Spotting effect in microarray experiments

Background  

Microarray data must be normalized because they suffer from multiple biases. We have identified a source of spatial experimental variability that significantly affects data obtained with Cy3/Cy5 spotted glass arrays. It yields a periodic pattern altering both signal (Cy3/Cy5 ratio) and intensity across the array.     

Practical FDR-based sample size calculations in microarray experiments

Motivation: Owing to the experimental cost and difficulty inobtaining biological materials, it is essential to considerappropriate sample sizes in microarray studies. With the growinguse of the False Discovery Rate (FDR) in microarray analysis,an FDR-based sample size calculation is essential. Method: We describe an approach to explicitly connect the samplesize to the FDR and the number of differentially expressed genesto be detected. The method fits parametric models for degreeof differential expression using the Expectation–Maximizationalgorithm. Results: The applicability of the method is illustrated withsimulations and studies of a lung microarray dataset. We proposeto use a small training set or published data from relevantbiological settings to calculate the sample size of an experiment. Availability: Code to implement the method in the statisticalpackage R is available from the authors. Contact: jhu{at}mdanderson.org     

Sample size for detecting differentially expressed genes in microarray experiments

Background  

Microarray experiments are often performed with a small number of biological replicates, resulting in low statistical power for detecting differentially expressed genes and concomitant high false positive rates. While increasing sample size can increase statistical power and decrease error rates, with too many samples, valuable resources are not used efficiently. The issue of how many replicates are required in a typical experimental system needs to be addressed. Of particular interest is the difference in required sample sizes for similar experiments in inbred vs. outbred populations (e.g. mouse and rat vs. human).     

Sample size calculations based on ranking and selection in microarray experiments

Summary .   We develop formulae to calculate sample sizes for ranking and selection of differentially expressed genes among different clinical subtypes or prognostic classes of disease in genome-wide screening studies with microarrays. The formulae aim to control the probability that a selected subset of genes with fixed size contains enough truly top-ranking informative genes, which can be assessed on the basis of the distribution of ordered statistics from independent genes. We provide strategies for conservative designs to cope with issues of unknown number of informative genes and unknown correlation structure across genes. Application of the formulae to a clinical study for multiple myeloma is given.     

Sample size for identifying differentially expressed genes in microarray experiments.

Microarray technology allows simultaneous comparison of expression levels of thousands of genes under each condition. This paper concerns sample size calculation in the identification of differentially expressed genes between a control and a treated sample. In a typical experiment, only a fraction of genes (altered genes) is expected to be differentially expressed between two samples. Sample size determination depends on a number of factors including the specified significance level (alpha), the desired statistical power (1-beta), the fraction (eta) of truly altered genes out of the total g genes studied, and the effect sizes (Delta) for the altered genes. This paper proposes a method to calculate the number of arrays required to detect at least 100lambda % (where 0 < lambda < or = 1) of the truly altered genes under the model of an equal effect size for all altered genes. The required numbers of arrays are tabulated for various values of alpha, beta, Delta, eta, and lambda for the one-sample and two-sample t-tests for g = 10,000. Based on the proposed approach, to identify up to 90% of truly altered genes among the unknown number of truly altered genes, the estimated numbers of arrays needed appear to be manageable. For instance, when the standardized effect size is at least 2.0, the number of arrays needed is less than or equal to 14 for the two-sample t-test and is less than or equal to 10 for the one-sample t-test. As the cost per array declines, such array numbers become practical. The proposed method offers a simple, intuitive, and practical way to determine the number of arrays needed in microarray experiments in which the true correlation structure among the genes under investigation cannot be reasonably assumed. An example dataset is used to illustrate the use of the proposed approach to plan microarray experiments.     

On methods for gene function scoring as a means of facilitating the interpretation of microarray results.

As gene annotation databases continue to evolve and improve, it has become feasible to incorporate the functional and pathway information about genes, available in these databases into the analysis of gene expression data, for a better understanding of the underlying mechanisms. A few methods have been proposed in the literature to formally convert individual gene results into gene function results. In this paper, we will compare the various methods, propose and examine some new ones, and offer a structured approach to incorporating gene function or pathway information into the analysis of expression data. We study the performance of the various methods and also compare them on real data, using a case study from the toxicogenomics area. Our results show that the approaches based on gene function scores yield a different, and functionally more interpretable, array of genes than methods that rely solely on individual gene scores. They also suggest that functional class scoring methods appear to perform better and more consistently than overrepresentation analysis and distributional score methods.     

Sample size determination in microarray experiments for class comparison and prognostic classification

Determining sample sizes for microarray experiments is important but the complexity of these experiments, and the large amounts of data they produce, can make the sample size issue seem daunting, and tempt researchers to use rules of thumb in place of formal calculations based on the goals of the experiment. Here we present formulae for determining sample sizes to achieve a variety of experimental goals, including class comparison and the development of prognostic markers. Results are derived which describe the impact of pooling, technical replicates and dye-swap arrays on sample size requirements. These results are shown to depend on the relative sizes of different sources of variability. A variety of common types of experimental situations and designs used with single-label and dual-label microarrays are considered. We discuss procedures for controlling the false discovery rate. Our calculations are based on relatively simple yet realistic statistical models for the data, and provide straightforward sample size calculation formulae.     

The effect of replication on gene expression microarray experiments

MOTIVATION: We examine the effect of replication on the detection of apparently differentially expressed genes in gene expression microarray experiments. Our analysis is based on a random sampling approach using real data sets from 16 published studies. We consider both the ability to find genes that meet particular statistical criteria as well as the stability of the results in the face of changing levels of replication. RESULTS: While dependent on the data source, our findings suggest that stable results are typically not obtained until at least five biological replicates have been used. Conversely, for most studies, 10-15 replicates yield results that are quite stable, and there is less improvement in stability as the number of replicates is further increased. Our methods will be of use in evaluating existing data sets and in helping to design new studies.     

Pooling mRNA in microarray experiments and its effect on power

MOTIVATION: Microarrays can simultaneously measure the expression levels of many genes and are widely applied to study complex biological problems at the genetic level. To contain costs, instead of obtaining a microarray on each individual, mRNA from several subjects can be first pooled and then measured with a single array. mRNA pooling is also necessary when there is not enough mRNA from each subject. Several studies have investigated the impact of pooling mRNA on inferences about gene expression, but have typically modeled the process of pooling as if it occurred in some transformed scale. This assumption is unrealistic. RESULTS: We propose modeling the gene expression levels in a pool as a weighted average of mRNA expression of all individuals in the pool on the original measurement scale, where the weights correspond to individual sample contributions to the pool. Based on these improved statistical models, we develop the appropriate F statistics to test for differentially expressed genes. We present formulae to calculate the power of various statistical tests under different strategies for pooling mRNA and compare resulting power estimates to those that would be obtained by following the approach proposed by Kendziorski et al. (2003). We find that the Kendziorski estimate tends to exceed true power and that the estimate we propose, while somewhat conservative, is less biased. We argue that it is possible to design a study that includes mRNA pooling at a significantly reduced cost but with little loss of information.     

GeneRank: Using search engine technology for the analysis of microarray experiments

Background  

Interpretation of simple microarray experiments is usually based on the fold-change of gene expression between a reference and a "treated" sample where the treatment can be of many types from drug exposure to genetic variation. Interpretation of the results usually combines lists of differentially expressed genes with previous knowledge about their biological function. Here we evaluate a method – based on the PageRank algorithm employed by the popular search engine Google – that tries to automate some of this procedure to generate prioritized gene lists by exploiting biological background information.     

Spearman's footrule as a measure of cDNA microarray reproducibility

Replication is a crucial aspect of microarray experiments, due to various sources of errors that persist even after systematic effects are removed. It has been confirmed that replication in microarray studies is not equivalent to duplication, and hence it is not a waste of scientific resources. Replication and reproducibility are the most important issues for microarray application in genomics. However, little attention has been paid to the assessment of reproducibility among replicates. Here we develop, using Spearman's footrule, a new measure of the reproducibility of cDNA microarrays, which is based on how consistently a gene's relative rank is maintained in two replicates. The reproducibility measure, termed index.R, has an R2-type operational interpretation. Index.R assesses reproducibility at the initial stage of the microarray data analysis even before normalization is done. We first define three layers of replicates, biological, technical, and hybridizational, which refer to different biological units, different mRNAs from the same tissue, and separate cDNAs from a cDNA pool. As the replicate layer moves down to a lower level, the experiment has fewer sources of errors and thus is expected to be more reproducible. To validate the method we apply index.R to two sets of controlled cDNA microarray experiments, each of which has two or three layers of replicates. Index.R shows a uniform increase as the layer of the replicates moves into a more homogeneous environment. We also note that index.R has a larger jump size than Pearson's correlation or Spearman's rank correlation for each replicate layer move, and therefore, it has greater expandability as a measure in [0,1] than these two other measures.     

Biological detection of low radiation doses by combining results of two microarray analysis methods

The accurate determination of the biological effects of low doses of pollutants is a major public health challenge. DNA microarrays are a powerful tool for investigating small intracellular changes. However, the inherent low reliability of this technique, the small number of replicates and the lack of suitable statistical methods for the analysis of such a large number of attributes (genes) impair accurate data interpretation. To overcome this problem, we combined results of two independent analysis methods (ANOVA and RELIEF). We applied this analysis protocol to compare gene expression patterns in Saccharomyces cerevisiae growing in the absence and continuous presence of varying low doses of radiation. Global distribution analysis highlights the importance of mitochondrial membrane functions in the response. We demonstrate that microarrays detect cellular changes induced by irradiation at doses that are 1000-fold lower than the minimal dose associated with mutagenic effects.     

Sources of variation in Affymetrix microarray experiments

Background  

A typical microarray experiment has many sources of variation which can be attributed to biological and technical causes. Identifying sources of variation and assessing their magnitude, among other factors, are important for optimal experimental design. The objectives of this study were: (1) to estimate relative magnitudes of different sources of variation and (2) to evaluate agreement between biological and technical replicates.     

Evolution in ecological field experiments: implications for effect size

Rapid evolution in response to strong selection, much of which is human-induced, has been indisputably documented. In this perspective, we suggest that adaptation may influence the effect size of treatments in ecological field experiments and alter our predictions of future dynamics in ecological systems. Field experiments often impose very strong and consistent selection over multiple generations. Focal populations may adapt to these treatments and, in the process, increase or decrease the magnitude of the treatment effect through time. We argue that how effect size changes through time will depend on the evolutionary history of the experimental population, the type of experimental manipulation, and the traits involved in adaptive responses. While no field study has conclusively demonstrated evolution in response to treatments with concomitant changes in ecological effect size, we present several examples that provide strong circumstantial evidence that such effects occur. We conclude with a consideration of the differences between plastic and genetic responses to treatments and discuss future research directions linking adaptation to ecological effect size.     

HAMSTER: visualizing microarray experiments as a set of minimum spanning trees

Background  

Visualization tools allow researchers to obtain a global view of the interrelationships between the probes or experiments of a gene expression (e.g. microarray) data set. Some existing methods include hierarchical clustering and k-means. In recent years, others have proposed applying minimum spanning trees (MST) for microarray clustering. Although MST-based clustering is formally equivalent to the dendrograms produced by hierarchical clustering under certain conditions; visually they can be quite different.