Importance of replication in microarray gene expression studies: Statistical methods and evidence from repetitive cDNA hybridizations

Abstract

We present statistical methods for analyzing replicated cDNA microarray expression data and report the results of a controlled experiment. The study was conducted to investigate inherent variability in gene expression data and the extent to which replication in an experiment produces more consistent and reliable findings. We introduce a statistical model to describe the probability that mRNA is contained in the target sample tissue, converted to probe, and ultimately detected on the slide. We also introduce a method to analyze the combined data from all replicates. Of the 288 genes considered in this controlled experiment, 32 would be expected to produce strong hybridization signals because of the known presence of repetitive sequences within them. Results based on individual replicates, however, show that there are 55, 36, and 58 highly expressed genes in replicates 1, 2, and 3, respectively. On the other hand, an analysis by using the combined data from all 3 replicates reveals that only 2 of the 288 genes are incorrectly classified as expressed. Our experiment shows that any single microarray output is subject to substantial variability. By pooling data from replicates, we can provide a more reliable analysis of gene expression data. Therefore, we conclude that designing experiments with replications will greatly reduce misclassification rates. We recommend that at least three replicates be used in designing experiments by using cDNA microarrays, particularly when gene expression data from single specimens are being analyzed.A lthough the high-throughput technology now available enables genetic researchers to study expression for thousands of genes simultaneously, experiments by using microarrays may be costly and time consuming. The manufacturers of microarray equipment do not stress the need for replication of studies. Production of arrays can be slow and the supply limited. As a result, most current molecular genetic studies that use microarray technology are sometimes done without replication. However, statistical analyses in many settings have demonstrated that important insights into the nature of inherent variability are obtained by the replication of experiments.In Section 1, we report the design of a controlled experiment involving replication of cDNA hybridizations. The study was conducted to investigate inherent variability in gene expression data and the extent to which replication in an experiment produces more consistent and reliable findings. In Sections 2.1 and 2.2, we introduce statistical models to describe the probability that an mRNA is contained in the target sample tissue, converted to probe, and ultimately detected on the slide as an observed expression. We use a mixed normal distribution to model the distribution of observed gene expressions. In Sections 2.3 and 2.4, we conduct a separate analysis for each replicate. In Sections 2.5 and 2.6, we introduce a model to provide a joint analysis based on the combined data collected from all replicates. In Section 2.7, we consider the reliabi...

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