Article

Vounou M, Nichols TE, Montana G, For the Alzheimer's disease neuroimaging initiative. Discovering genetic associations with high-dimensional neuroimaging phenotypes: a sparse reduced-rank regression approach. Neuroimage 53: 1147-1159

Statistics Section, Department of Mathematics, Imperial College London, UK.
NeuroImage (Impact Factor: 6.36). 11/2010; 53(3):1147-59. DOI: 10.1016/j.neuroimage.2010.07.002
Source: PubMed

ABSTRACT

There is growing interest in performing genome-wide searches for associations between genetic variants and brain imaging phenotypes. While much work has focused on single scalar valued summaries of brain phenotype, accounting for the richness of imaging data requires a brain-wide, genome-wide search. In particular, the standard approach based on mass-univariate linear modelling (MULM) does not account for the structured patterns of correlations present in each domain. In this work, we propose sparse reduced rank regression (sRRR), a strategy for multivariate modelling of high-dimensional imaging responses (measurements taken over regions of interest or individual voxels) and genetic covariates (single nucleotide polymorphisms or copy number variations), which enforces sparsity in the regression coefficients. Such sparsity constraints ensure that the model performs simultaneous genotype and phenotype selection. Using simulation procedures that accurately reflect realistic human genetic variation and imaging correlations, we present detailed evaluations of the sRRR method in comparison with the more traditional MULM approach. In all settings considered, sRRR has better power to detect deleterious genetic variants compared to MULM. Important issues concerning model selection and connections to existing latent variable models are also discussed. This work shows that sRRR offers a promising alternative for detecting brain-wide, genome-wide associations.

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    • "Incontrasttounivariateanalyses,becauseanapproach likeICAestimatesallthevariablesjointly,bydefinitionthe voxelsinthe'network'arefunctioningcoherentlywithone another.ThispropertyofICAmethods(andinextension, p-ICA)providesthreemajorbenefits.First,ithelpswith interpretation,asonecanaccuratelyassumetheregion(or genes)inagivencomponentcovarytogether.Secondly,it providesrobustnesstonoise.Forexample,againtodraw onthefMRIexample,correlation-basedapproachescanbe 'tricked'byphenomenasuchasphaserandomizednoise whichcanappeartorepresentrealsignal(Handwerkeretal., 2012).However,inthecaseofICA,theassumptionsare strongerinthatoneisidentifyingpatternsandthusthe sametypeofrandomizednoisewillnotresemblerealsignal. ThisisnottosaythatICA-basedmethodsareimperviousto noise,buttheydotendtobemorerobustthanunivariate correlationastheyareworkingwithpatternsratherthan justpairedrelationships.ICA-basedmethodsarenotthe onlyapproachesthathavethisadvantage,forexample,other multivariateapproachesbecomingwidelyusedincludesparse reducedrankregression(Vounouetal.,2010)andsparse canonicalcorrelationanalysis(Linetal.,2014a,b).Andfinally, becausethestatisticaltestingisdoneatthelevelofnetworks, correctionformultiplecomparisonsisappropriatelybasedonthe numberofnetworktested,ratherthanthenumberofSNPsor voxels. "
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    • "A Stein's unbiased risk estimation (SURE) based approach is developed for choosing the regularization parameters automatically. The differences between our method and the method in [36] are the following: first, [36] uses a suboptimal algorithm that estimates the RRR components sequentially; second, it does not use wavelet expansion; and third, it uses other simplifying assumptions that are only valid in the application domain where the algorithm was developed in, i.e., [36] develops an algorithm for genomics. "
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    • "We utilized the same simulation design as the work in Hua and Ghosh (2014), where a linear model y r = h(x) + ǫ r with r = 1, ..., q was used to associate the phenotypes (y = (y 1 , ..., y q )) and genotypes (x = (x 1 , ..., x p )). The structure of the responses (y 1 , ..., y q ) was modelled using a covariance matrix˜Σ based on the eight (q = 8) positive correlated frontal cortex regions using the 358 mild cognitive impairment (MCI) subjects (Figure 2a), since the MRI scans of the MCI samples are relatively more uniform than both the healthy and disease groups Vounou et al. (2010). Therefore, the multivariate responses were according to all ǫ's that were generated from multivariate normal MVN(0, ˜ Σ). "
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