A regularized Hotelling's T2 test for pathway analysis in proteomic studies

Finite sample t-tests for high-dimensional means

When sample sizes are small, it becomes challenging for an asymptotic test requiring diverging sample sizes to maintain an accurate Type I error rate. In this paper, we consider one-sample, two-sample and ANOVA tests for mean vectors when data are high-dimensional but sample sizes are very small. We establish asymptotic t -distributions of the proposed U -statistics, which only require data dimensionality to diverge but sample sizes to be fixed and no less than 3. The proposed tests maintain accurate Type I error rates for a wide range of sample sizes and data dimensionality. Moreover, the tests are nonparametric and can be applied to data which are normally distributed or heavy-tailed. Simulation studies confirm the theoretical results for the tests. We also apply the proposed tests to an fMRI dataset to demonstrate the practical implementation of the methods.

Modified T2 Statistics for Improved Detection of Aided Cortical Auditory Evoked Potentials in Hearing-Impaired Infants

The cortical auditory evoked potential (CAEP) is a change in neural activity in response to sound, and is of interest for audiological assessment of infants, especially those who use hearing aids. Within this population, CAEP waveforms are known to vary substantially across individuals, which makes detecting the CAEP through visual inspection a challenging task. It also means that some of the best automated CAEP detection methods used in adults are probably not suitable for this population. This study therefore evaluates and optimizes the performance of new and existing methods for aided (i.e., the stimuli are presented through subjects' hearing aid(s)) CAEP detection in infants with hearing loss. Methods include the conventional Hotellings T2 test, various modified q-sample statistics, and two novel variants of T2 statistics, which were designed to exploit the correlation structure underlying the data. Various additional methods from the literature were also evaluated, including the previously best-performing methods for adult CAEP detection. Data for the assessment consisted of aided CAEPs recorded from 59 infant hearing aid users with mild to profound bilateral hearing loss, and simulated signals. The highest test sensitivities were observed for the modified T2 statistics, followed by the modified q-sample statistics, and lastly by the conventional Hotelling's T2 test, which showed low detection rates for ensemble sizes <80 epochs. The high test sensitivities at small ensemble sizes observed for the modified T2 and q-sample statistics are especially relevant for infant testing, as the time available for data collection tends to be limited in this population.

Lipidome profile predictive of disease evolution and activity in rheumatoid arthritis

Lipid mediators are crucial for the pathogenesis of rheumatoid arthritis (RA); however, global analyses have not been undertaken to systematically define the lipidome underlying the dynamics of disease evolution, activation, and resolution. Here, we performed untargeted lipidomics analysis of synovial fluid and serum from RA patients at different disease activities and clinical phases (preclinical phase to active phase to sustained remission). We found that the lipidome profile in RA joint fluid was severely perturbed and that this correlated with the extent of inflammation and severity of synovitis on ultrasonography. The serum lipidome profile of active RA, albeit less prominent than the synovial lipidome, was also distinguishable from that of RA in the sustained remission phase and from that of noninflammatory osteoarthritis. Of note, the serum lipidome profile at the preclinical phase of RA closely mimicked that of active RA. Specifically, alterations in a set of lysophosphatidylcholine, phosphatidylcholine, ether-linked phosphatidylethanolamine, and sphingomyelin subclasses correlated with RA activity, reflecting treatment responses to anti-rheumatic drugs when monitored serially. Collectively, these results suggest that analysis of lipidome profiles is useful for identifying biomarker candidates that predict the evolution of preclinical to definitive RA and could facilitate the assessment of disease activity and treatment outcomes.

T2-DAG: a powerful test for differentially expressed gene pathways via graph-informed structural equation modeling

MOTIVATION

A major task in genetic studies is to identify genes related to human diseases and traits to understand functional characteristics of genetic mutations and enhance patient diagnosis. Compared with marginal analyses of individual genes, identification of gene pathways, i.e. a set of genes with known interactions that collectively contribute to specific biological functions, can provide more biologically meaningful results. Such gene pathway analysis can be formulated into a high-dimensional two-sample testing problem. Given the typically limited sample size of gene expression datasets, most existing two-sample tests tend to have compromised powers because they ignore or only inefficiently incorporate the auxiliary pathway information on gene interactions.

RESULTS

We propose T2-DAG, a Hotelling's T2-type test for detecting differentially expressed gene pathways, which efficiently leverages the auxiliary pathway information on gene interactions from existing pathway databases through a linear structural equation model. We further establish its asymptotic distribution under pertinent assumptions. Simulation studies under various scenarios show that T2-DAG outperforms several representative existing methods with well-controlled type-I error rates and substantially improved powers, even with incomplete or inaccurate pathway information or unadjusted confounding effects. We also illustrate the performance of T2-DAG in an application to detect differentially expressed KEGG pathways between different stages of lung cancer.

AVAILABILITY AND IMPLEMENTATION

The R (R Development Core Team, 2021) package T2DAG which implements the proposed T2-DAG test is available on Github at https://github.com/Jin93/T2DAG.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Multiomic analysis identifies CPT1A as a potential therapeutic target in platinum-refractory, high-grade serous ovarian cancer

Resistance to platinum compounds is a major determinant of patient survival in high-grade serous ovarian cancer (HGSOC). To understand mechanisms of platinum resistance and identify potential therapeutic targets in resistant HGSOC, we generated a data resource composed of dynamic (±carboplatin) protein, post-translational modification, and RNA sequencing (RNA-seq) profiles from intra-patient cell line pairs derived from 3 HGSOC patients before and after acquiring platinum resistance. These profiles reveal extensive responses to carboplatin that differ between sensitive and resistant cells. Higher fatty acid oxidation (FAO) pathway expression is associated with platinum resistance, and both pharmacologic inhibition and CRISPR knockout of carnitine palmitoyltransferase 1A (CPT1A), which represents a rate limiting step of FAO, sensitize HGSOC cells to platinum. The results are further validated in patient-derived xenograft models, indicating that CPT1A is a candidate therapeutic target to overcome platinum resistance. All multiomic data can be queried via an intuitive gene-query user interface (https://sites.google.com/view/ptrc-cell-line).

Statistical inference of genetic pathway analysis in high dimensions

Genetic pathway analysis has become an important tool for investigating the association between a group of genetic variants and traits. With dense genotyping and extensive imputation, the number of genetic variants in biological pathways has increased considerably and sometimes exceeds the sample size [Formula: see text]. Conducting genetic pathway analysis and statistical inference in such settings is challenging. We introduce an approach that can handle pathways whose dimension [Formula: see text] could be greater than [Formula: see text]. Our method can be used to detect pathways that have nonsparse weak signals, as well as pathways that have sparse but stronger signals. We establish the asymptotic distribution for the proposed statistic and conduct theoretical analysis on its power. Simulation studies show that our test has correct Type I error control and is more powerful than existing approaches. An application to a genome-wide association study of high-density lipoproteins demonstrates the proposed approach.

Diagonal likelihood ratio test for equality of mean vectors in high-dimensional data

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

Generalized Hotelling's test for paired compositional data with application to human microbiome studies

The human microbiome is a dynamic system that changes due to diseases, medication, change in diet, etc. The paired design is a common approach to evaluate the microbial changes while controlling for the inherent differences between people. For example, microbiome data may be collected from the same individuals before and after a treatment. Two challenges exist in analyzing this type of data. First, microbiome data are compositional such that the reads for all taxa in each sample are constrained to sum to a constant. Second, the number of taxa can be much larger than the sample size. Few statistical methods exist to analyze such data besides methods that test one taxon at a time. In this paper, we propose to first conduct a log-ratio transformation of the compositions, and then develop a generalized Hotelling's test (GHT) to evaluate whether the average microbiome compositions are equivalent in the paired samples. We replace the sample covariance matrix in standard Hotelling's statistic by a shrinkage-based covariance, calculated as a weighted average of the sample covariance and a positive definite target matrix. The optimal weighting can be obtained for many commonly used target matrices. We develop a permutation procedure to assess the statistical significance. Extensive simulations show that our proposed method has well-controlled type I error and better power than a few ad hoc approaches. We apply our method to examine the vaginal microbiome changes in response to treatments for menopausal hot flashes. An R package " GHT" is freely available at https://github.com/zhaoni153/GHT.

Exploratory plasma proteomic analysis in a randomized crossover trial of aspirin among healthy men and women

Long-term use of aspirin is associated with lower risk of colorectal cancer and other cancers; however, the mechanism of chemopreventive effect of aspirin is not fully understood. Animal studies suggest that COX-2, NFκB signaling and Wnt/β-catenin pathways may play a role, but no clinical trials have systematically evaluated the biological response to aspirin in healthy humans. Using a high-density antibody array, we assessed the difference in plasma protein levels after 60 days of regular dose aspirin (325 mg/day) compared to placebo in a randomized double-blinded crossover trial of 44 healthy non-smoking men and women, aged 21-45 years. The plasma proteome was analyzed on an antibody microarray with ~3,300 full-length antibodies, printed in triplicate. Moderated paired t-tests were performed on individual antibodies, and gene-set analyses were performed based on KEGG and GO pathways. Among the 3,000 antibodies analyzed, statistically significant differences in plasma protein levels were observed for nine antibodies after adjusting for false discoveries (FDR adjusted p-value<0.1). The most significant protein was succinate dehydrogenase subunit C (SDHC), a key enzyme complex of the mitochondrial tricarboxylic acid (TCA) cycle. The other statistically significant proteins (NR2F1, MSI1, MYH1, FOXO1, KHDRBS3, NFKBIE, LYZ and IKZF1) are involved in multiple pathways, including DNA base-pair repair, inflammation and oncogenic pathways. None of the 258 KEGG and 1,139 GO pathways was found to be statistically significant after FDR adjustment. This study suggests several chemopreventive mechanisms of aspirin in humans, which have previously been reported to play a role in anti- or pro-carcinogenesis in cell systems; however, larger, confirmatory studies are needed.

Statistical Aspects in Proteomic Biomarker Discovery

In the pursuit of a personalized medicine, i.e., the individual treatment of a patient, many medical decision problems are desired to be supported by biomarkers that can help to make a diagnosis, prediction, or prognosis. Proteomic biomarkers are of special interest since they can not only be detected in tissue samples but can also often be easily detected in diverse body fluids. Statistical methods play an important role in the discovery and validation of proteomic biomarkers. They are necessary in the planning of experiments, in the processing of raw signals, and in the final data analysis. This review provides an overview on the most frequent experimental settings including sample size considerations, and focuses on exploratory data analysis and classifier development.

Set-Based Test Procedures for the Functional Analysis of Protein Lists from Differential Analysis

The analysis of most high-throughput proteomics experiments involves the selection of differentially expressed proteins or peptides between two different sets of samples, e.g., from two experimental groups. As a result, a large list of selected features is reported, typically sorted by a measure for the expression fold change and a p-value from a statistical test. The biological interpretation of such a list is usually difficult since the features can typically be assigned to a large variety of biological classes. To facilitate the biological interpretation, set-based procedures focus on the analysis of feature subsets that all belong to the same biological class (e.g., same cellular component, biological process, molecular function, or pathway). Set-based procedures can roughly be divided into "enrichment methods" and "global test procedures," where the first involve all features of an experiment and the second only those features of a particular set. In this chapter we detail the working principle of these kind of statistical methods and describe how features can be classified into molecular subsets. We illustrate the use of the methods on a data example from a proteomics Parkinson study.

A selective overview of feature screening for ultrahigh-dimensional data

High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of high-dimensional data poses many challenges for statisticians. Feature selection and variable selection are fundamental for high-dimensional data analysis. The sparsity principle, which assumes that only a small number of predictors contribute to the response, is frequently adopted and deemed useful in the analysis of high-dimensional data. Following this general principle, a large number of variable selection approaches via penalized least squares or likelihood have been developed in the recent literature to estimate a sparse model and select significant variables simultaneously. While the penalized variable selection methods have been successfully applied in many high-dimensional analyses, modern applications in areas such as genomics and proteomics push the dimensionality of data to an even larger scale, where the dimension of data may grow exponentially with the sample size. This has been called ultrahigh-dimensional data in the literature. This work aims to present a selective overview of feature screening procedures for ultrahigh-dimensional data. We focus on insights into how to construct marginal utilities for feature screening on specific models and motivation for the need of model-free feature screening procedures.

Power calculation for overall hypothesis testing with high-dimensional commensurate outcomes

The complexity of system biology means that any metabolic, genetic, or proteomic pathway typically includes so many components (e.g., molecules) that statistical methods specialized for overall testing of high-dimensional and commensurate outcomes are required. While many overall tests have been proposed, very few have power and sample size methods. We develop accurate power and sample size methods and software to facilitate study planning for high-dimensional pathway analysis. With an account of any complex correlation structure between high-dimensional outcomes, the new methods allow power calculation even when the sample size is less than the number of variables. We derive the exact (finite-sample) and approximate non-null distributions of the 'univariate' approach to repeated measures test statistic, as well as power-equivalent scenarios useful to generalize our numerical evaluations. Extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large. We derive a minimum set of constants and parameters sufficient and practical for power calculation. Using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin B6 deficiency helps illustrate the practical value of the new results. Free software implementing the power and sample size methods applies to a wide range of designs, including one group pre-intervention and post-intervention comparisons, multiple parallel group comparisons with one-way or factorial designs, and the adjustment and evaluation of covariate effects.

Adaption of the global test idea to proteomics data with missing values

MOTIVATION

Global test procedures are frequently used in gene expression analysis to study the relationship between a functional subset of RNA transcripts and an experimental group factor. However, these procedures have been rarely used for the analysis of high-throughput data from other sources, such as proteome expression data. The main difficulties in transferring global test procedures from genomics to proteomics data are the more complicated way of obtaining functional annotations and the handling of missing values in some types of proteomics data.

RESULTS

We propose a simple mixed linear model in combination with a permutation procedure and missing values imputation to conduct global tests in proteomics experiments. This new approach is motivated by protein expression data obtained by means of 2-D gel electrophoresis within a mouse experiment of our current research. A simulation study yielded that power and testing level of the mixed model alone can be affected by missing values in the dataset. Imputation of missing values was able to correct for a bias in some simulation settings. Our new approach provides the possibility to rank Gene Ontology (GO) terms associated with protein sets. It is also helpful in the case in which a specific protein is represented by multiple spots on a 2-D gel by considering these spots also as a protein set. Analysis of our data points at correlations between the deficiency of the protein 'calreticulin' and protein sets related to biological processes in the heart muscle.

AVAILABILITY AND IMPLEMENTATION

Our proposed approach is included in the R-package 'RepeatedHighDim', which already contains a global test procedure for gene expression data. The package can be retrieved from http://cran.r-project.org/.

CONTACT

klaus.jung@ams.med.uni-goettingen.de.

A penalized EM algorithm incorporating missing data mechanism for Gaussian parameter estimation

Missing data rates could depend on the targeted values in many settings, including mass spectrometry-based proteomic profiling studies. Here, we consider mean and covariance estimation under a multivariate Gaussian distribution with non-ignorable missingness, including scenarios in which the dimension (p) of the response vector is equal to or greater than the number (n) of independent observations. A parameter estimation procedure is developed by maximizing a class of penalized likelihood functions that entails explicit modeling of missing data probabilities. The performance of the resulting "penalized EM algorithm incorporating missing data mechanism (PEMM)" estimation procedure is evaluated in simulation studies and in a proteomic data illustration.

Smoothed Linear Modeling for Smooth Spectral Data

Classification and prediction problems using spectral data lead to high-dimensional data sets. Spectral data are, however, different from most other high-dimensional data sets in that information usually varies smoothly with wavelength, suggesting that fitted models should also vary smoothly with wavelength. Functional data analysis, widely used in the analysis of spectral data, meets this objective by changing perspective from the raw spectra to approximations using smooth basis functions. This paper explores linear regression and linear discriminant analysis fitted directly to the spectral data, imposing penalties on the values and roughness of the fitted coefficients, and shows by example that this can lead to better fits than existing standard methodologies.

Feature Screening via Distance Correlation Learning

This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance correlation (DC-SIS, for short). The DC-SIS can be implemented as easily as the sure independence screening procedure based on the Pearson correlation (SIS, for short) proposed by Fan and Lv (2008). However, the DC-SIS can significantly improve the SIS. Fan and Lv (2008) established the sure screening property for the SIS based on linear models, but the sure screening property is valid for the DC-SIS under more general settings including linear models. Furthermore, the implementation of the DC-SIS does not require model specification (e.g., linear model or generalized linear model) for responses or predictors. This is a very appealing property in ultrahigh dimensional data analysis. Moreover, the DC-SIS can be used directly to screen grouped predictor variables and for multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the DC-SIS performs much better than the SIS in various models. We also illustrate the DC-SIS through a real data example.