Morphometricity is Biased by Image Smoothness

1974 

Abstract Submission 

Nicolas Salvy¹, Thomas Nichols²

¹Télécom Paris, Palaiseau, France, ²University of Oxford, Oxford, United Kingdom

Nicolas Salvy  
Télécom Paris
Palaiseau, France

Thomas Nichols  
University of Oxford
Oxford, United Kingdom

Morphometricity is the proportion of phenotypic variation that can be explained by macroscopic brain morphology. It is estimated in a manner similar to heritability, with intersubject similarity of brain images replacing genetic relatedness [4]. It provides a simple approach to summarize the link between a phenotype and high-dimensional brain data with a single value. However, recent results have found unexpectedly large morphometricity values, e.g. brain structure explaining over 90% variation in BMI [2]. In this work we explore the role of smoothness in morphometricity in theory, simulation and real data evaluations, showing that image smoothness induces a positive bias that can help explain these unusual results.

Estimation of morphometricity relies on the equivalence between two linear mixed models (LMM). We call one LMM the 'generative' model, and it relates the response (e.g. BMI) to the voxel-wise (or element-wise) brain data. This model is impractical to fit since there are 10^5-10^6 predictors. We call the other the 'fitted' model, and it relates the response to a correlated latent random effect, where the correlation is exactly that predicted by inter-subject similarity of the brain data (Fig 1). This equivalence, however, assumes independence of the voxel-specific contributions in the generative model. Although this standard assumption might be tenable in genetics, its application in neuroimaging implies that the contribution from one voxel is independent from that of the next. This seems like a highly questionable assumption due to organisation of brain function, finite resolution of the imaging device and inevitable processing-induced blurring.

We have derived a generalised version of morphometricity that incorporates smoothness in the voxel-specific contributions in the generative model, and found the corresponding fitted model.

Through simulations in different generative scenarios using real MRI images, we investigated the impact of model misspecification on morphometricity by having smooth random influences in the generative model while assuming independence in the fitted model. We also evaluate the feasibility of recovering the true level of smoothness by model selection on the fitted model, using AIC [1].

We use data from the UK Biobank [3], with N=500 subjects and M=154,055 voxel values from gray matter VBM images. In our simulations, the phenotype is directly generated from the image data and we generated 250 realisations for each scenario. We use R's lmekin [5] for estimating the fitted model. We also evaluated morphometricity for BMI, with covariates: sex, age, intracranial volume, Townsend deprivation index at recruitment, date, assessment centre and head motion.

We found that model misspecification due to assuming independence significantly biases estimation, with even very modest smoothness (2mm FWHM) dramatically shifting the estimates (Fig 2 top left). With the knowledge of the true smoothness, it is possible to recover morphometricity on average, though there is substantial uncertainty in the estimates (Fig 2 top right). Depending on true unknown smoothness, the real dataset is consistent with anywhere from 93 to 0% of morphometricity (Fig 2 bottom left). And, attempts to choose the correct generative model with AIC do not work consistently (Fig 2 bottom right).

Morphometricity, as conventionally computed, is biased depending on the correlation structure of the voxel-wise contributions in the generative model. If the true correlation structure is known, an unbiased morphometricity could be recovered but it appears very unstable, and learning the true correlation on real data may not be practical. All of these considerations suggest that morphometricity should be not used until new methods are developed that account for the impact of smoothness.

Methods Development ²

Multivariate Approaches ¹

Other - Morphometricity; Population Neuroimaging