Projection regression models for multivariate imaging phenotype

Imaging genetics of schizophrenia in the post-GWAS era

Imaging genetics is a research methodology studying the effect of genetic variation on brain structure, function, behavior, and risk for psychopathology. Since the early 2000s, imaging genetics has been increasingly used in the research of schizophrenia (SZ). SZ is a severe mental disorder with no precise knowledge of its underlying neurobiology, however, new genetic and neurobiological data generate a climate for new avenues. The accumulating data of genome wide association studies (GWAS) continuously decode SZ risk genes. Global neuroimaging consortia produce collections of brain phenotypes from tens of thousands of people. In this context, imaging genetics will be strategically important both for the validation and discovery of SZ related findings. Thus, the study of GWAS supported risk variants as candidate genes to validate by neuroimaging is one trend. The study of epigenetic differences in relation to variations of brain phenotypes and the study of large scale multivariate analysis of genome wide and brain wide associations are other trends. While these studies hold a big potential for understanding the neurobiology of SZ, the problem of reproducibility appears as a major challenge, which requires standardizations in study designs and compensations of methodological limitations such as sensitivity and specificity. On the other hand, advancements of neuroimaging, optical and electron microscopy along with the use of genetically encoded fluorescent probes and robust statistical approaches will not only catalyze integrative methodologies but also will help better design the imaging genetics studies. In this invited paper, I will discuss the current perspective of imaging genetics and emerging opportunities of SZ research.

Adaptive testing for multiple traits in a proportional odds model with applications to detect SNP-brain network associations

There has been increasing interest in developing more powerful and flexible statistical tests to detect genetic associations with multiple traits, as arising from neuroimaging genetic studies. Most of existing methods treat a single trait or multiple traits as response while treating an SNP as a predictor coded under an additive inheritance mode. In this paper, we follow an earlier approach in treating an SNP as an ordinal response while treating traits as predictors in a proportional odds model (POM). In this way, it is not only easier to handle mixed types of traits, e.g., some quantitative and some binary, but it is also potentially more robust to the commonly adopted additive inheritance mode. More importantly, we develop an adaptive test in a POM so that it can maintain high power across many possible situations. Compared to the existing methods treating multiple traits as responses, e.g., in a generalized estimating equation (GEE) approach, the proposed method can be applied to a high dimensional setting where the number of phenotypes (p) can be larger than the sample size (n), in addition to a usual small P setting. The promising performance of the proposed method was demonstrated with applications to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, in which either structural MRI driven phenotypes or resting-state functional MRI (rs-fMRI) derived brain functional connectivity measures were used as phenotypes. The applications led to the identification of several top SNPs of biological interest. Furthermore, simulation studies showed competitive performance of the new method, especially for p>n.

Genome-wide association analysis of secondary imaging phenotypes from the Alzheimer's disease neuroimaging initiative study

The aim of this paper is to systematically evaluate a biased sampling issue associated with genome-wide association analysis (GWAS) of imaging phenotypes for most imaging genetic studies, including the Alzheimer's Disease Neuroimaging Initiative (ADNI). Specifically, the original sampling scheme of these imaging genetic studies is primarily the retrospective case-control design, whereas most existing statistical analyses of these studies ignore such sampling scheme by directly correlating imaging phenotypes (called the secondary traits) with genotype. Although it has been well documented in genetic epidemiology that ignoring the case-control sampling scheme can produce highly biased estimates, and subsequently lead to misleading results and suspicious associations, such findings are not well documented in imaging genetics. We use extensive simulations and a large-scale imaging genetic data analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data to evaluate the effects of the case-control sampling scheme on GWAS results based on some standard statistical methods, such as linear regression methods, while comparing it with several advanced statistical methods that appropriately adjust for the case-control sampling scheme.

Principal component of explained variance: An efficient and optimal data dimension reduction framework for association studies

The genomics era has led to an increase in the dimensionality of data collected in the investigation of biological questions. In this context, dimension-reduction techniques can be used to summarise high-dimensional signals into low-dimensional ones, to further test for association with one or more covariates of interest. This paper revisits one such approach, previously known as principal component of heritability and renamed here as principal component of explained variance (PCEV). As its name suggests, the PCEV seeks a linear combination of outcomes in an optimal manner, by maximising the proportion of variance explained by one or several covariates of interest. By construction, this method optimises power; however, due to its computational complexity, it has unfortunately received little attention in the past. Here, we propose a general analytical PCEV framework that builds on the assets of the original method, i.e. conceptually simple and free of tuning parameters. Moreover, our framework extends the range of applications of the original procedure by providing a computationally simple strategy for high-dimensional outcomes, along with exact and asymptotic testing procedures that drastically reduce its computational cost. We investigate the merits of the PCEV using an extensive set of simulations. Furthermore, the use of the PCEV approach is illustrated using three examples taken from the fields of epigenetics and brain imaging.

A cautionary note on using secondary phenotypes in neuroimaging genetic studies

Almost all genome-wide association studies (GWASs), including Alzheimer's Disease Neuroimaging Initiative (ADNI), are based on the case-control study design, implying that the resulting case-control data are likely a biased, not random, sample of the target population. Although association analysis of the disease (e.g. Alzheimer's disease in the ADNI) can be conducted using a standard logistic regression by ignoring the biased case-control sampling, a standard linear regression analysis on a secondary phenotype (e.g. any neuroimaging phenotype in the ADNI) may in general lead to biased inference, including biased parameter estimates, inflated Type I errors and reduced power for association testing. Despite of this well known result in genetic epidemiology, to our surprise, all the published studies on secondary phenotypes with the ADNI data have ignored this potential problem. Here we aim to answer whether such a standard analysis of a secondary phenotype is valid or problematic with the ADNI data. Through both real data analyses and simulation studies, we found that, strikingly, such an analysis was generally valid (with only small biases or slightly inflated Type I errors) for the ADNI data, though cautions must be taken when analyzing other data. We also illustrate applications and possible problems of two methods specifically developed for valid analysis of secondary phenotypes.

An Adaptive Association Test for Multiple Phenotypes with GWAS Summary Statistics

We study the problem of testing for single marker-multiple phenotype associations based on genome-wide association study (GWAS) summary statistics without access to individual-level genotype and phenotype data. For most published GWASs, because obtaining summary data is substantially easier than accessing individual-level phenotype and genotype data, while often multiple correlated traits have been collected, the problem studied here has become increasingly important. We propose a powerful adaptive test and compare its performance with some existing tests. We illustrate its applications to analyses of a meta-analyzed GWAS dataset with three blood lipid traits and another with sex-stratified anthropometric traits, and further demonstrate its potential power gain over some existing methods through realistic simulation studies. We start from the situation with only one set of (possibly meta-analyzed) genome-wide summary statistics, then extend the method to meta-analysis of multiple sets of genome-wide summary statistics, each from one GWAS. We expect the proposed test to be useful in practice as more powerful than or complementary to existing methods.

Highly adaptive tests for group differences in brain functional connectivity

Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of method development as highlighted by Varoquaux and Craddock (2013) that “there is currently no unique solution, but a spectrum of related methods and analytical strategies” to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters.

The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data.

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Rigorous testing for genuinely altered functional networks between two groups

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The proposed tests are high powered and general across a wide range of scenarios.

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Data-driven penalized network estimation

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Data-driven choice between correlations and partial correlations to describe association

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Some key differences between network estimation and testing are highlighted.

Approximate score-based testing with application to multivariate trait association analysis

For genome-wide association studies and DNA sequencing studies, several powerful score-based tests, such as kernel machine regression and sum of powered score tests, have been proposed in the last few years. However, extensions of these score-based tests to more complex models, such as mixed-effects models for analysis of multiple and correlated traits, have been hindered by the unavailability of the score vector, due to either no output from statistical software or no closed-form solution at all. We propose a simple and general method to asymptotically approximate the score vector based on an asymptotically normal and consistent estimate of a parameter vector to be tested and its (consistent) covariance matrix. The proposed method is applicable to both maximum-likelihood estimation and estimating function-based approaches. We use the derived approximate score vector to extend several score-based tests to mixed-effects models. We demonstrate the feasibility and possible power gains of these tests in association analysis of multiple and correlated quantitative or binary traits with both real and simulated data. The proposed method is easy to implement with a wide applicability.

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression

The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling's T² test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods.

Testing for association with multiple traits in generalized estimation equations, with application to neuroimaging data

There is an increasing need to develop and apply powerful statistical tests to detect multiple traits-single locus associations, as arising from neuroimaging genetics and other studies. For example, in the Alzheimer's Disease Neuroimaging Initiative (ADNI), in addition to genome-wide single nucleotide polymorphisms (SNPs), thousands of neuroimaging and neuropsychological phenotypes as intermediate phenotypes for Alzheimer's disease, have been collected. Although some classic methods like MANOVA and newly proposed methods may be applied, they have their own limitations. For example, MANOVA cannot be applied to binary and other discrete traits. In addition, the relationships among these methods are not well understood. Importantly, since these tests are not data adaptive, depending on the unknown association patterns among multiple traits and between multiple traits and a locus, these tests may or may not be powerful. In this paper we propose a class of data-adaptive weights and the corresponding weighted tests in the general framework of generalized estimation equations (GEE). A highly adaptive test is proposed to select the most powerful one from this class of the weighted tests so that it can maintain high power across a wide range of situations. Our proposed tests are applicable to various types of traits with or without covariates. Importantly, we also analytically show relationships among some existing and our proposed tests, indicating that many existing tests are special cases of our proposed tests. Extensive simulation studies were conducted to compare and contrast the power properties of various existing and our new methods. Finally, we applied the methods to an ADNI dataset to illustrate the performance of the methods. We conclude with the recommendation for the use of the GEE-based Score test and our proposed adaptive test for their high and complementary performance.

A review of multivariate analyses in imaging genetics

Recent advances in neuroimaging technology and molecular genetics provide the unique opportunity to investigate genetic influence on the variation of brain attributes. Since the year 2000, when the initial publication on brain imaging and genetics was released, imaging genetics has been a rapidly growing research approach with increasing publications every year. Several reviews have been offered to the research community focusing on various study designs. In addition to study design, analytic tools and their proper implementation are also critical to the success of a study. In this review, we survey recent publications using data from neuroimaging and genetics, focusing on methods capturing multivariate effects accommodating the large number of variables from both imaging data and genetic data. We group the analyses of genetic or genomic data into either a priori driven or data driven approach, including gene-set enrichment analysis, multifactor dimensionality reduction, principal component analysis, independent component analysis (ICA), and clustering. For the analyses of imaging data, ICA and extensions of ICA are the most widely used multivariate methods. Given detailed reviews of multivariate analyses of imaging data available elsewhere, we provide a brief summary here that includes a recently proposed method known as independent vector analysis. Finally, we review methods focused on bridging the imaging and genetic data by establishing multivariate and multiple genotype-phenotype-associations, including sparse partial least squares, sparse canonical correlation analysis, sparse reduced rank regression and parallel ICA. These methods are designed to extract latent variables from both genetic and imaging data, which become new genotypes and phenotypes, and the links between the new genotype-phenotype pairs are maximized using different cost functions. The relationship between these methods along with their assumptions, advantages, and limitations are discussed.