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  • Review Article
  • Published:

Microarray data analysis: from disarray to consolidation and consensus

Nature Reviews Genetics volume 7, pages 55–65 (2006)Cite this article

A Corrigendum to this article was published on 01 May 2006

Key Points

  • We examine emerging consensus points for five key components of microarray analysis — design, preprocessing, inference, classification and validation.

  • Biological replication is important in the design of microarray experiments. The evidence indicates that a minimum of five biological cases per group should be analysed. Technical replicates are rarely warranted when testing for differential expression.

  • Modern methods (such as those used by the PowerAtlas resource) should be used for estimating the required sample size before conducting experiments.

  • mRNA pooling can be beneficial in certain cases in which identifying differential expression is the goal.

  • Microarray experiments should be designed to avoid confounding by extraneous factors.

  • Many methods exist for image processing, normalization and transformation with respect to different microarray platforms. However, which preprocessing algorithms to use and under what conditions remains an area of active research.

  • For inference in microarray experiments, test statistics for determining differential expression should consider variability; fold change does not achieve this. Test statistics that incorporate variance shrinkage are generally preferred.

  • False-discovery-rate estimation procedures are generally recommended over family-wise error rate control procedures.

  • Gene-class testing is encouraged when testing for differential expression.

  • The assessment of intersections of findings when testing multiple related propositions and how to appropriately use resampling-based inference are areas for which many questions remain.

  • Before undertaking cluster analysis, it is important to consider whether it actually addresses the question being asked and whether sufficient sample sizes can be obtained to yield reliable results.

  • When using supervised-classification procedures, cross-validation should be carried out using data that have had no role whatsoever in the derivation of the prediction rule.

  • Although discussed frequently in microarray research, validation of results is an area that requires further attention. When and how validation should be carried out, in addition to which criteria determine validation, are topics that remain to be addressed.

Abstract

In just a few years, microarrays have gone from obscurity to being almost ubiquitous in biological research. At the same time, the statistical methodology for microarray analysis has progressed from simple visual assessments of results to a weekly deluge of papers that describe purportedly novel algorithms for analysing changes in gene expression. Although the many procedures that are available might be bewildering to biologists who wish to apply them, statistical geneticists are recognizing commonalities among the different methods. Many are special cases of more general models, and points of consensus are emerging about the general approaches that warrant use and elaboration.

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Figure 1: Visualization tools for microarray analysis.
Figure 2: Guidelines for the statistical analysis of microarray experiments.

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Acknowledgements

The authors are supported in part by grants from the US National Institutes of Health, National Science Foundation and Department of Defense. We are grateful to C. Kendziorski for her helpful discussion on this document.

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Authors and Affiliations

  1. Department of Biostatistics, Section on Statistical Genetics, Ryals Public Health Building, 1665 University Avenue, University of Alabama, Birmingham, 35294-0022, Alabama, USA

    David B. Allison, Xiangqin Cui, Grier P. Page & Mahyar Sabripour

  2. Clinical Nutrition Research Center, University of Alabama, Birmingham, 35294-0022, Alabama, USA

    David B. Allison

  3. Department of Medicine, University of Alabama, Birmingham, 35294-0022, Alabama, USA

    David B. Allison & Xiangqin Cui

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  1. David B. Allison
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DATABASES

OMIM

Werner syndrome

FURTHER INFORMATION

AffyComp II software

A free online microarray analysis course from the University of Alabama at Birmingham

ArrayExpress microarray data repository

BioConductor open source software for bioinformatics

Cyber-T statistics program

ermineJ — Gene Ontology analysis for microarry data

Gene Expression Omnibus data repository

Gene Ontology Database

HDBStat! High Dimension Biology Statistical analysis software

MAANOVA 2.0 software

PowerAtlas software

Stanford MicroArray Database

Glossary

Fold change

A metric for comparing a gene's mRNA-expression level between two distinct experimental conditions. Its arithmetic definition differs between investigators.

Case

In a microarray experiment, a case is the biological unit under study; for example, one soybean, one mouse or one human.

Power

This is classically defined as the probability of rejecting a null hypothesis that is false. However, power has been defined in several ways for microarray studies.

False-discovery rate

(FDR). The expected proportion of rejected null hypotheses that are false positives. When no null hypotheses are rejected, FDR is taken to be zero.

Normalization

The process by which microarray spot intensities are adjusted to take into account the variability across different experiments and platforms.

Transformation

The application of a specific mathematical function so that data are changed into a different form. Often, the new form of the data satisfies assumptions of statistical tests. The most common transformation in microarray studies is log2.

Plasmode

A real (not computer simulated) data set for which the true structure is known and is used as a way of testing a proposed analytical method.

Parameter

A quantity (for example, mean) that characterizes some aspect of a (usually theoretically infinite) population.

Type 1 error

A false positive, or the rejection of a true null hypothesis; for example, declaring a gene to be differentially expressed when it is not.

Type 2 error

A false negative, or failing to reject a false null hypothesis; for example, not declaring a gene to be differentially expressed when it is.

Long-range error rate

The expected error rate if experiments and analyses of the type under consideration were repeated an infinite number of times.

t-tests

Statistical tests that are used to determine a statistically significant difference between two groups by looking at differences between two independent means.

ANOVA

Analysis of variance. A statistical test for determining differences in mean values between two or more groups.

Logistic regression

A regression technique that is used in cases where the outcome variable is binary (dichotomous).

Survival analysis

A statistical methodology for analysing time-to-event data.

α-value

The nominal probability (set by the investigator) of making a type 1 error.

Bonferroni correction

A family-wise error rate (FWER) control procedure that sets the α-value level for each test and strongly controls the FWER for any dependency structure among the tests.

Bayesian probability

The probability of a proposition being true, which is conditional on the observed data.

Gene Ontology

A way of describing gene products in terms of their associated biological processes, cellular components and molecular functions in a species-independent manner.

Null hypothesis

The hypothesis that is being tested in a statistical test. Typically in a microarray setting it is the hypothesis that states: there is no difference between gene-expression levels across groups or conditions.

p-value

The probability, were the null hypothesis true, of obtaining results that are as discrepant or more discrepant from those expected under the null hypothesis than those actually obtained.

Permutation test

A statistical hypothesis test in which some elements of the data are permuted (shuffled) to create multiple new pseudo-data sets. One then evaluates whether a statistic quantifying departure from the null hypothesis is greater in the observed data than a large proportion of the corresponding statistics calculated on the multiple pseudo-data sets.

Intersection-union tests

Multicomponent tests in which the compound null hypothesis consists of the union of two or more component null hypotheses.

Chi-square test of independence

A test of the independence of two categorical variables that is based on the chi-square distribution. The test is valid only under the assumption that all cases are independent.

Min-test

A statistical IUT test in which the union of a null hypotheses is rejected if, and only if, for each component null hypothesis the p-value <α.

Posterior probability

The Bayesian probability that a hypothesis is correct, which is conditional on the observed data.

Bootstrap analysis

A form of computer-intensive resampling-based inference. Pseudo-data sets are created by sampling from the observed data with replacement (that is, after a case is resampled, it is returned to the original data and can, potentially, be drawn again).

Sampling variation

The variability in statistics that occurs among random samples from the same population and is due solely to the process of random sampling.

Overfitting

This occurs when an excessively complex model with too many parameters is developed from a small sample of 'training' data. The model fits those data well, but does so by capitalizing on chance variations and, therefore, will fit a fresh set 'test' data poorly.

Selection bias

This occurs when the prediction accuracy of a rule is estimated using cases that had some role in the derivation of the rule. It is an upward bias — that is, one that overestimates the predictive accuracy.

Operational validation

Re-testing a hypothesis using the original methodology (also referred to as operational replication).

Constructive validation

Testing a hypothesis through a different methodology (also referred to as constructive replication).

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Allison, D., Cui, X., Page, G. et al. Microarray data analysis: from disarray to consolidation and consensus. Nat Rev Genet 7, 55–65 (2006). https://doi.org/10.1038/nrg1749

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