Integrative Analysis of High‐throughput Cancer Studies With Contrasted Penalization

In cancer studies with high‐throughput genetic and genomic measurements, integrative analysis provides a way to effectively pool and analyze heterogeneous raw data from multiple independent studies and outperforms “classic” meta‐analysis and single‐dataset analysis. When marker selection is of interest, the genetic basis of multiple datasets can be described using the homogeneity model or the heterogeneity model. In this study, we consider marker selection under the heterogeneity model, which includes the homogeneity model as a special case and can be more flexible. Penalization methods have been developed in the literature for marker selection. This study advances from the published ones by introducing the contrast penalties, which can accommodate the within‐ and across‐dataset structures of covariates/regression coefficients and, by doing so, further improve marker selection performance. Specifically, we develop a penalization method that accommodates the across‐dataset structures by smoothing over regression coefficients. An effective iterative algorithm, which calls an inner coordinate descent iteration, is developed. Simulation shows that the proposed method outperforms the benchmark with more accurate marker identification. The analysis of breast cancer and lung cancer prognosis studies with gene expression measurements shows that the proposed method identifies genes different from those using the benchmark and has better prediction performance.     

Integrative sparse principal component analysis of gene expression data

In the analysis of gene expression data, dimension reduction techniques have been extensively adopted. The most popular one is perhaps the PCA (principal component analysis). To generate more reliable and more interpretable results, the SPCA (sparse PCA) technique has been developed. With the “small sample size, high dimensionality” characteristic of gene expression data, the analysis results generated from a single dataset are often unsatisfactory. Under contexts other than dimension reduction, integrative analysis techniques, which jointly analyze the raw data of multiple independent datasets, have been developed and shown to outperform “classic” meta‐analysis and other multidatasets techniques and single‐dataset analysis. In this study, we conduct integrative analysis by developing the iSPCA (integrative SPCA) method. iSPCA achieves the selection and estimation of sparse loadings using a group penalty. To take advantage of the similarity across datasets and generate more accurate results, we further impose contrasted penalties. Different penalties are proposed to accommodate different data conditions. Extensive simulations show that iSPCA outperforms the alternatives under a wide spectrum of settings. The analysis of breast cancer and pancreatic cancer data further shows iSPCA's satisfactory performance.     

Integrative analysis of multiple cancer genomic datasets under the heterogeneity model

In the analysis of cancer studies with high‐dimensional genomic measurements, integrative analysis provides an effective way of pooling information across multiple heterogeneous datasets. The genomic basis of multiple independent datasets, which can be characterized by the sets of genomic markers, can be described using the homogeneity model or heterogeneity model. Under the homogeneity model, all datasets share the same set of markers associated with responses. In contrast, under the heterogeneity model, different studies have overlapping but possibly different sets of markers. The heterogeneity model contains the homogeneity model as a special case and can be much more flexible. Marker selection under the heterogeneity model calls for bi‐level selection to determine whether a covariate is associated with response in any study at all as well as in which studies it is associated with responses. In this study, we consider two minimax concave penalty‐based penalization approaches for marker selection under the heterogeneity model. For each approach, we describe its rationale and an effective computational algorithm. We conduct simulations to investigate their performance and compare with the existing alternatives. We also apply the proposed approaches to the analysis of gene expression data on multiple cancers. Copyright © 2013 John Wiley & Sons, Ltd.     

Penalized integrative semiparametric interaction analysis for multiple genetic datasets

In this article, we consider a semiparametric additive partially linear interaction model for the integrative analysis of multiple genetic datasets. The goals are to identify important genetic predictors and gene-gene interactions and to estimate the nonparametric functions that describe the environmental effects at the same time. To find the similarities and differences of the genetic effects across different datasets, we impose a group structure on the regression coefficients matrix under the homogeneity assumption, ie, models for different datasets share the same sparsity structure, but the coefficients may differ across datasets. We develop an iterative approach to estimate the parameters of main effects, interactions and nonparametric functions, where a reparametrization of interaction parameters is implemented to meet the strong hierarchy assumption. We demonstrate the advantages of the proposed method in identification, estimation, and prediction in a series of numerical studies. We also apply the proposed method to the Skin Cutaneous Melanoma data and the lung cancer data from the Cancer Genome Atlas.     

Incorporating Network Structure in Integrative Analysis of Cancer Prognosis Data

In high‐throughput cancer genomic studies, markers identified from the analysis of single datasets may have unsatisfactory properties because of low sample sizes. Integrative analysis pools and analyzes raw data from multiple studies, and can effectively increase sample size and lead to improved marker identification results. In this study, we consider the integrative analysis of multiple high‐throughput cancer prognosis studies. In the existing integrative analysis studies, the interplay among genes, which can be described using the network structure, has not been effectively accounted for. In network analysis, tightly connected nodes (genes) are more likely to have related biological functions and similar regression coefficients. The goal of this study is to develop an analysis approach that can incorporate the gene network structure in integrative analysis. To this end, we adopt an AFT (accelerated failure time) model to describe survival. A weighted least squares approach, which has low computational cost, is adopted for estimation. For marker selection, we propose a new penalization approach. The proposed penalty is composed of two parts. The first part is a group MCP penalty, and conducts gene selection. The second part is a Laplacian penalty, and smoothes the differences of coefficients for tightly connected genes. A group coordinate descent approach is developed to compute the proposed estimate. Simulation study shows satisfactory performance of the proposed approach when there exist moderate‐to‐strong correlations among genes. We analyze three lung cancer prognosis datasets, and demonstrate that incorporating the network structure can lead to the identification of important genes and improved prediction performance.     

POLARIS: Polygenic LD‐adjusted risk score approach for set‐based analysis of GWAS data

Polygenic risk scores (PRSs) are a method to summarize the additive trait variance captured by a set of SNPs, and can increase the power of set‐based analyses by leveraging public genome‐wide association study (GWAS) datasets. PRS aims to assess the genetic liability to some phenotype on the basis of polygenic risk for the same or different phenotype estimated from independent data. We propose the application of PRSs as a set‐based method with an additional component of adjustment for linkage disequilibrium (LD), with potential extension of the PRS approach to analyze biologically meaningful SNP sets. We call this method POLARIS: POlygenic Ld‐Adjusted RIsk Score. POLARIS identifies the LD structure of SNPs using spectral decomposition of the SNP correlation matrix and replaces the individuals' SNP allele counts with LD‐adjusted dosages. Using a raw genotype dataset together with SNP effect sizes from a second independent dataset, POLARIS can be used for set‐based analysis. MAGMA is an alternative set‐based approach employing principal component analysis to account for LD between markers in a raw genotype dataset. We used simulations, both with simple constructed and real LD‐structure, to compare the power of these methods. POLARIS shows more power than MAGMA applied to the raw genotype dataset only, but less or comparable power to combined analysis of both datasets. POLARIS has the advantages that it produces a risk score per person per set using all available SNPs, and aims to increase power by leveraging the effect sizes from the discovery set in a self‐contained test of association in the test dataset.     

Pathway‐Based Approaches for Sequencing‐Based Genome‐Wide Association Studies

For analyzing complex trait association with sequencing data, most current studies test aggregated effects of variants in a gene or genomic region. Although gene‐based tests have insufficient power even for moderately sized samples, pathway‐based analyses combine information across multiple genes in biological pathways and may offer additional insight. However, most existing pathway association methods are originally designed for genome‐wide association studies, and are not comprehensively evaluated for sequencing data. Moreover, region‐based rare variant association methods, although potentially applicable to pathway‐based analysis by extending their region definition to gene sets, have never been rigorously tested. In the context of exome‐based studies, we use simulated and real datasets to evaluate pathway‐based association tests. Our simulation strategy adopts a genome‐wide genetic model that distributes total genetic effects hierarchically into pathways, genes, and individual variants, allowing the evaluation of pathway‐based methods with realistic quantifiable assumptions on the underlying genetic architectures. The results show that, although no single pathway‐based association method offers superior performance in all simulated scenarios, a modification of Gene Set Enrichment Analysis approach using statistics from single‐marker tests without gene‐level collapsing (weighted Kolmogrov‐Smirnov [WKS]‐Variant method) is consistently powerful. Interestingly, directly applying rare variant association tests (e.g., sequence kernel association test) to pathway analysis offers a similar power, but its results are sensitive to assumptions of genetic architecture. We applied pathway association analysis to an exome‐sequencing data of the chronic obstructive pulmonary disease, and found that the WKS‐Variant method confirms associated genes previously published.     

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.     

MF‐TOWmuT: Testing an optimally weighted combination of common and rare variants with multiple traits using family data

With rapid advancements of sequencing technologies and accumulations of electronic health records, a large number of genetic variants and multiple correlated human complex traits have become available in many genetic association studies. Thus, it becomes necessary and important to develop new methods that can jointly analyze the association between multiple genetic variants and multiple traits. Compared with methods that only use a single marker or trait, the joint analysis of multiple genetic variants and multiple traits is more powerful since such an analysis can fully incorporate the correlation structure of genetic variants and/or traits and their mutual dependence patterns. However, most of existing methods that simultaneously analyze multiple genetic variants and multiple traits are only applicable to unrelated samples. We develop a new method called MF‐TOWmuT to detect association of multiple phenotypes and multiple genetic variants in a genomic region with family samples. MF‐TOWmuT is based on an optimally weighted combination of variants. Our method can be applied to both rare and common variants and both qualitative and quantitative traits. Our simulation results show that (1) the type I error of MF‐TOWmuT is preserved; (2) MF‐TOWmuT outperforms two existing methods such as Multiple Family‐based Quasi‐Likelihood Score Test and Multivariate Family‐based Rare Variant Association Test in terms of power. We also illustrate the usefulness of MF‐TOWmuT by analyzing genotypic and phenotipic data from the Genetics of Kidneys in Diabetes study. R program is available at https://github.com/gaochengPRC/MF-TOWmuT .     

Integrative analysis of multiple cancer prognosis studies with gene expression measurements

Although in cancer research microarray gene profiling studies have been successful in identifying genetic variants predisposing to the development and progression of cancer, the identified markers from analysis of single datasets often suffer low reproducibility. Among multiple possible causes, the most important one is the small sample size hence the lack of power of single studies. Integrative analysis jointly considers multiple heterogeneous studies, has a significantly larger sample size, and can improve reproducibility. In this article, we focus on cancer prognosis studies, where the response variables are progression-free, overall, or other types of survival. A group minimax concave penalty (GMCP) penalized integrative analysis approach is proposed for analyzing multiple heterogeneous cancer prognosis studies with microarray gene expression measurements. An efficient group coordinate descent algorithm is developed. The GMCP can automatically accommodate the heterogeneity across multiple datasets, and the identified markers have consistent effects across multiple studies. Simulation studies show that the GMCP provides significantly improved selection results as compared with the existing meta-analysis approaches, intensity approaches, and group Lasso penalized integrative analysis. We apply the GMCP to four microarray studies and identify genes associated with the prognosis of breast cancer.     

Variable selection for multiply‐imputed data with application to dioxin exposure study

Multiple imputation (MI) is a commonly used technique for handling missing data in large‐scale medical and public health studies. However, variable selection on multiply‐imputed data remains an important and longstanding statistical problem. If a variable selection method is applied to each imputed dataset separately, it may select different variables for different imputed datasets, which makes it difficult to interpret the final model or draw scientific conclusions. In this paper, we propose a novel multiple imputation‐least absolute shrinkage and selection operator (MI‐LASSO) variable selection method as an extension of the least absolute shrinkage and selection operator (LASSO) method to multiply‐imputed data. The MI‐LASSO method treats the estimated regression coefficients of the same variable across all imputed datasets as a group and applies the group LASSO penalty to yield a consistent variable selection across multiple‐imputed datasets. We use a simulation study to demonstrate the advantage of the MI‐LASSO method compared with the alternatives. We also apply the MI‐LASSO method to the University of Michigan Dioxin Exposure Study to identify important circumstances and exposure factors that are associated with human serum dioxin concentration in Midland, Michigan. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐dependent summary receiver operating characteristics for meta‐analysis of prognostic studies

Prognostic studies are widely conducted to examine whether biomarkers are associated with patient's prognoses and play important roles in medical decisions. Because findings from one prognostic study may be very limited, meta‐analyses may be useful to obtain sound evidence. However, prognostic studies are often analyzed by relying on a study‐specific cut‐off value, which can lead to difficulty in applying the standard meta‐analysis techniques. In this paper, we propose two methods to estimate a time‐dependent version of the summary receiver operating characteristics curve for meta‐analyses of prognostic studies with a right‐censored time‐to‐event outcome. We introduce a bivariate normal model for the pair of time‐dependent sensitivity and specificity and propose a method to form inferences based on summary statistics reported in published papers. This method provides a valid inference asymptotically. In addition, we consider a bivariate binomial model. To draw inferences from this bivariate binomial model, we introduce a multiple imputation method. The multiple imputation is found to be approximately proper multiple imputation, and thus the standard Rubin's variance formula is justified from a Bayesian view point. Our simulation study and application to a real dataset revealed that both methods work well with a moderate or large number of studies and the bivariate binomial model coupled with the multiple imputation outperforms the bivariate normal model with a small number of studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Genetic Association With Multiple Traits in the Presence of Population Stratification

Testing association between a genetic marker and multiple‐dependent traits is a challenging task when both binary and quantitative traits are involved. The inverted regression model is a convenient method, in which the traits are treated as predictors although the genetic marker is an ordinal response. It is known that population stratification (PS) often affects population‐based association studies. However, how it would affect the inverted regression for pleiotropic association, especially with the mixed types of traits (binary and quantitative), is not examined and the performance of existing methods to correct for PS using the inverted regression analysis is unknown. In this paper, we focus on the methods based on genomic control and principal component analysis, and investigate type I error of pleiotropic association using the inverted regression model in the presence of PS with allele frequencies and the distributions (or disease prevalences) of multiple traits varying across the subpopulations. We focus on common alleles but simulation results for a rare variant are also reported. An application to the HapMap data is used for illustration.     

Integrative Analysis of Cancer Prognosis Data With Multiple Subtypes Using Regularized Gradient Descent

In cancer research, high‐throughput profiling studies have been extensively conducted, searching for genes/single nucleotide polymorphisms (SNPs) associated with prognosis. Despite seemingly significant differences, different subtypes of the same cancer (or different types of cancers) may share common susceptibility genes. In this study, we analyze prognosis data on multiple subtypes of the same cancer but note that the proposed approach is directly applicable to the analysis of data on multiple types of cancers. We describe the genetic basis of multiple subtypes using the heterogeneity model that allows overlapping but different sets of susceptibility genes/SNPs for different subtypes. An accelerated failure time (AFT) model is adopted to describe prognosis. We develop a regularized gradient descent approach that conducts gene‐level analysis and identifies genes that contain important SNPs associated with prognosis. The proposed approach belongs to the family of gradient descent approaches, is intuitively reasonable, and has affordable computational cost. Simulation study shows that when prognosis‐associated SNPs are clustered in a small number of genes, the proposed approach outperforms alternatives with significantly more true positives and fewer false positives. We analyze an NHL (non‐Hodgkin lymphoma) prognosis study with SNP measurements and identify genes associated with the three major subtypes of NHL, namely, DLBCL, FL, and CLL/SLL. The proposed approach identifies genes different from using alternative approaches and has the best prediction performance.     

Integrative analysis of gene–environment interactions under a multi‐response partially linear varying coefficient model

Consider the integrative analysis of genetic data with multiple correlated response variables. The goal is to identify important gene–environment (G × E) interactions along with main gene and environment effects that are associated with the responses. The homogeneity and heterogeneity models can be adopted to describe the genetic basis of multiple responses. To accommodate possible nonlinear effects of some environment effects, a multi‐response partially linear varying coefficient model is assumed. Penalization is adopted for marker selection. The proposed penalization method can select genetic variants with G × E interactions, no G × E interactions, and no main effects simultaneously. It adopts different penalties to accommodate the homogeneity and heterogeneity models. The proposed method can be effectively computed using a coordinate descent algorithm. Simulation study and the analysis of Health Professionals Follow‐up Study, which has two correlated continuous traits, SNP measurements and multiple environment effects, show superior performance of the proposed method over its competitors. Copyright © 2014 John Wiley & Sons, Ltd.     

Random‐effects meta‐analysis of the clinical utility of tests and prediction models

The use of data from multiple studies or centers for the validation of a clinical test or a multivariable prediction model allows researchers to investigate the test's/model's performance in multiple settings and populations. Recently, meta‐analytic techniques have been proposed to summarize discrimination and calibration across study populations. Here, we rather consider performance in terms of net benefit, which is a measure of clinical utility that weighs the benefits of true positive classifications against the harms of false positives. We posit that it is important to examine clinical utility across multiple settings of interest. This requires a suitable meta‐analysis method, and we propose a Bayesian trivariate random‐effects meta‐analysis of sensitivity, specificity, and prevalence. Across a range of chosen harm‐to‐benefit ratios, this provides a summary measure of net benefit, a prediction interval, and an estimate of the probability that the test/model is clinically useful in a new setting. In addition, the prediction interval and probability of usefulness can be calculated conditional on the known prevalence in a new setting. The proposed methods are illustrated by 2 case studies: one on the meta‐analysis of published studies on ear thermometry to diagnose fever in children and one on the validation of a multivariable clinical risk prediction model for the diagnosis of ovarian cancer in a multicenter dataset. Crucially, in both case studies the clinical utility of the test/model was heterogeneous across settings, limiting its usefulness in practice. This emphasizes that heterogeneity in clinical utility should be assessed before a test/model is routinely implemented.     

Integrative and regularized principal component analysis of multiple sources of data

Integration of data of disparate types has become increasingly important to enhancing the power for new discoveries by combining complementary strengths of multiple types of data. One application is to uncover tumor subtypes in human cancer research in which multiple types of genomic data are integrated, including gene expression, DNA copy number, and DNA methylation data. In spite of their successes, existing approaches based on joint latent variable models require stringent distributional assumptions and may suffer from unbalanced scales (or units) of different types of data and non‐scalability of the corresponding algorithms. In this paper, we propose an alternative based on integrative and regularized principal component analysis, which is distribution‐free, computationally efficient, and robust against unbalanced scales. The new method performs dimension reduction simultaneously on multiple types of data, seeking data‐adaptive sparsity and scaling. As a result, in addition to feature selection for each type of data, integrative clustering is achieved. Numerically, the proposed method compares favorably against its competitors in terms of accuracy (in identifying hidden clusters), computational efficiency, and robustness against unbalanced scales. In particular, compared with a popular method, the new method was competitive in identifying tumor subtypes associated with distinct patient survival patterns when applied to a combined analysis of DNA copy number, mRNA expression, and DNA methylation data in a glioblastoma multiforme study. Copyright © 2016 John Wiley & Sons, Ltd.     

Combining fractional polynomial model building with multiple imputation

Multivariable fractional polynomial (MFP) models are commonly used in medical research. The datasets in which MFP models are applied often contain covariates with missing values. To handle the missing values, we describe methods for combining multiple imputation with MFP modelling, considering in turn three issues: first, how to impute so that the imputation model does not favour certain fractional polynomial (FP) models over others; second, how to estimate the FP exponents in multiply imputed data; and third, how to choose between models of differing complexity. Two imputation methods are outlined for different settings. For model selection, methods based on Wald‐type statistics and weighted likelihood‐ratio tests are proposed and evaluated in simulation studies. The Wald‐based method is very slightly better at estimating FP exponents. Type I error rates are very similar for both methods, although slightly less well controlled than analysis of complete records; however, there is potential for substantial gains in power over the analysis of complete records. We illustrate the two methods in a dataset from five trauma registries for which a prognostic model has previously been published, contrasting the selected models with that obtained by analysing the complete records only. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Selection of nonlinear interactions by a forward stepwise algorithm: Application to identifying environmental chemical mixtures affecting health outcomes

In this paper, we propose a stepwise forward selection algorithm for detecting the effects of a set of correlated exposures and their interactions on a health outcome of interest when the underlying relationship could potentially be nonlinear. Though the proposed method is very general, our application in this paper remains to be on analysis of multiple pollutants and their interactions. Simultaneous exposure to multiple environmental pollutants could affect human health in a multitude of complex ways. For understanding the health effects of multiple environmental exposures, it is often important to identify and estimate complex interactions among exposures. However, this issue becomes analytically challenging in the presence of potential nonlinearity in the outcome-exposure response surface and a set of correlated exposures. Through simulation studies and analyses of test datasets that were simulated as a part of a data challenge in multipollutant modeling organized by the National Institute of Environmental Health Sciences ( http://www.niehs.nih.gov/about/events/pastmtg/2015/statistical/ ), we illustrate the advantages of our proposed method in comparison with existing alternative approaches. A particular strength of our method is that it demonstrates very low false positives across empirical studies. Our method is also used to analyze a dataset that was released from the Health Outcomes and Measurement of the Environment Study as a benchmark beta-tester dataset as a part of the same workshop.     

Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve

In biomedical studies, it is often of interest to classify/predict a subject's disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on area under the receiver operating characteristic curve (AUC). Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient‐based algorithms to find the best marker combination, which often result in suboptimal local solutions. In this paper, we address these two problems by proposing a new kernel‐based AUC optimization method called ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data are generated from a semiparametric generalized linear model, just as the smoothed AUC method. Through simulation studies and real data examples, we demonstrate that RAUC outperforms smooth AUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. Copyright © 2016 John Wiley & Sons, Ltd.