Warped Bayesian linear regression for normative modelling of big data

Normative modelling is becoming more popular in neuroimaging due to its ability to make predictions of deviation from a normal trajectory at the level of individual participants. It allows the user to model the distribution of several neuroimaging modalities, giving an estimation for the mean and ce...

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Autores principales:	Charlotte J. Fraza, Richard Dinga, Christian F. Beckmann, Andre F. Marquand
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Machine learning UK Biobank Big data Bayesian linear regression Normative modelling Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
Acceso en línea:	https://doaj.org/article/a7db1f76a25a4ddca2aa6236565dc09e
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id	oai:doaj.org-article:a7db1f76a25a4ddca2aa6236565dc09e
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spelling	oai:doaj.org-article:a7db1f76a25a4ddca2aa6236565dc09e2021-11-18T04:44:57ZWarped Bayesian linear regression for normative modelling of big data1095-957210.1016/j.neuroimage.2021.118715https://doaj.org/article/a7db1f76a25a4ddca2aa6236565dc09e2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1053811921009873https://doaj.org/toc/1095-9572Normative modelling is becoming more popular in neuroimaging due to its ability to make predictions of deviation from a normal trajectory at the level of individual participants. It allows the user to model the distribution of several neuroimaging modalities, giving an estimation for the mean and centiles of variation. With the increase in the availability of big data in neuroimaging, there is a need to scale normative modelling to big data sets. However, the scaling of normative models has come with several challenges.So far, most normative modelling approaches used Gaussian process regression, and although suitable for smaller datasets (up to a few thousand participants) it does not scale well to the large cohorts currently available and being acquired. Furthermore, most neuroimaging modelling methods that are available assume the predictive distribution to be Gaussian in shape. However, deviations from Gaussianity can be frequently found, which may lead to incorrect inferences, particularly in the outer centiles of the distribution. In normative modelling, we use the centiles to give an estimation of the deviation of a particular participant from the ‘normal’ trend. Therefore, especially in normative modelling, the correct estimation of the outer centiles is of utmost importance, which is also where data are sparsest.Here, we present a novel framework based on Bayesian linear regression with likelihood warping that allows us to address these problems, that is, to correctly model non-Gaussian predictive distributions and scale normative modelling elegantly to big data cohorts. In addition, this method provides likelihood-based statistics, which are useful for model selection.To evaluate this framework, we use a range of neuroimaging-derived measures from the UK Biobank study, including image-derived phenotypes (IDPs) and whole-brain voxel-wise measures derived from diffusion tensor imaging. We show good computational scaling and improved accuracy of the warped BLR for certain IDPs and voxels if there was a deviation from normality of these parameters in their residuals.The present results indicate the advantage of a warped BLR in terms of; computational scalability and the flexibility to incorporate non-linearity and non-Gaussianity of the data, giving a wider range of neuroimaging datasets that can be correctly modelled.Charlotte J. FrazaRichard DingaChristian F. BeckmannAndre F. MarquandElsevierarticleMachine learningUK BiobankBig dataBayesian linear regressionNormative modellingNeurosciences. Biological psychiatry. NeuropsychiatryRC321-571ENNeuroImage, Vol 245, Iss , Pp 118715- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Machine learning UK Biobank Big data Bayesian linear regression Normative modelling Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
spellingShingle	Machine learning UK Biobank Big data Bayesian linear regression Normative modelling Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571 Charlotte J. Fraza Richard Dinga Christian F. Beckmann Andre F. Marquand Warped Bayesian linear regression for normative modelling of big data
description	Normative modelling is becoming more popular in neuroimaging due to its ability to make predictions of deviation from a normal trajectory at the level of individual participants. It allows the user to model the distribution of several neuroimaging modalities, giving an estimation for the mean and centiles of variation. With the increase in the availability of big data in neuroimaging, there is a need to scale normative modelling to big data sets. However, the scaling of normative models has come with several challenges.So far, most normative modelling approaches used Gaussian process regression, and although suitable for smaller datasets (up to a few thousand participants) it does not scale well to the large cohorts currently available and being acquired. Furthermore, most neuroimaging modelling methods that are available assume the predictive distribution to be Gaussian in shape. However, deviations from Gaussianity can be frequently found, which may lead to incorrect inferences, particularly in the outer centiles of the distribution. In normative modelling, we use the centiles to give an estimation of the deviation of a particular participant from the ‘normal’ trend. Therefore, especially in normative modelling, the correct estimation of the outer centiles is of utmost importance, which is also where data are sparsest.Here, we present a novel framework based on Bayesian linear regression with likelihood warping that allows us to address these problems, that is, to correctly model non-Gaussian predictive distributions and scale normative modelling elegantly to big data cohorts. In addition, this method provides likelihood-based statistics, which are useful for model selection.To evaluate this framework, we use a range of neuroimaging-derived measures from the UK Biobank study, including image-derived phenotypes (IDPs) and whole-brain voxel-wise measures derived from diffusion tensor imaging. We show good computational scaling and improved accuracy of the warped BLR for certain IDPs and voxels if there was a deviation from normality of these parameters in their residuals.The present results indicate the advantage of a warped BLR in terms of; computational scalability and the flexibility to incorporate non-linearity and non-Gaussianity of the data, giving a wider range of neuroimaging datasets that can be correctly modelled.
format	article
author	Charlotte J. Fraza Richard Dinga Christian F. Beckmann Andre F. Marquand
author_facet	Charlotte J. Fraza Richard Dinga Christian F. Beckmann Andre F. Marquand
author_sort	Charlotte J. Fraza
title	Warped Bayesian linear regression for normative modelling of big data
title_short	Warped Bayesian linear regression for normative modelling of big data
title_full	Warped Bayesian linear regression for normative modelling of big data
title_fullStr	Warped Bayesian linear regression for normative modelling of big data
title_full_unstemmed	Warped Bayesian linear regression for normative modelling of big data
title_sort	warped bayesian linear regression for normative modelling of big data
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/a7db1f76a25a4ddca2aa6236565dc09e
work_keys_str_mv	AT charlottejfraza warpedbayesianlinearregressionfornormativemodellingofbigdata AT richarddinga warpedbayesianlinearregressionfornormativemodellingofbigdata AT christianfbeckmann warpedbayesianlinearregressionfornormativemodellingofbigdata AT andrefmarquand warpedbayesianlinearregressionfornormativemodellingofbigdata
_version_	1718425059007135744

Warped Bayesian linear regression for normative modelling of big data

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