Number of samples. tumor: 519, fallopian tubes (normal): 8.
Data extraction and normalization: mean non-background corrected M and U signal intensities for each locus were extracted from Illumina BeadStudio (or GenomeStudio) software. The beta value DNA methylation scores for each sample and locus were calculated as M/(M+U). Detection p-values were calculated by comparing the set of analytical probe replicates for each locus to the set of 16 negative control probes. The negative controls are modeled by normal distribution. The detection p-value for the probe with intensity I probe , is calculated as: 1-Z( (|Iprobe-μneg |)/σneg ). In this formula, μneg and σneg are the average and the standard deviation of the signals from the negative controls, and Z is the one-sided tail probability of the standard normal distribution. For each probe, the detection pvalues are calculated separately for methylated and unmethylated probe signal intensities, and the smaller detection p-value was taken as the final detection p-value for the probe. Data points with detection p-values > 0.05 were deemed not significantly different from background, and were masked as "NA". In addition, data for probes that contain known single nucleotide polymorphisms (SNPs) after comparison to the dbSNP database (Build 128) and data for probes that contain repetitive element DNA sequences in more than 10 bp of each 50 bp probe sequence are masked with an “NA” descriptor. Level 3 data contains ~2 million NAs which can probably be attributed to the p value and SNPs.
Analysis of the batch effect: Prevalent batch effects were observed in the DNA methylation dataset (affecting 78.8% of the features, F test), consisting of 489 tumor samples, as also discussed by Leek et al (PMID: 20838408). Principal component analysis (PCA) shows that the second PC is significantly associated with batch (adjusted R-square = 0.59) (they did SVD using the corpcor package). A natural solution would be to employ normalization tools to remove the technical variation associated with batch. However, DNA methylation data expressed as beta values do not fit the assumptions for existing normalization methods developed for gene expression, such as quantile normalization and loess normalization(PMID: 20125086). Most of these methods assume that most genes are not expressed and/or that most genes are not differentially expressed. However, neither assumptions hold for DNA methylation data, where global hypomethylation observed in many cancers may affect a majority of probes. Moreover, samples can differ substantially in their total methylcytosine content. Quantile normalization would erase such differences. Meanwhile, for beta-distributed data like DNA methylation beta values, the variance is associated with the mean (heteroscedasticity). Therefore, we cannot apply linear model-based methods without transforming the data properly (logit or probit). This heteroscedasticity also hinders us from a simple application of empirical Bayes normalization methods like ComBat (PMID: 16632515) since the variances of different probes cannot be modeled as the same. In other words, there is a lack of a reasonable prior. What is more, there are substantial biological differences across batches. For example, five-year survival rate (Logrank test, p=0.04, for differences across batches) differ from 0% (Batch 9) to 58% (Batch 11). The known or unknown confounding biological differences between batches may result in removing biology in the normalization process. While putting in a design matrix to adjust for the known biological factors is feasible, the unknown confounding biological difference is a more serious problem. While well-established methods to remove unknown factors such as surrogate variable analysis (PMID: 17907809) are outstanding methods in dealing with unknown factors, will actually be undesirably harsh for unsupervised analyses aimed at finding molecular subtypes. We, however, advise the use of this method in supervised analyses with TCGA data. This confounding biology reemphasizes the importance of randomized experimental design in high-throughput studies, as has been emphasized by Verdugo et al and Leek et al (PMID: 19617374, 17907809). We chose not to normalize the data in a way that might remove biological differences or introduce artifacts, but rather focus our analyses on probes with large biological variation and limited technological variation. We were able to obtain a dataset (858 probes) in which the large biological variation predominates over the weak technical variation. None of the top ten PCs were associated with batch in the reduced data set used for clustering.
On average, only about 2.8% of the variance for each probe is explained by batch in the dataset used for clustering.
For the correlation with gene expression data. Obtained a union of all genes present on all gene expression platforms. If a gene is represented on all platforms then an average value of its expression was taken. Calculated pairwise correlation between gene expression and CpG loci (Spearman correlation). To identify epigenetically silenced genes they used a relaxed threshold of -0.2 and a stringent threshold of -0.3. Total number of epigenetically silenced genes identified: 168. Examples: BRCA1, RAB25 etc. The complete list is provided in the supplementary materials.
Unsupervised clustering of 858 probes. Developed signatures for the clusters by selecting the top 50 probes for each cluster compared to the other clusters. These clusters had some overlap with gene expression clusters. Age at the diagnosis was significantly different between 4 clusters as well as the survival.
On average, only about 2.8% of the variance for each probe is
explained by batch in the dataset used for clustering.

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