) the outcome analysis of the scores. Importantly, derived deviation scores are based on differences of observed data with the normative population mean/median (e.g., developmental charts).
In this work we propose two fundamental innovations to how normative modelling is conducted. First, instead of separately deriving a score and modelling that score as an outcome in an analysis, we create a single unified model that integrates the normative and final analyses. Second, instead of defining the deviation score as a difference of noisy observed data and a reference, we propose that a predicted fit replaces the role of the observed data; a sufficiently rich model will produce a prediction that is unbiased and much less variable than the raw data.
We apply our integrated model to the concept of "brain reserve" (the neurobiological capacity to cope with pathology; Stern et al., 2020) in a time-to-event analysis of a large cohort of MS patients.

Normative model. We consider a set of baseline covariates X (e.g. age, sex, medical history, etc.) and a single exposure variable of interest Z (in our case an ordinal score of disease severity, EDSS). The outcome Y is a quantitative MRI-derived measure linked brain reserve (e.g., total brain volume or T2 lesion load). The normative model for Y is based on Bayesian Additive Regression Trees (BART, Chipman et al., 2010).
Deviation scores. We define individual deviation scores d as the difference between predicted outcome and posterior population average for each category in Z.
Time-to-event model. We use a Cox proportional hazards (CPH) model with individual deviation scores d as predictor variable. Additionally, the data is stratified into 3 groups of low (d < -1SD), medium (-1SD ≤ d ≤ +1SD) or high (d > +1SD) brain reserve, with the two extreme groups indicating high deviation from the population mean (Sormani et al., 2017). For each of these groups, we estimate the probability of a disease worsening event T (defined as persistent increase in EDSS) occurring within a timeframe of 5 years after baseline.
Bayesian hierarchical model. The full model is illustrated in Fig.1. Parameter estimation and model inference is based on draws from the posterior distributions using MCMC techniques.
Application. For empirical validation, we use a subset of the NO.MS dataset with 9k subjects from 10 clinical studies and including 7 different treatment arms (Dahlke et al., 2021); 67% female, age (mean±SD) 40.3±10.7 years, median EDSS 3.0.

Results from the time-to-event analysis are shown in Fig.2. We use individual deviations of normalised brain volume (conditional on EDSS category) as a proxy for brain reserve. Stratification of the patient population into groups of low, medium and high NBV at baseline shows a strong association of deviation scores derived from the unified model with risk of experiencing a disability worsening event (Fig.2B). Whereas deviation scores based on residuals (Fig.2C) are much less informative.

Our proposed unified normative modelling approach using a Bayesian hierarchical model that combines normative modelling of brain reserve (individual deviations in brain volume from a reference population of MS patients) with a time-to-event analysis of disability worsening outperforms classical residual based methods. MS patients with low "brain reserve" at baseline have higher risk of accumulating disability compared to patients with higher brain reserve but otherwise similar characteristics (e.g., age, sex, disease duration, etc.).

Bayesian Modeling ²

Methods Development ¹

Modeling

MRI

Statistical Methods