Power and sample size estimation in microarray studies

Background  

Before conducting a microarray experiment, one important issue that needs to be determined is the number of arrays required in order to have adequate power to identify differentially expressed genes. This paper discusses some crucial issues in the problem formulation, parameter specifications, and approaches that are commonly proposed for sample size estimation in microarray experiments. Common methods for sample size estimation are formulated as the minimum sample size necessary to achieve a specified sensitivity (proportion of detected truly differentially expressed genes) on average at a specified false discovery rate (FDR) level and specified expected proportion (π ₁) of the true differentially expression genes in the array. Unfortunately, the probability of detecting the specified sensitivity in such a formulation can be low. We formulate the sample size problem as the number of arrays needed to achieve a specified sensitivity with 95% probability at the specified significance level. A permutation method using a small pilot dataset to estimate sample size is proposed. This method accounts for correlation and effect size heterogeneity among genes.     

A comparative review of estimates of the proportion unchanged genes and the false discovery rate

Background  

In the analysis of microarray data one generally produces a vector of p-values that for each gene give the likelihood of obtaining equally strong evidence of change by pure chance. The distribution of these p-values is a mixture of two components corresponding to the changed genes and the unchanged ones. The focus of this article is how to estimate the proportion unchanged and the false discovery rate (FDR) and how to make inferences based on these concepts. Six published methods for estimating the proportion unchanged genes are reviewed, two alternatives are presented, and all are tested on both simulated and real data. All estimates but one make do without any parametric assumptions concerning the distributions of the p-values. Furthermore, the estimation and use of the FDR and the closely related q-value is illustrated with examples. Five published estimates of the FDR and one new are presented and tested. Implementations in R code are available.     

Rank-invariant resampling based estimation of false discovery rate for analysis of small sample microarray data

Background  

The evaluation of statistical significance has become a critical process in identifying differentially expressed genes in microarray studies. Classical p-value adjustment methods for multiple comparisons such as family-wise error rate (FWER) have been found to be too conservative in analyzing large-screening microarray data, and the False Discovery Rate (FDR), the expected proportion of false positives among all positives, has been recently suggested as an alternative for controlling false positives. Several statistical approaches have been used to estimate and control FDR, but these may not provide reliable FDR estimation when applied to microarray data sets with a small number of replicates.     

Estimating effect sizes of differentially expressed genes for power and sample-size assessments in microarray experiments

Summary In microarray screening for differentially expressed genes using multiple testing, assessment of power or sample size is of particular importance to ensure that few relevant genes are removed from further consideration prematurely. In this assessment, adequate estimation of the effect sizes of differentially expressed genes is crucial because of its substantial impact on power and sample‐size estimates. However, conventional methods using top genes with largest observed effect sizes would be subject to overestimation due to random variation. In this article, we propose a simple estimation method based on hierarchical mixture models with a nonparametric prior distribution to accommodate random variation and possible large diversity of effect sizes across differential genes, separated from nuisance, nondifferential genes. Based on empirical Bayes estimates of effect sizes, the power and false discovery rate (FDR) can be estimated to monitor them simultaneously in gene screening. We also propose a power index that concerns selection of top genes with largest effect sizes, called partial power. This new power index could provide a practical compromise for the difficulty in achieving high levels of usual overall power as confronted in many microarray experiments. Applications to two real datasets from cancer clinical studies are provided.     

Correlation and prediction of gene expression level from amino acid and dipeptide composition of its protein

Background  

A large number of papers have been published on analysis of microarray data with particular emphasis on normalization of data, detection of differentially expressed genes, clustering of genes and regulatory network. On other hand there are only few studies on relation between expression level and composition of nucleotide/protein sequence, using expression data. There is a need to understand why particular genes/proteins express more in particular conditions. In this study, we analyze 3468 genes of Saccharomyces cerevisiae obtained from Holstege et al., (1998) to understand the relationship between expression level and amino acid composition.     

A mixture model for estimating the local false discovery rate in DNA microarray analysis

MOTIVATION: Statistical methods based on controlling the false discovery rate (FDR) or positive false discovery rate (pFDR) are now well established in identifying differentially expressed genes in DNA microarray. Several authors have recently raised the important issue that FDR or pFDR may give misleading inference when specific genes are of interest because they average the genes under consideration with genes that show stronger evidence for differential expression. The paper proposes a flexible and robust mixture model for estimating the local FDR which quantifies how plausible each specific gene expresses differentially. RESULTS: We develop a special mixture model tailored to multiple testing by requiring the P-value distribution for the differentially expressed genes to be stochastically smaller than the P-value distribution for the non-differentially expressed genes. A smoothing mechanism is built in. The proposed model gives robust estimation of local FDR for any reasonable underlying P-value distributions. It also provides a single framework for estimating the proportion of differentially expressed genes, pFDR, negative predictive values, sensitivity and specificity. A cervical cancer study shows that the local FDR gives more specific and relevant quantification of the evidence for differential expression that can be substantially different from pFDR. AVAILABILITY: An R function implementing the proposed model is available at http://www.geocities.com/jg_liao/software     

Investigating the effect of paralogs on microarray gene-set analysis

Background  

In order to interpret the results obtained from a microarray experiment, researchers often shift focus from analysis of individual differentially expressed genes to analyses of sets of genes. These gene-set analysis (GSA) methods use previously accumulated biological knowledge to group genes into sets and then aim to rank these gene sets in a way that reflects their relative importance in the experimental situation in question. We suspect that the presence of paralogs affects the ability of GSA methods to accurately identify the most important sets of genes for subsequent research.     

Candidate genes involved in tanshinone biosynthesis in hairy roots of <Emphasis Type="Italic">Salvia miltiorrhiza</Emphasis> revealed by cDNA microarray

Salvia miltiorrhiza is a valuable Chinese herb (Danshen) that is widely used in traditional Chinese medicine. Diterpene quinones, known as tanshinones, are the main bioactive components of S. miltiorrhiza; however, there is only limited information regarding the molecular mechanisms underlying secondary metabolism in this plant. We used cDNA microarray analysis to identify changes in the gene expression profile at different stages of hairy root development in S. miltiorrhiza. A total of 203 genes were singled out from 4,354 cDNA clones on the microarray, and 114 unique differentially expressed cDNA clones were identified: six genes differentially expressed in 45-day hairy root compared with 30-day hairy root; 96 genes differentially expressed in 60-day hairy root compared with 30-day hairy root; and 12 genes unstably expressed at different stages. Among the 96 genes differentially expressed in 60-day hairy root compared with 30-day hairy root, a total of 57 genes were up-regulated, and 26 genes represent 29 metabolism-related enzymes. Copalyl diphosphate synthase, which catalyzes the conversion of the universal diterpenoid precursor (E,E,E)-geranylgeranyl diphosphate to copalyl diphosphate, was up-regulated 6.63 fold, and another six genes involved in tanshinone biosynthesis and eight candidate P450 genes were also differentially expressed. These data provide new insights for further identification of the enzymes involved in tanshinone biosynthesis.     

Insights from the clustering of microarray data associated with the heart disease

Heart failure (HF) is the major of cause of mortality and morbidity in the developed world. Gene expression profiles of animal model of heart failure have been used in number of studies to understand human cardiac disease. In this study, statistical methods of analysing microarray data on cardiac tissues from dogs with pacing induced HF were used to identify differentially expressed genes between normal and two abnormal tissues. The unsupervised techniques principal component analysis (PCA) and cluster analysis were explored to distinguish between three different groups of 12 arrays and to separate the genes which are up regulated in different conditions among 23912 genes in heart failure canines'' microarray data. It was found that out of 23912 genes, 1802 genes were differentially expressed in the three groups at 5% level of significance and 496 genes were differentially expressed at 1% level of significance using one way analysis of variance (ANOVA). The genes clustered using PCA and clustering analysis were explored in the paper to understand HF and a small number of differentially expressed genes related to HF were identified.     

BATS: a Bayesian user-friendly software for Analyzing Time Series microarray experiments

Background  

Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.     

Mixture models for gene expression experiments with two species

Cross-species research in drug development is novel and challenging. A bivariate mixture model utilizing information across two species was proposed to solve the fundamental problem of identifying differentially expressed genes in microarray experiments in order to potentially improve the understanding of translation between preclinical and clinical studies for drug development. The proposed approach models the joint distribution of treatment effects estimated from independent linear models. The mixture model posits up to nine components, four of which include groups in which genes are differentially expressed in both species. A comprehensive simulation to evaluate the model performance and one application on a real world data set, a mouse and human type II diabetes experiment, suggest that the proposed model, though highly structured, can handle various configurations of differential gene expression and is practically useful on identifying differentially expressed genes, especially when the magnitude of differential expression due to different treatment intervention is weak. In the mouse and human application, the proposed mixture model was able to eliminate unimportant genes and identify a list of genes that were differentially expressed in both species and could be potential gene targets for drug development.     

sdef: an R package to synthesize lists of significant features in related experiments

Background  

In microarray studies researchers are often interested in the comparison of relevant quantities between two or more similar experiments, involving different treatments, tissues, or species. Typically each experiment reports measures of significance (e.g. p-values) or other measures that rank its features (e.g genes). Our objective is to find a list of features that are significant in all experiments, to be further investigated. In this paper we present an R package called sdef, that allows the user to quantify the evidence of communality between the experiments using previously proposed statistical methods based on the ranked lists of p-values. sdef implements two approaches that address this objective: the first is a permutation test of the maximal ratio of observed to expected common features under the hypothesis of independence between the experiments. The second approach, set in a Bayesian framework, is more flexible as it takes into account the uncertainty on the number of genes differentially expressed in each experiment.     

A Hierarchical Semiparametric Model for Incorporating Intergene Information for Analysis of Genomic Data

Summary For analysis of genomic data, e.g., microarray data from gene expression profiling experiments, the two‐component mixture model has been widely used in practice to detect differentially expressed genes. However, it naïvely imposes strong exchangeability assumptions across genes and does not make active use of a priori information about intergene relationships that is currently available, e.g., gene annotations through the Gene Ontology (GO) project. We propose a general strategy that first generates a set of covariates that summarizes the intergene information and then extends the two‐component mixture model into a hierarchical semiparametric model utilizing the generated covariates through latent nonparametric regression. Simulations and analysis of real microarray data show that our method can outperform the naïve two‐component mixture model.     

Not proper ROC curves as new tool for the analysis of differentially expressed genes in microarray experiments

Background  

Most microarray experiments are carried out with the purpose of identifying genes whose expression varies in relation with specific conditions or in response to environmental stimuli. In such studies, genes showing similar mean expression values between two or more groups are considered as not differentially expressed, even if hidden subclasses with different expression values may exist. In this paper we propose a new method for identifying differentially expressed genes, based on the area between the ROC curve and the rising diagonal (ABCR). ABCR represents a more general approach than the standard area under the ROC curve (AUC), because it can identify both proper (i.e., concave) and not proper ROC curves (NPRC). In particular, NPRC may correspond to those genes that tend to escape standard selection methods.     

Ranking analysis for identifying differentially expressed genes

Microarrays allow researchers to examine the expression of thousands of genes simultaneously. However, identification of genes differentially expressed in microarray experiments is challenging. With an optimal test statistic, we rank genes and estimate a threshold above which genes are considered to be differentially expressed genes (DE). This overcomes the embarrassing shortcoming of many statistical methods to determine the cut-off values in ranking analysis. Experiments demonstrate that our method is a good performance and avoids the problems with graphical examination and multiple hypotheses testing that affect alternative approaches. Comparing to those well known methods, our method is more sensitive to data sets with small differentially expressed values and not biased in favor of data sets based on certain distribution models.     

Grouping Gene Ontology terms to improve the assessment of gene set enrichment in microarray data

Background  

Gene Ontology (GO) terms are often used to assess the results of microarray experiments. The most common way to do this is to perform Fisher's exact tests to find GO terms which are over-represented amongst the genes declared to be differentially expressed in the analysis of the microarray experiment. However, due to the high degree of dependence between GO terms, statistical testing is conservative, and interpretation is difficult.     

A comparison of probe-level and probeset models for small-sample gene expression data

Background  

Statistical methods to tentatively identify differentially expressed genes in microarray studies typically assume larger sample sizes than are practical or even possible in some settings.     

DiffCoEx: a simple and sensitive method to find differentially coexpressed gene modules

Background  

Large microarray datasets have enabled gene regulation to be studied through coexpression analysis. While numerous methods have been developed for identifying differentially expressed genes between two conditions, the field of differential coexpression analysis is still relatively new. More specifically, there is so far no sensitive and untargeted method to identify gene modules (also known as gene sets or clusters) that are differentially coexpressed between two conditions. Here, sensitive and untargeted means that the method should be able to construct de novo modules by grouping genes based on shared, but subtle, differential correlation patterns.