DNA methylation microarrays : experimental design and statistical analysis /

Contents
1 Applied Statistics 23
1.1 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . 23
1.1.1 Frequency distribution . . . . . . . . . . . . . . . . . . 24
1.1.2 Central tendency and variability . . . . . . . . . . . . 24
1.1.3 Correlation . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2 Inferential statistics . . . . . . . . . . . . . . . . . . . . . . . 27
1.2.1 Probability distribution . . . . . . . . . . . . . . . . . 27
1.2.2 Central limit theorem and normal distribution . . . . 29
1.2.3 Statistical hypothesis testing . . . . . . . . . . . . . . 29
1.2.4 Two-sample t-test . . . . . . . . . . . . . . . . . . . . 31
1.2.5 Non-parametric test . . . . . . . . . . . . . . . . . . . 31
1.2.6 One-factor ANOVA and F-test . . . . . . . . . . . . . 32
1.2.7 Simple linear regression . . . . . . . . . . . . . . . . . 33
1.2.8 Chi-square test of contingency . . . . . . . . . . . . . 35
1.2.9 Statistical power analysis . . . . . . . . . . . . . . . . 36
2 DNA Methylation Microarrays and Quality Control 39
2.1 DNA methylation microarrays . . . . . . . . . . . . . . . . . 40
2.2 Workflow of methylome experiment . . . . . . . . . . . . . . 43
2.2.1 Restriction enzyme based enrichment . . . . . . . . . 43
2.2.2 Immunoprecipitation based enrichment . . . . . . . . 43
2.3 Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Visualization of raw data . . . . . . . . . . . . . . . . . . . . 48
2.5 Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.1 Positive and negative controls by exogenous sequences 54
2.5.2 Intensity fold-change and p-value . . . . . . . . . . . . 54
2.5.3 DNA unmethylation profiling . . . . . . . . . . . . . . 55
2.5.4 Correlation of intensities between tiling arrays . . . . 55
3 Experimental Design 57
3.1 Goals of experiment . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.1 Class comparison and class prediction . . . . . . . . . 58
3.1.2 Class discovery . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Reference design . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.1 Dye swaps . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3 Balanced block design . . . . . . . . . . . . . . . . . . . . . . 61
3.4 Loop design . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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3.5 Factorial design . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.6 Time course experimental design . . . . . . . . . . . . . . . . 69
3.7 How many samples/arrays are needed? . . . . . . . . . . . . 71
3.7.1 Biological vs technical replicates . . . . . . . . . . . . 71
3.7.2 Statistical power analysis . . . . . . . . . . . . . . . . 71
3.7.3 Pooling biological samples . . . . . . . . . . . . . . . . 77
3.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Data Normalization 81
4.1 Measure of methylation . . . . . . . . . . . . . . . . . . . . . 81
4.2 The need for normalization . . . . . . . . . . . . . . . . . . . 83
4.3 Strategy for normalization . . . . . . . . . . . . . . . . . . . 84
4.4 Two-color CpG island microarray normalization . . . . . . . 85
4.4.1 Global dependence of log methylation ratios . . . . . . 86
4.4.2 Dependence of log ratios on intensity . . . . . . . . . . 87
4.4.3 Dependence of log ratios on print-tips . . . . . . . . . 89
4.4.4 Normalized Cy3- and Cy5-intensities . . . . . . . . . . 92
4.4.5 Between-array normalization . . . . . . . . . . . . . . 93
4.5 Oligonucleotide arrays normalization . . . . . . . . . . . . . 94
4.5.1 Background correction, PM-MM? . . . . . . . . . . . . 94
4.5.2 Quantile normalization . . . . . . . . . . . . . . . . . . 95
4.5.3 Probeset summarization . . . . . . . . . . . . . . . . . 97
4.6 Normalization using control sequences . . . . . . . . . . . . . 98
4.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Significant Differential Methylation 103
5.1 Fold change . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Linear model for log-ratios or log-intensities . . . . . . . . . 106
5.2.1 Microarrays reference design or oligonucleotide chips . 106
5.2.2 Sequence-specific dye effect in two-color microarrays . 109
5.3 t -test for contrasts . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4 F-test for joint contrasts . . . . . . . . . . . . . . . . . . . . 111
5.5 P-value adjustment for multiple testing . . . . . . . . . . . . 114
5.5.1 Bonferroni correction . . . . . . . . . . . . . . . . . . . 114
5.5.2 False discovery rate . . . . . . . . . . . . . . . . . . . 114
5.6 Modified t - and F-test . . . . . . . . . . . . . . . . . . . . . 116
5.7 Significant variation within and between groups . . . . . . . 117
5.7.1 Within-group variation . . . . . . . . . . . . . . . . . 117
5.7.2 Between-group variation . . . . . . . . . . . . . . . . . 118
5.8 Significant correlation with a co-variate . . . . . . . . . . . . 119
5.9 Permutation test for bisulfite sequence data . . . . . . . . . . 122
5.9.1 Euclidean distance . . . . . . . . . . . . . . . . . . . . 123
5.9.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.10 Missing data values . . . . . . . . . . . . . . . . . . . . . . . 125
5.11 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
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5.11.1 Factorial design . . . . . . . . . . . . . . . . . . . . . . 126
5.11.2 Time-course experiments . . . . . . . . . . . . . . . . 127
5.11.3 Balanced block design . . . . . . . . . . . . . . . . . . 128
5.11.4 Loop design . . . . . . . . . . . . . . . . . . . . . . . . 129
6 High Density Genomic Tiling Arrays 131
6.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.1.1 Intra- and interarray normalization . . . . . . . . . . . 132
6.1.2 Sequence based probe effects . . . . . . . . . . . . . . 132
6.2 Wilcoxon test in a sliding window . . . . . . . . . . . . . . . 134
6.2.1 Probe score or scan statistic . . . . . . . . . . . . . . . 140
6.2.2 False positive rate . . . . . . . . . . . . . . . . . . . . 141
6.3 Boundaries of methylation regions . . . . . . . . . . . . . . . 141
6.4 Principal component analysis and biplot . . . . . . . . . . . 143
7 Cluster Analysis 147
7.1 Measure of dissimilarity . . . . . . . . . . . . . . . . . . . . . 147
7.2 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . 148
7.3 Hierarchical clustering . . . . . . . . . . . . . . . . . . . . . . 151
7.3.1 Bottom-up approach . . . . . . . . . . . . . . . . . . . 151
7.3.2 Top-down approach . . . . . . . . . . . . . . . . . . . 154
7.4 K-means clustering . . . . . . . . . . . . . . . . . . . . . . . 155
7.5 Model-based clustering . . . . . . . . . . . . . . . . . . . . . 159
7.6 Quality of clustering . . . . . . . . . . . . . . . . . . . . . . . 161
7.7 Statistically significance of clusters . . . . . . . . . . . . . . . 161
7.8 Reproducibility of clusters . . . . . . . . . . . . . . . . . . . 164
7.9 Repeated measurements . . . . . . . . . . . . . . . . . . . . . 165
8 Statistical Classification 167
8.1 Feature selection . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2 Discriminant function . . . . . . . . . . . . . . . . . . . . . . 170
8.2.1 Linear discriminant analysis . . . . . . . . . . . . . . . 171
8.2.2 Diagonal linear discriminant analysis . . . . . . . . . . 172
8.3 K-nearest neighbor . . . . . . . . . . . . . . . . . . . . . . . 172
8.4 Performance assessment . . . . . . . . . . . . . . . . . . . . . 173
8.4.1 Leave-one-out cross validation . . . . . . . . . . . . . . 174
8.4.2 Receiver operating characteristic analysis . . . . . . . 176
9 Interdependency Network of DNA Methylation 181
9.1 Graphs and networks . . . . . . . . . . . . . . . . . . . . . . 182
9.2 Partial correlation . . . . . . . . . . . . . . . . . . . . . . . . 182
9.3 Dependence networks from DNA methylation microarrays . . 183
9.4 Network analysis . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.4.1 Distribution of connectivities . . . . . . . . . . . . . . 187
9.4.2 Active epigenetically regulated loci . . . . . . . . . . . 187
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9.4.3 Correlation of connectivities . . . . . . . . . . . . . . . 188
9.4.4 Modularity . . . . . . . . . . . . . . . . . . . . . . . . 189
10 Time Series Experiment 197
10.1 Regulatory networks from microarray data . . . . . . . . . . 199
10.2 Dynamic model of regulation . . . . . . . . . . . . . . . . . . 200
10.3 A penalized likelihood score for parsimonious model . . . . . 200
10.4 Optimization by genetic algorithms . . . . . . . . . . . . . . 202
11 Online Annotations 205
11.1 Gene centric resources . . . . . . . . . . . . . . . . . . . . . . 205
11.1.1 GenBank: a nucleotide sequence database . . . . . . . 205
11.1.2 UniGene: an organized view of transcriptomes . . . . 206
11.1.3 RefSeq: reviews of sequences and annotations . . . . . 206
11.1.4 PubMed: a bibliographic database of biomedical journals
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
11.1.5 dbSNP: database for nucleotide sequence variation . . 208
11.1.6 OMIM: a directory of human genes and genetic disorders
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
11.1.7 Entrez Gene: a Web portal of genes . . . . . . . . . . 208
11.2 PubMeth: a cancer methylation database . . . . . . . . . . . 210
11.3 Gene Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . 211
11.4 Kyoto Encyclopedia of Genes and Genomes . . . . . . . . . . 213
11.5 UniProt/Swiss-Prot knowledgebase . . . . . . . . . . . . . . 214
11.6 The International HapMap Project . . . . . . . . . . . . . . 216
11.7 UCSC human genome browser . . . . . . . . . . . . . . . . . 216
12 Public Microarray Data Repositories 223
12.1 Epigenetics Society . . . . . . . . . . . . . . . . . . . . . . . 223
12.2 Microarray Gene Expression Data Society . . . . . . . . . . . 224
12.3 Minimum Information About a Microarray Experiment . . . 224
12.4 Public repositories for high-throughput arrays . . . . . . . . 226
12.4.1 Gene Expression Omnibus at NCBI . . . . . . . . . . 226
12.4.2 ArrayExpress at EBI . . . . . . . . . . . . . . . . . . . 226
12.4.3 Center for Information BiologyGene Expression at DDBJ
228
13 Open Source Software for Microarray Data Analysis 229
13.1 R ¿ a language and environment for statistical computing and
graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
13.2 Bioconductor . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
13.2.1 marray package . . . . . . . . . . . . . . . . . . . . . . 233
13.2.2 affy package . . . . . . . . . . . . . . . . . . . . . . . 233
13.2.3 limma package . . . . . . . . . . . . . . . . . . . . . . 233
13.2.4 stats package . . . . . . . . . . . . . . . . . . . . . . 233
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13.2.5 tilingArray package . . . . . . . . . . . . . . . . . . 235
13.2.6 Ringo package . . . . . . . . . . . . . . . . . . . . . . 235
13.2.7 cluster package . . . . . . . . . . . . . . . . . . . . . 235
13.2.8 class package . . . . . . . . . . . . . . . . . . . . . . 235
13.2.9 GeneNet package . . . . . . . . . . . . . . . . . . . . . 235
13.2.10inetwork package . . . . . . . . . . . . . . . . . . . . 235
13.2.11GOstats package . . . . . . . . . . . . . . . . . . . . . 236
13.2.12annotate package . . . . . . . . . . . . . . . . . . . . 236
References 237