Integrated Normative and Survival Modelling in MS: A Bayesian Modularised Inference Approach
Poster No:
1076
Submission Type:
Abstract Submission
Authors:
Bernd Taschler1, Dieter Häring2, Piet Aarden2, Laura Gaetano2, Thomas Nichols1, Habib Ganjgahi1
Institutions:
1University of Oxford, Oxford, United Kingdom, 2Novartis Pharma AG, Basel, Switzerland
First Author:
Co-Author(s):
Introduction:
Modularised inference is a statistical modelling approach that addresses the challenge of model misspecification by breaking down complex models into smaller "modules" [1]. It also allows for the integration of consecutive modelling steps without fitting a full joint model.
In this work we propose several innovations for normative modelling and normative score outcome modelling. First, we explicitly account for variation due to non-biological confounds via image quality measures in the estimation of the normative model. 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; we propose that a sufficiently rich model will produce a prediction that is unbiased and much less variable than the raw data. Third, instead of separately estimating deviation scores that are used in a second modelling step as inputs to an outcome model, we propose a unified Bayesian model that combines normative and final analyses with proper uncertainty propagation.
We apply our model to a large clinical trials database of multiple sclerosis (MS) patients (N=8320).
In this work we propose several innovations for normative modelling and normative score outcome modelling. First, we explicitly account for variation due to non-biological confounds via image quality measures in the estimation of the normative model. 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; we propose that a sufficiently rich model will produce a prediction that is unbiased and much less variable than the raw data. Third, instead of separately estimating deviation scores that are used in a second modelling step as inputs to an outcome model, we propose a unified Bayesian model that combines normative and final analyses with proper uncertainty propagation.
We apply our model to a large clinical trials database of multiple sclerosis (MS) patients (N=8320).
Methods:
Normative model. We consider baseline covariates X (incl. age, sex, clinical tests, etc.) and a single exposure variable Z (here, an ordinal score of disease severity, EDSS). The outcome Y is a quantitative MRI-derived measure (total brain volume or T2 lesion load). The normative model for Y is based on Bayesian Additive Regression Trees (BART) [2]. We account for non-biological confounds by integrating out the effect of 60 image quality measures using counterfactual prediction with BART.
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 BART approach for interval-censored survival data based on a modified data augmentation scheme [3], with individual deviation scores and a subset of demographic covariates as predictors. We estimate the probability of a disease worsening event T (defined as persistent increase in EDSS) occurring within 2 years after baseline.
Integrated 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. Variability of deviation scores is incorporated by using posterior draws from the normative module when fitting the survival module.
Application. For empirical validation, we use a subset of the NO.MS dataset with 8k subjects from 10 clinical studies and including 7 different treatment arms; 67% female, age (mean±SD) 40.3±10.7 years, median EDSS 3.0 [4].
Simulations. For additional validation, we compare our model to a conventional 2-step approach in simulation settings based on Friedman's non-linear test function.
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 BART approach for interval-censored survival data based on a modified data augmentation scheme [3], with individual deviation scores and a subset of demographic covariates as predictors. We estimate the probability of a disease worsening event T (defined as persistent increase in EDSS) occurring within 2 years after baseline.
Integrated 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. Variability of deviation scores is incorporated by using posterior draws from the normative module when fitting the survival module.
Application. For empirical validation, we use a subset of the NO.MS dataset with 8k subjects from 10 clinical studies and including 7 different treatment arms; 67% female, age (mean±SD) 40.3±10.7 years, median EDSS 3.0 [4].
Simulations. For additional validation, we compare our model to a conventional 2-step approach in simulation settings based on Friedman's non-linear test function.
Results:
Fig. 2 shows results from the normative module (A-B), the time-to-event analysis (C-D) and model calibration in a simulation setting (E-F). Stratification of the patient population into groups of low, medium and high NBV at baseline shows a strong association of deviation scores with risk of experiencing a disability worsening event within two years (HR: 0.83, p=0.007). In simulation settings with non-linear risk dependence and large measurement errors for the normative variable of interest, our integrated model demonstrates better model calibration and a lower false positive rate in the survival module.
Conclusions:
Our proposed unified normative modelling approach using a Bayesian hierarchical model combines individual deviations in an MRI phenotype from a reference population of MS patients with a time-to-event analysis of disability worsening. The model accounts for non-biological confounding and noisy MRI measures. It propagates uncertainty in the estimated deviation scores and captures non-linear risk profiles.
Modeling and Analysis Methods:
Bayesian Modeling 1
Methods Development 2
Keywords:
Modeling
MRI
Statistical Methods
1|2Indicates the priority used for review
Abstract Information
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Were any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.
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Provide references using APA citation style.
1, pp. 266-298. https://www.jstor.org/stable/27801587
[3] Basak, P. (2022). Semiparametric Analysis of Clustered Interval-Censored Survival Data Using Soft Bayesian Additive Regression Trees (SBART). Biometrics, Volume 78, Issue 3. https://doi.org/10.1111/biom.13478
[4] Dahlke, F. (2021). Characterisation of MS phenotypes across the age span using a novel data set integrating
34 clinical trials (NO.MS cohort): Age is a key contributor to presentation. Multiple Sclerosis Journal, Vol. 27,
No. 13. https://doi.org/10.1177/1352458520988637
[1] Jacob, P. E. (2017). Better together? Statistical learning in models made of modules. arXiv:1708.08719 [stat.ME]. https://doi.org/10.48550/arXiv.1708.08719