Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data

MOTIVATION: An important application of microarray technology is to relate gene expression profiles to various clinical phenotypes of patients. Success has been demonstrated in molecular classification of cancer in which the gene expression data serve as predictors and different types of cancer serve as a categorical outcome variable. However, there has been less research in linking gene expression profiles to the censored survival data such as patients' overall survival time or time to cancer relapse. It would be desirable to have models with good prediction accuracy and parsimony property. RESULTS: We propose to use the L(1) penalized estimation for the Cox model to select genes that are relevant to patients' survival and to build a predictive model for future prediction. The computational difficulty associated with the estimation in the high-dimensional and low-sample size settings can be efficiently solved by using the recently developed least-angle regression (LARS) method. Our simulation studies and application to real datasets on predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed procedure, which we call the LARS-Cox procedure, can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. The LARS-Cox regression gives better predictive performance than the L(2) penalized regression and a few other dimension-reduction based methods. CONCLUSIONS: We conclude that the proposed LARS-Cox procedure can be very useful in identifying genes relevant to survival phenotypes and in building a parsimonious predictive model that can be used for classifying future patients into clinically relevant high- and low-risk groups based on the gene expression profile and survival times of previous patients.     

CASPAR: a hierarchical bayesian approach to predict survival times in cancer from gene expression data

MOTIVATION: DNA microarrays allow the simultaneous measurement of thousands of gene expression levels in any given patient sample. Gene expression data have been shown to correlate with survival in several cancers, however, analysis of the data is difficult, since typically at most a few hundred patients are available, resulting in severely underdetermined regression or classification models. Several approaches exist to classify patients in different risk classes, however, relatively little has been done with respect to the prediction of actual survival times. We introduce CASPAR, a novel method to predict true survival times for the individual patient based on microarray measurements. CASPAR is based on a multivariate Cox regression model that is embedded in a Bayesian framework. A hierarchical prior distribution on the regression parameters is specifically designed to deal with high dimensionality (large number of genes) and low sample size settings, that are typical for microarray measurements. This enables CASPAR to automatically select small, most informative subsets of genes for prediction. RESULTS: Validity of the method is demonstrated on two publicly available datasets on diffuse large B-cell lymphoma (DLBCL) and on adenocarcinoma of the lung. The method successfully identifies long and short survivors, with high sensitivity and specificity. We compare our method with two alternative methods from the literature, demonstrating superior results of our approach. In addition, we show that CASPAR can further refine predictions made using clinical scoring systems such as the International Prognostic Index (IPI) for DLBCL and clinical staging for lung cancer, thus providing an additional tool for the clinician. An analysis of the genes identified confirms previously published results, and furthermore, new candidate genes correlated with survival are identified.     

Bayesian model averaging: development of an improved multi-class, gene selection and classification tool for microarray data

MOTIVATION: Selecting a small number of relevant genes for accurate classification of samples is essential for the development of diagnostic tests. We present the Bayesian model averaging (BMA) method for gene selection and classification of microarray data. Typical gene selection and classification procedures ignore model uncertainty and use a single set of relevant genes (model) to predict the class. BMA accounts for the uncertainty about the best set to choose by averaging over multiple models (sets of potentially overlapping relevant genes). RESULTS: We have shown that BMA selects smaller numbers of relevant genes (compared with other methods) and achieves a high prediction accuracy on three microarray datasets. Our BMA algorithm is applicable to microarray datasets with any number of classes, and outputs posterior probabilities for the selected genes and models. Our selected models typically consist of only a few genes. The combination of high accuracy, small numbers of genes and posterior probabilities for the predictions should make BMA a powerful tool for developing diagnostics from expression data. AVAILABILITY: The source codes and datasets used are available from our Supplementary website.     

Optimized between-group classification: a new jackknife-based gene selection procedure for genome-wide expression data

Background  

A recent publication described a supervised classification method for microarray data: Between Group Analysis (BGA). This method which is based on performing multivariate ordination of groups proved to be very efficient for both classification of samples into pre-defined groups and disease class prediction of new unknown samples. Classification and prediction with BGA are classically performed using the whole set of genes and no variable selection is required. We hypothesize that an optimized selection of highly discriminating genes might improve the prediction power of BGA.     

Between-group analysis of microarray data

MOTIVATION: Most supervised classification methods are limited by the requirement for more cases than variables. In microarray data the number of variables (genes) far exceeds the number of cases (arrays), and thus filtering and pre-selection of genes is required. We describe the application of Between Group Analysis (BGA) to the analysis of microarray data. A feature of BGA is that it can be used when the number of variables (genes) exceeds the number of cases (arrays). BGA is based on carrying out an ordination of groups of samples, using a standard method such as Correspondence Analysis (COA), rather than an ordination of the individual microarray samples. As such, it can be viewed as a method of carrying out COA with grouped data. RESULTS: We illustrate the power of the method using two cancer data sets. In both cases, we can quickly and accurately classify test samples from any number of specified a priori groups and identify the genes which characterize these groups. We obtained very high rates of correct classification, as determined by jack-knife or validation experiments with training and test sets. The results are comparable to those from other methods in terms of accuracy but the power and flexibility of BGA make it an especially attractive method for the analysis of microarray cancer data.     

Nearest template prediction: a single-sample-based flexible class prediction with confidence assessment

Gene-expression signature-based disease classification and clinical outcome prediction has not been widely introduced in clinical medicine as initially expected, mainly due to the lack of extensive validation needed for its clinical deployment. Obstacles include variable measurement in microarray assay, inconsistent assay platform, analytical requirement for comparable pair of training and test datasets, etc. Furthermore, as medical device helping clinical decision making, the prediction needs to be made for each single patient with a measure of its reliability. To address these issues, there is a need for flexible prediction method less sensitive to difference in experimental and analytical conditions, applicable to each single patient, and providing measure of prediction confidence. The nearest template prediction (NTP) method provides a convenient way to make class prediction with assessment of prediction confidence computed in each single patient's gene-expression data using only a list of signature genes and a test dataset. We demonstrate that the method can be flexibly applied to cross-platform, cross-species, and multiclass predictions without any optimization of analysis parameters.     

Determination of Minimum Training Sample Size for Microarray-Based Cancer Outcome Prediction–An Empirical Assessment

The promise of microarray technology in providing prediction classifiers for cancer outcome estimation has been confirmed by a number of demonstrable successes. However, the reliability of prediction results relies heavily on the accuracy of statistical parameters involved in classifiers. It cannot be reliably estimated with only a small number of training samples. Therefore, it is of vital importance to determine the minimum number of training samples and to ensure the clinical value of microarrays in cancer outcome prediction. We evaluated the impact of training sample size on model performance extensively based on 3 large-scale cancer microarray datasets provided by the second phase of MicroArray Quality Control project (MAQC-II). An SSNR-based (scale of signal-to-noise ratio) protocol was proposed in this study for minimum training sample size determination. External validation results based on another 3 cancer datasets confirmed that the SSNR-based approach could not only determine the minimum number of training samples efficiently, but also provide a valuable strategy for estimating the underlying performance of classifiers in advance. Once translated into clinical routine applications, the SSNR-based protocol would provide great convenience in microarray-based cancer outcome prediction in improving classifier reliability.     

Transforming RNA-Seq Data to Improve the Performance of Prognostic Gene Signatures

Gene expression measurements have successfully been used for building prognostic signatures, i.e for identifying a short list of important genes that can predict patient outcome. Mostly microarray measurements have been considered, and there is little advice available for building multivariable risk prediction models from RNA-Seq data. We specifically consider penalized regression techniques, such as the lasso and componentwise boosting, which can simultaneously consider all measurements and provide both, multivariable regression models for prediction and automated variable selection. However, they might be affected by the typical skewness, mean-variance-dependency or extreme values of RNA-Seq covariates and therefore could benefit from transformations of the latter. In an analytical part, we highlight preferential selection of covariates with large variances, which is problematic due to the mean-variance dependency of RNA-Seq data. In a simulation study, we compare different transformations of RNA-Seq data for potentially improving detection of important genes. Specifically, we consider standardization, the log transformation, a variance-stabilizing transformation, the Box-Cox transformation, and rank-based transformations. In addition, the prediction performance for real data from patients with kidney cancer and acute myeloid leukemia is considered. We show that signature size, identification performance, and prediction performance critically depend on the choice of a suitable transformation. Rank-based transformations perform well in all scenarios and can even outperform complex variance-stabilizing approaches. Generally, the results illustrate that the distribution and potential transformations of RNA-Seq data need to be considered as a critical step when building risk prediction models by penalized regression techniques.     

Bayesian variable selection for the analysis of microarray data with censored outcomes

MOTIVATION: A common task in microarray data analysis consists of identifying genes associated with a phenotype. When the outcomes of interest are censored time-to-event data, standard approaches assess the effect of genes by fitting univariate survival models. In this paper, we propose a Bayesian variable selection approach, which allows the identification of relevant markers by jointly assessing sets of genes. We consider accelerated failure time (AFT) models with log-normal and log-t distributional assumptions. A data augmentation approach is used to impute the failure times of censored observations and mixture priors are used for the regression coefficients to identify promising subsets of variables. The proposed method provides a unified procedure for the selection of relevant genes and the prediction of survivor functions. RESULTS: We demonstrate the performance of the method on simulated examples and on several microarray datasets. For the simulation study, we consider scenarios with large number of noisy variables and different degrees of correlation between the relevant and non-relevant (noisy) variables. We are able to identify the correct covariates and obtain good prediction of the survivor functions. For the microarray applications, some of our selected genes are known to be related to the diseases under study and a few are in agreement with findings from other researchers. AVAILABILITY: The Matlab code for implementing the Bayesian variable selection method may be obtained from the corresponding author. CONTACT: mvannucci@stat.tamu.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Logistic regression for disease classification using microarray data: model selection in a large p and small n case

MOTIVATION: Logistic regression is a standard method for building prediction models for a binary outcome and has been extended for disease classification with microarray data by many authors. A feature (gene) selection step, however, must be added to penalized logistic modeling due to a large number of genes and a small number of subjects. Model selection for this two-step approach requires new statistical tools because prediction error estimation ignoring the feature selection step can be severely downward biased. Generic methods such as cross-validation and non-parametric bootstrap can be very ineffective due to the big variability in the prediction error estimate. RESULTS: We propose a parametric bootstrap model for more accurate estimation of the prediction error that is tailored to the microarray data by borrowing from the extensive research in identifying differentially expressed genes, especially the local false discovery rate. The proposed method provides guidance on the two critical issues in model selection: the number of genes to include in the model and the optimal shrinkage for the penalized logistic regression. We show that selecting more than 20 genes usually helps little in further reducing the prediction error. Application to Golub's leukemia data and our own cervical cancer data leads to highly accurate prediction models. AVAILABILITY: R library GeneLogit at http://geocities.com/jg_liao     

On sparse Fisher discriminant method for microarray data analysis

One of the applications of the discriminant analysis on microarray data is to classify patient and normal samples based on gene expression values. The analysis is especially important in medical trials and diagnosis of cancer subtypes. The main contribution of this paper is to propose a simple Fisher-type discriminant method on gene selection in microarray data. In the new algorithm, we calculate a weight for each gene and use the weight values as an indicator to identify the subsets of relevant genes that categorize patient and normal samples. A l(2) - l(1) norm minimization method is implemented to the discriminant process to automatically compute the weights of all genes in the samples. The experiments on two microarray data sets have shown that the new algorithm can generate classification results as good as other classification methods, and effectively determine relevant genes for classification purpose. In this study, we demonstrate the gene selection's ability and the computational effectiveness of the proposed algorithm. Experimental results are given to illustrate the usefulness of the proposed model.     

Complementary hierarchical clustering

When applying hierarchical clustering algorithms to cluster patient samples from microarray data, the clustering patterns generated by most algorithms tend to be dominated by groups of highly differentially expressed genes that have closely related expression patterns. Sometimes, these genes may not be relevant to the biological process under study or their functions may already be known. The problem is that these genes can potentially drown out the effects of other genes that are relevant or have novel functions. We propose a procedure called complementary hierarchical clustering that is designed to uncover the structures arising from these novel genes that are not as highly expressed. Simulation studies show that the procedure is effective when applied to a variety of examples. We also define a concept called relative gene importance that can be used to identify the influential genes in a given clustering. Finally, we analyze a microarray data set from 295 breast cancer patients, using clustering with the correlation-based distance measure. The complementary clustering reveals a grouping of the patients which is uncorrelated with a number of known prognostic signatures and significantly differing distant metastasis-free probabilities.     

Gene-expression profiles predict survival of patients with lung adenocarcinoma

Histopathology is insufficient to predict disease progression and clinical outcome in lung adenocarcinoma. Here we show that gene-expression profiles based on microarray analysis can be used to predict patient survival in early-stage lung adenocarcinomas. Genes most related to survival were identified with univariate Cox analysis. Using either two equivalent but independent training and testing sets, or 'leave-one-out' cross-validation analysis with all tumors, a risk index based on the top 50 genes identified low-risk and high-risk stage I lung adenocarcinomas, which differed significantly with respect to survival. This risk index was then validated using an independent sample of lung adenocarcinomas that predicted high- and low-risk groups. This index included genes not previously associated with survival. The identification of a set of genes that predict survival in early-stage lung adenocarcinoma allows delineation of a high-risk group that may benefit from adjuvant therapy.     

Integrating functional knowledge during sample clustering for microarray data using unsupervised decision trees

Clustering of microarray gene expression data is performed routinely, for genes as well as for samples. Clustering of genes can exhibit functional relationships between genes; clustering of samples on the other hand is important for finding e.g. disease subtypes, relevant patient groups for stratification or related treatments. Usually this is done by first filtering the genes for high-variance under the assumption that they carry most of the information needed for separating different sample groups. If this assumption is violated, important groupings in the data might be lost. Furthermore, classical clustering methods do not facilitate the biological interpretation of the results. Therefore, we propose to methodologically integrate the clustering algorithm with prior biological information. This is different from other approaches as knowledge about classes of genes can be directly used to ease the interpretation of the results and possibly boost clustering performance. Our approach computes dendrograms that resemble decision trees with gene classes used to split the data at each node which can help to find biologically meaningful differences between the sample groups. We have tested the proposed method both on simulated and real data and conclude its usefulness as a complementary method, especially when assumptions of few differentially expressed genes along with an informative mapping of genes to different classes are met.     

Data pattern analysis for the individualised pretherapeutic identification of high-risk diffuse large B-cell lymphoma (DLBCL) patients by cytomics.

BACKGROUND: Clinical outcome predictions in phase III studies are mostly derived for patient groups, but not for individual patients, although individualised predictions are an ultimate goal to permit a personalised fine tuning of therapy. This may permit earlier application of target therapies, minimise general damage to the organism, and result in improved complete remission rates in malignant diseases. METHODS: In this study, Lymphochip cDNA microarray gene expression results of DLBCL patients, from a published prospective meta-analysis study on the prediction of group prognosis, were analysed for individualised predictions using a nonstatistical data pattern classification approach. The training set was comprised of the same 160 DLBCL patients as in the prognosis study, with the validation set of 80 patients remaining unknown to the learning process. This permits the assessment of prospective classifier performance towards unknown patients. RESULTS: Pretherapeutic predictions for the training and validation set patients were correct in 98.1% and 78.3% of the cases for nonsurvival and in 67.3% and 45.3% for survival. The discriminatory data pattern consisted of 14 known and 10 unknown gene products. CONCLUSIONS: The better than 95% correct pretherapeutic prediction for about one-half of the ultimately nonsurviving high-risk patients of the training set is promising for clinical considerations about individualised therapy in such cases. Reliable individualised survival predictions are not possible with the information content of the present dataset. It seems necessary to investigate additional gene products, since survival may significantly depend on non-lymphocyte-associated genes that escape to the lymphocyte-oriented Lymphochip gene activation analysis.     

Increasing the Number of Thyroid Lesions Classes in Microarray Analysis Improves the Relevance of Diagnostic Markers

Background

Genetic markers for thyroid cancers identified by microarray analysis have offered limited predictive accuracy so far because of the few classes of thyroid lesions usually taken into account. To improve diagnostic relevance, we have simultaneously analyzed microarray data from six public datasets covering a total of 347 thyroid tissue samples representing 12 histological classes of follicular lesions and normal thyroid tissue. Our own dataset, containing about half the thyroid tissue samples, included all categories of thyroid lesions.

Methodology/Principal Findings

Classifier predictions were strongly affected by similarities between classes and by the number of classes in the training sets. In each dataset, sample prediction was improved by separating the samples into three groups according to class similarities. The cross-validation of differential genes revealed four clusters with functional enrichments. The analysis of six of these genes (APOD, APOE, CLGN, CRABP1, SDHA and TIMP1) in 49 new samples showed consistent gene and protein profiles with the class similarities observed. Focusing on four subclasses of follicular tumor, we explored the diagnostic potential of 12 selected markers (CASP10, CDH16, CLGN, CRABP1, HMGB2, ALPL2, ADAMTS2, CABIN1, ALDH1A3, USP13, NR2F2, KRTHB5) by real-time quantitative RT-PCR on 32 other new samples. The gene expression profiles of follicular tumors were examined with reference to the mutational status of the Pax8-PPARγ, TSHR, GNAS and NRAS genes.

Conclusion/Significance

We show that diagnostic tools defined on the basis of microarray data are more relevant when a large number of samples and tissue classes are used. Taking into account the relationships between the thyroid tumor pathologies, together with the main biological functions and pathways involved, improved the diagnostic accuracy of the samples. Our approach was particularly relevant for the classification of microfollicular adenomas.     

SurvJamda: an R package to predict patients' survival and risk assessment using joint analysis of microarray gene expression data

SurvJamda (Survival prediction by joint analysis of microarray data) is an R package that utilizes joint analysis of microarray gene expression data to predict patients' survival and risk assessment. Joint analysis can be performed by merging datasets or meta-analysis to increase the sample size and to improve survival prognosis. The prognosis performance derived from the combined datasets can be assessed to determine which feature selection approach, joint analysis method and bias estimation provide the most robust prognosis for a given set of datasets. AVAILABILITY: The survJamda package is available at the Comprehensive R Archive Network, http://cran.r-project.org. CONTACT: hyasrebi@yahoo.com.     

Annotation-based distance measures for patient subgroup discovery in clinical microarray studies

MOTIVATION: Clustering algorithms are widely used in the analysis of microarray data. In clinical studies, they are often applied to find groups of co-regulated genes. Clustering, however, can also stratify patients by similarity of their gene expression profiles, thereby defining novel disease entities based on molecular characteristics. Several distance-based cluster algorithms have been suggested, but little attention has been given to the distance measure between patients. Even with the Euclidean metric, including and excluding genes from the analysis leads to different distances between the same objects, and consequently different clustering results. RESULTS: We describe a new clustering algorithm, in which gene selection is used to derive biologically meaningful clusterings of samples by combining expression profiles and functional annotation data. According to gene annotations, candidate gene sets with specific functional characterizations are generated. Each set defines a different distance measure between patients, leading to different clusterings. These clusterings are filtered using a resampling-based significance measure. Significant clusterings are reported together with the underlying gene sets and their functional definition. CONCLUSIONS: Our method reports clusterings defined by biologically focused sets of genes. In annotation-driven clusterings, we have recovered clinically relevant patient subgroups through biologically plausible sets of genes as well as new subgroupings. We conjecture that our method has the potential to reveal so far unknown, clinically relevant classes of patients in an unsupervised manner. AVAILABILITY: We provide the R package adSplit as part of Bioconductor release 1.9 and on http://compdiag.molgen.mpg.de/software.     

Molecular basis of the differences between normal and tumor tissues of gastric cancer

To be able to describe the differences between the normal and tumor tissues of gastric cancer at a molecular level would be essential in the study of the disease. We investigated the gene expression pattern in the two types of tissues from gastric cancer by performing expression profiling of 86 tissues on 17K complementary DNA microarrays. To select for the differentially expressed genes, class prediction algorithm was employed. For predictor selection, samples were first divided into a training (n=58), and a test set (n=28). A group of 894 genes was selected by a t-test in a training set, which was used for cross-validation in the training set and class (normal or tumor) prediction in the test set. Smaller groups of 894 genes were individually tested for their ability to correctly predict the normal or tumor samples based on gene expression pattern. The expression ratios of the 5 genes chosen from microarray data can be validated by real time RT-PCR over 6 tissue samples, resulting in a high level of correlation, individually or combined. When a representative predictor set of 92 genes was examined, pathways of 'focal adhesion' (with gene components of THBS2, PDGFD, MAPK1, COL1A2, COL6A3), 'ECM-receptor interaction' pathway (THBS2, COL1A2, COL6A3, FN1) and 'TGF-beta signaling' (THBS2, MAPK1, INHBA) represent some of the main differences between normal and tumor of gastric cancer at a molecular level.