## Analysis of Variance for Gene Expression Microarray Data (2000)

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Venue: | Journal of Computational Biology |

Citations: | 214 - 5 self |

### BibTeX

@ARTICLE{Kerr00analysisof,

author = {M. Kathleen Kerr and Mitchell Martin and Gary A. Churchill},

title = {Analysis of Variance for Gene Expression Microarray Data},

journal = {Journal of Computational Biology},

year = {2000},

volume = {7},

pages = {819--837}

}

### Years of Citing Articles

### OpenURL

### Abstract

Spotted cDNA microarrays are emerging as a powerful and cost-effective tool for largescale analysis of gene expression. Microarrays can be used to measure the relative quantities of speci � c mRNAs in two or more tissue samples for thousands of genes simultaneously. While the power of this technology has been recognized, many open questions remain about appropriate analysis of microarray data. One question is how to make valid estimates of the relative expression for genes that are not biased by ancillary sources of variation. Recognizing that there is inherent “noise ” in microarray data, how does one estimate the error variation associated with an estimated change in expression, i.e., how does one construct the error bars? We demonstrate that ANOVA methods can be used to normalize microarray data and provide estimates of changes in gene expression that are corrected for potential confounding effects. This approach establishes a framework for the general analysis and interpretation of microarray data. Key words: Gene expression microarray, differential expression, analysis of variance, bootstrap.

### Citations

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Citation Context ...onstant error variance 2 . To further examine the distribution of residuals, we plotted the absolute value of each residual against the � tted values log.yij \ kg/ and � t a local regression curve (=-=Hastie and Tibshirani, 1990-=-, p. 29). Fig. 3a shows there is no overwhelming trend in the absolute size of the residuals, with only a very slight trend towards larger residuals for the smallest and largest � tted values. The fac... |

547 |
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Citation Context ...d allows more degrees of freedom for estimating error variance. It is common practice in applied statistics to seek a transformation of the raw data to obtain normal residuals with constant variance (=-=Draper and Smith, 1998-=-). In this study we have applied a logarithm transformation to the � uorescent intensities. The residual distribution on the log scale is nonnormal, but we did not detect any dramatic evidence against... |

526 |
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Citation Context ...rom the experiment (Fisher, 1935, p. 60). Looking ahead, we believe they will also be useful in assessing the quality of the results from higher-order analyses such as clustering (Eisen et al., 1999; =-=Tamayo et al., 1999-=-). In this work, we perform analysis of variance on microarray data from two designed experiments that used independent arrays to study the same tissue samples. We employ a bootstrapping technique to ... |

312 | The Design of Experiments - Fisher - 1935 |

256 |
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(Show Context)
Citation Context ...pression pro� les of many genes can provide additional insights into physiological processes or disease etiology that is mediated by the coordinated action of sets of genes. Spotted cDNA microarrays (=-=Brown and Botstein, 1999-=-) are emerging as a powerful and cost-effective tool for large scale analysis of gene expression. In the � rst step of the technique, DNA clones with known sequence content are spotted and immobilized... |

251 | Randomization, bootstrap and Monte Carlo methods - Manly - 1997 |

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Citation Context ...rectly normalizes microarray data and yields reproducible estimates. DISCUSSION A common practice with microarray data is to compute ratios of the raw signals as estimates of differential expression (=-=Chen et al., 1997-=-). We � nd this approach to be inadequate for several reasons. It is natural and convenient to speak of fold change in expression, but it can also be misleading becauses832 KERR ET AL. ratios expressi... |

199 |
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Citation Context ...ed, as illustrated in Fig. 2a. These observations suggest that the usual con� dence intervals based on normal theory are not appropriate. Therefore, we employed a bootstrap analysis of the residuals (=-=Efron and Tibshirani, 1986-=-) to address this question.s824 KERR ET AL. Using the bootstrap, we produced a set of simulated datasets log.yij kg/ ¤ , where log.yij kg/ ¤ D O C OAi C ODj C OVk C OGg C .cAG/ig C . cVG/kg C ¤ ij ... |

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Citation Context ...be too extreme. This can be addressed by treating the gene and variety£gene terms as random effects in the ANOVA model (Robinson, 1991). This approach leads to “shrinkage” estimators for these terms (=-=Newton et al., 2000-=-). We view these problems as areas that are ripe for further investigation in the context of the analysis of well-designed microarray experiments. Tissue acquisition METHODS Human liver and skeletal m... |

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Citation Context ...to the design factors, array and Table 1. The Latin Square Design Array Dye 1 2 Red Liver Muscle Green Muscle Livers822 KERR ET AL. dye, the layout of the tissue varieties forms a 2 £ 2 Latin square (=-=Cochran and Cox, 1992-=-). We therefore refer to this as the Latin square design (it is sometimes called a “dye-swap” experiment). Given the factors in our model, there are sixteen possible effects when we consider interacti... |

76 |
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Citation Context ...e being estimated, the estimates of the highest and lowest effects will tend to be too extreme. This can be addressed by treating the gene and variety£gene terms as random effects in the ANOVA model (=-=Robinson, 1991-=-). This approach leads to “shrinkage” estimators for these terms (Newton et al., 2000). We view these problems as areas that are ripe for further investigation in the context of the analysis of well-d... |

15 |
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(Show Context)
Citation Context ...sible for microarrays because only one sample can correspond to each array–dye combination. However it is possible to derive ef� cient designs that satisfy the constraints imposed by this technology (=-=John and Mitchell, 1977-=-; Cheng, 1978). In general, for a given number of arrays, designs that are balanced across the samples of interest will provide the greatest ef� ciency. In our studies, using two arrays each, we prefe... |

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Citation Context ...ause only one sample can correspond to each array–dye combination. However it is possible to derive ef� cient designs that satisfy the constraints imposed by this technology (John and Mitchell, 1977; =-=Cheng, 1978-=-). In general, for a given number of arrays, designs that are balanced across the samples of interest will provide the greatest ef� ciency. In our studies, using two arrays each, we prefer the Latin s... |

4 | Expression pro� ling using cDNA microarrays. Nature Genetics Supplement - Duggan, Bittner, et al. - 1999 |

2 |
Estimating the posterior probability of gene expression from microarray data. Unpublished manuscript, The Jackson Laboratory. (http://www.jax.org/research/churchill
- Sapir, Churchill
- 2000
(Show Context)
Citation Context ...tios (Eisen, 1999). Further, exploration of untransformed data and the examination of other transformations (square-root, reciprocal, etc.) led us to conclude that the log transform is a good choice (=-=Sapir and Churchill, 2000-=-). The terms A, D, and V in the ANOVA model are used to capture differences that occur between different arrays, dyes, and varieties. However, these terms also capture all of the higher-order interact... |

2 | The approximate randomization test as an alternative to the F test in analysis of variance - Still, White - 1981 |