 Methodology article
 Open Access
 Published:
Methylation Linear Discriminant Analysis (MLDA) for identifying differentially methylated CpG islands
BMC Bioinformatics volume 9, Article number: 337 (2008)
Abstract
Background
Hypermethylation of promoter CpG islands is strongly correlated to transcriptional gene silencing and epigenetic maintenance of the silenced state. As well as its role in tumor development, CpG island methylation contributes to the acquisition of resistance to chemotherapy. Differential Methylation Hybridisation (DMH) is one technique used for genomewide DNA methylation analysis. The study of such microarray data sets should ideally account for the specific biological features of DNA methylation and the nonsymmetrical distribution of the ratios of unmethylated and methylated sequences hybridised on the array. We have therefore developed a novel algorithm tailored to this type of data, Methylation Linear Discriminant Analysis (MLDA).
Results
MLDA was programmed in R (version 2.7.0) and the package is available at CRAN [1]. This approach utilizes linear regression models of nonnormalised hybridisation data to define methylation status. Logtransformed signal intensities of unmethylated controls on the microarray are used as a reference. The signal intensities of DNA samples digested with methylation sensitive restriction enzymes and mock digested are then transformed to the likelihood of a locus being methylated using this reference. We tested the ability of MLDA to identify loci differentially methylated as analysed by DMH between cisplatin sensitive and resistant ovarian cancer cell lines. MLDA identified 115 differentially methylated loci and 23 out of 26 of these loci have been independently validated by Methylation Specific PCR and/or bisulphite pyrosequencing.
Conclusion
MLDA has advantages for analyzing methylation data from CpG island microarrays, since there is a clear rational for the definition of methylation status, it uses DMH data without betweengroup normalisation and is less influenced by crosshybridisation of loci. The MLDA algorithm successfully identified differentially methylated loci between two classes of samples analysed by DMH using CpG island microarrays.
Background
DNA methylation frequently occurs in mammalian DNA at the 5 position of cytosine in CpG dinucleotides. It has been estimated that over 70% of cytosines of CpG dinucleotides are methylated in the human genome. CpG dinucleotides are underrepresented in the genome and methylated CpG dinucleotides predominantly occur within repetitive elements [2]. However, there are CpG rich regions of the genome which generally remain unmethylated [3]. These CpG rich regions are known as CpG islands and are frequently located in the promoter or the first exon regions of approximately 60% of all genes [4]. The unmethylated status of CpG islands is thought to be a prerequisite state to maintain the linked gene in an active transcribed and transcriptional permissive state.
Differential Methylation Hybridisation (DMH) is one of several techniques for examining CpG island methylation at a genomewide scale that has been applied to the identification of aberrantly methylated gene promoters in various cancers [5–12]. Nouzova et al[13] modified the original method by using digestion with a methylationdependent enzyme, Mcr BC. This enzyme only cleaves methylated CpG DNA sequences. Withinsample comparison is applied after competitive hybridisation with Mcr BC digested DNA and undigested (mock digested) DNA labelled with Cy3 and Cy5. If a locus is unmethylated the signal intensities of Cy3 and Cy5 are equivalent, while if methylated the Cy5/Cy3 (undigested/digested) ratio is greater than one. However, no common reference is generally used in the modified DMH method, and the unequal representation of methylated and unmethylated sequences due to competitive hybridisation may reduce sensitivity and specificity to detect differential methylation.
Currently, Significance Analysis of Microarrays (SAM) [14] and Prediction Analysis for Microarrays (PAM) [15] are commonly applied in DNA methylation analysis. Based on the change in hybridisation relative to the standard deviation of repeated measurements, SAM assigns each gene a score that is an extension of the tstatistic. For significant genes with a score over a certain threshold, SAM uses permutations to estimate the false discovery rate (FDR). It has been implemented in many studies of gene expression data [16–21] as well as DMH data, e.g. Wei et al. [22] applied SAM to find the differential methylation of CpG island loci between ovarian caner patient groups with short and long progressionfree survival (PFS). However, SAM assumes that the microarray data conform to approximate normality and symmetry, leading to the loss of power in the analysis of DMH data that are inherently skewed due to the biological features of DNA methylation in cancer and competitive hybridisation on DMH arrays (Figure 1).
In the modified DMH method, the ratios of raw signal intensities (undigested/digested) greater than 1 reflect the various methylation levels [13]. A ratio cutoff is generally used to identify the hypermethylated loci [7]. However, this is an arbitrary value and does not necessarily accurately reflect the various sources of variation in the experiment. It is therefore desirable to develop an algorithm to more objectively assess the methylation status of loci from DMH data.
PAM is a nearest centroid shrinkage method that identifies those genes that discriminate best between classes. This technique shrinks the class gene centroid towards the overall centroid by a "threshold" amount after standardizing each gene by its within class standard deviation. The "threshold" is identified by crossvalidation. This approach was applied in the study by Wei et al. [22] and showed certain power in the identification of differentially methylated loci, but PAM is designed for class prediction rather than class comparison. Although the class predictor used in PAM can reflect the difference between classes, a large number of loci actually differentially methylated between the classes are excluded to improve the accuracy of prediction.
Although normalisation has become a standard procedure for the study of microarray data and is necessary for SAM and PAM analysis, unbalanced shifts in methylation status between class samples in DMH limit the use of betweenclass normalisation which assumes the changes are roughly symmetric. Thus, the differential methylation can be masked by the overcorrection of normalisation and it would be preferable to use a method of analysis that does not require normalisation of the data.
Since PAM and SAM may have limitations for analysing DMH data, we have developed an alternative approach based on the specific features and known biological properties of the arrays used for DMH analysis. The algorithm is named as Methylation Linear Discriminant Analysis (MLDA) and has been applied to identify a set of loci differentially methylated between ovarian cisplatin sensitive and resistant cancer cell lines.
Results
Outline of MLDA
In this study, we have developed a novel approach, named MLDA, for analysing CpG island microarray hybridisation data that allows the identification of differentially methylated loci. MLDA was programmed in R (version 2.7.0) and the package is available at CRAN [1]. This approach uses three relatively simple linear regression models. The first one is constructed by the logtransformed signal intensities of unmethylated features and used as the reference for unmethylation (Figure 2b). The second one is the intermediate model constructed through the point corresponding to the 97.5quantiles residual below the first linear regression line (Figure 2c). The features with a standardised residual less than 2 from this intermediate model are used to generate the third model which is used as the reference for methylation (Figure 2d). The log likelihood ratio of a locus being methylated is then proportional to the difference between the squared standardised residual from the methylated line and that from the unmethylated line. The log likelihood threshold of zero then provides a more rational basis for distinguishing between methylated and unmethylated loci than a robust undigested/digested ratio of 1.5, as it takes into account the observed variability in the experiment.
In our approach the consistency and inconsistency rates of log likelihood ratios on dyeswapped/duplicate arrays are used to determine methylation and unmethylation cutoffs, which keep the consistency rate (CR) relatively high (about 140%) and the inconsistency rate (IR) low (about 1%). Each loci is assigned a score based on the cutoffs using the weighted methylation scoring scheme. The feature consistently identified as methylated candidates on dyeswapped/duplicate arrays are scored as 1; similarly unmethylated features are scored as 1; the rest of the feature are assigned a weighted score corresponding to their location on the plot of loglikelihood ratios (Figure 3).
The averaged score for each locus is calculated in each sample class (e.g. resistant or sensitive) and plotted against each other. A robust regression model is then fitted to these data. The standardised residuals from the robust regression model are assumed to follow a normal distribution N(μ, σ^{2}). The outliers of the standardised residuals are identified as the differentially methylated loci between the class samples.
DMH dataset
MLDA was applied to identify the CGIs differentially methylated from DMH data derived from sensitive A2780 derivatives (A2780, A2780p3, A2780p5, A2780p6, A2780p13, A2780p14) and isogenically matched, resistant lines [23] derived by multiple exposures to cytotoxic levels of cisplatin and which are 2–5 fold resistant to cisplatin in clonogenic assays (A2780cp70, A2780/MCP1, A2780/MCP2, A2780/MCP3, A2780/MCP4, A2780/MCP5, A2780/MCP6, A2780/MCP7, A2780/MCP8, A2780/MCP9). After background correction, the logtransformed digested and undigested intensities of the 13056 microarray probes show three approximately parallel linear patterns (Figure 2a). The first pattern (digested/undigested is close to 1) represents the unmethylated sequences. The second pattern represents either hemimethylated sequences or the unmethylated sequences crosshybridised with the methylated ones on the panel. The third pattern represents the methylated sequences in target DNA. The methylated and unmethylated loci in target DNA can be characterised by a linear regression model for each pattern. As previously mentioned, normalisation may not be appropriate for DMH data, so the log ratios of signal intensities in two classes of samples are not at the same level (Figure 4). Normalisation is not required for MLDA as the determination of the methylation score is based on the data within each experiment.
Mitochondrial DNA is unmethylated [24], therefore, the signal intensities of both channels of microarray probes for mitochondrial sequences are expected to be equal. However, a bimodal distribution is observed in the logtransformed fluorescence ratios (digested/undigested) of 121 mitochondrial sequences. The first peak represents the unmethylated mitochondrial sequences and the second lower peak is assumed to be the mitochondrial sequences crosshybridised with other methylated sequences on the panel. Thus, we selected 94 of 121 mitochondrial sequences that were consistently unmethylated through all the cell lines and used them as the unmethylation reference in target DNA.
The parameters of those two models in all 16 cell lines were estimated (Table 1). The slope of the unmethylated regression line constructed by 94 mitochondrial sequences is indeed close to 1. After computing the loglikelihood ratios, the methylation and unmethylation cutoffs and associated IRs and CRs were determined from the dyeswapped array pairs (details in Method section). As shown in Figure 5, IR tends to rise with the increase of CR slowly, but starts to increase dramatically when the CR goes above 140%, at which point IR is generally about 1%. We have therefore used CR > 140% and IR < 1% as the criteria for determining the methylation and unmethylation cutoffs. Each locus was scored using the weighted scoring scheme based on those cutoffs. The averaged scores in 6 cisplatinsensitive cell lines and 10 cisplatinresistant cell lines were used to construct a robust regression model. Figure 6a shows that the standardised residuals (residual/σ) from the robust regression model roughly follow a normal distribution. The positive and negative outliers are determined as described in Method section.
Finally, 115 loci were identified as candidates differentially methylated between A2780 sensitive and these resistant cell lines (additional file 1). Noticeably, 113 of 115 loci (p = 8.8 × 10^{3}, outlier detection test [25]) were hypermethylated, but only 2 loci (p < 0.001, outlier detection test) lost methylation in the resistant cell lines (Figure 6b). This is consistent with the unbalanced shift in DMH data and indicates cisplatin treatment of cells selects preferentially for hypermethylation of loci, rather than hypomethylation in these tumor cells.
Validation of differential methylation
To confirm the differential methylation of loci identified in this study, we experimentally tested the methylation of 26 loci by methylationspecific PCR (MSP) and/or pyrosequencing of bisulphite modified DNA [26] in sensitive A2780 derivatives and cisplatin resistant derivatives. Twentythree out of the 26 loci have been confirmed as differentially methylated (additional file 1). It should be noted that MSP and pyrosequencing only examine methylation at a limited number of CpG sites of the sequence present on the DMH analysis. It is possible that the loci which were not confirmed as differentially methylated are methylated at other CpG sites which are detected by DMH but not targeted by MSP and/or pyrosequencing primers and so 23 out of 26 loci confirmed as differentially methylated is a minimum estimation.
To compare the results from MLDA, SAM and PAM, we analysed the DMH dataset by all three methods. MLDA identified 115 loci (113 hypermethylated and 2 hypomethylated loci, misclassification error < 0.001), SAM identified 152 loci (149 hypermethylated and 3 hypomethylated loci, misclassification error = 0.227, FDR = 6.17 × 10^{3}), and PAM found 24 hypermethylated loci (misclassification error = 0.084, FDR < 0.001) in the resistant cell lines. Twentyfour loci identified by all three methods are listed in Table 2.
Discussion
Hypermethylation of promoter CpG islands is strongly correlated to transcriptional gene silencing and epigenetic maintenance of the silenced state and is a potential rich source of biomarkers of cancer. Differential Methylation Hybridisation (DMH) is one technique used for genomewide DNA methylation analysis. The study of such microarray data sets should ideally account for the specific biological features of DNA methylation and the nonsymmetrical distribution of the ratios of unmethylated and methylated sequences hybridised on the array. We have therefore developed a novel algorithm tailored to this type of data, Methylation Linear Discriminant Analysis (MLDA). MLDA utilises log likelihood ratios representing the relative probability that loci are methylated instead of log ratios of signal intensities used in previous studies [6–10, 27]. Validation of 23/26 identified loci using independent methods of methylation analysis shows that MLDA can robustly identify differential methylated loci between ovarian cancer sensitive and resistant cell lines without requiring the data to be normalised.
Although a log likelihood ratio above zero means that the locus tends to be methylated, we did not use zero as the cutoff to determine the number of methylated and unmethylated sequences, as the existence of crosshybridisation and measurement errors in the DMH assay makes this unreliable. To increase the precision of the methylation classification, we used the inconsistency (IR) and consistency (CR) rates between the dyeswap arrays to determine likelihood ratio cutoffs for methylation and unmethylation and assigned each locus a methylation score based on the position relative to these cutoffs. As shown in Figure 5, not all cell lines can reach the point that CR is around 140% and IR is about 1%. IR and CR need to be carefully selected as the methylation scores of loci are consequently influenced by the change of IR and CR. We also observed a lower CR (about 120%) and a higher IR (about 2%) in another CpG island array using DMH (data not shown), therefore, further examination of what factors influence the achievable CR and IR rates may improve the utility of the MLDA approach.
Data on methylation status for 121 mitochondrial derived sequences were available in this study. Mitochondrial sequences would be expected to be unmethylated. We used 94 mitochondrial sequences to construct unmethylated linear model at the beginning of the study, and indeed, 93 of 121 mitochondrial loci were defined as unmethylated and 25 loci being of uncertain methylation status by MLDA. However, three mitochondrial loci were identified as hypermethylated candidates in the resistant ovarian carcinoma cell lines by both MLDA and SAM. One explanation of this discrepancy is that all these three loci have more than one BLAT hit indicating the existence of homology with nuclear DNA sequences, raising the possibility of hybridisation with these nuclear DNA sequences which may be differentially methylated. As shown in Figure 2a, the loci in the middle pattern represent either hemimethylated sequences or the unmethylated sequences crosshybridised with the methylated ones on the panel. No specific allowance is made for these intermediate points in analysis by SAM and PAM, whereas MLDA attempts specifically to downweight these points in the identification of the methylation regression line. By giving a lower weighted score (close to 0) (Figure 3) to those loci, MLDA reduces the influence of crosshybridisation among this group of sequences. Of course crosshybridisation may also occur in the loci in the other two patterns (methylated and unmethylated patterns), but it is not possible for any mathematical approach to identify this.
The misclassification error of MLDA based on the methylation score is much lower than that for either SAM or PAM based on the log ratios, indicating the potential of MLDA methylation scores to be used as a reliable discriminator between classes of samples.
Conclusion
We have developed a novel method, named MLDA, for genomewide DNA methylation studies. MLDA can transform the signal intensities to loglikelihood ratios through three linear regression models. Using this approach MLDA allows determination of the methylation status of a locus based on dyeswapped/duplicate arrays. The method has been applied to assess the methylation status of each locus and identified 115 loci that exhibit differential methylation between A2780 sensitive and resistant cell lines. A minimum of 23 out of 26 loci have been confirmed by independent methods as differentially methylated.
Methods
First, all intensity values were log transformed. A multiplicative background correction was applied to correct signal intensities for the background noise in each array. After background correction, the logtransformed digested and undigested intensities show three approximately parallel linear patterns (Figure 2a). The first pattern (digested/undigested is close to 1) represents the unmethylated sequences. The second pattern represents either hemimethylated sequences or the unmethylated sequences crosshybridised with the methylated ones on the panel. The third pattern represents the methylated sequences in target DNA. The methylated and unmethylated loci in target DNA can be characterised by a linear regression model for each pattern. The distance of each spot to the methylated and unmethylated lines respectively can then be estimated by standardised residuals. The log likelihood ratio of a locus being methylated is then proportional to the difference between the squared standardised residual from the methylated line and that from the unmethylated one. The algorithm based around this regression approach is named Methylation Linear Discriminant Analysis (MLDA) and was programmed in R version 2.7.0.
Loglikelihood ratio transformation
a An univariate linear regression model was constructed for the unmethylated probes (e.g. mitochondrial derived features) using formula (1) where α is the intercept, β is the slope of the model, and ξ is the error representing the unpredicted or unexplained variation in the model (Figure 2b). The parameters of regression line were estimated by the method of least squares (formula 2 and 3).G_{ i }= α + βR_{ i }+ ξ_{ i }i = 1,2,3.......k
k is the number of unmethylated controls on DMH array. G_{ i }and R_{ i }are the logarithmictransformed digested and undigested intensities of microarray probes for mitochondrial sequences, respectively. $\overline{G}$ and $\overline{R}$ are the averaged logarithmictransformed undigested and digested intensities of the k unmethylated controls.

b.
The scale estimate σ_{mito} associated with the error term in the linear regression model was estimated from the residuals from the observed k points to the fitted line. The most extreme 10% of residuals was omitted from either end of the distribution to minimise the impact of extreme residuals on this estimate.

c.
The standardised residuals of all the microarray probes to the unmethylation regression line were calculated as formula (4).
$$S{R}_{mito}=\frac{residual{s}_{mito}}{{\sigma}_{mito}}$$(4) 
d.
The point corresponding to the 97.5quantiles residual below the unmethylation line is represented as X (R.975, G.975). The intermediate linear model (Figure 2c) was constructed through point X with a slope assumed to be 1 and the intercept estimated as formula (5).
$$\widehat{\alpha}={G}_{.975}{R}_{.975}+1.96{\sigma}_{mito}$$(5) 
e.
The standardised residuals of all the microarray probes to the line with slope 1 and intercept estimated from (5) were calculated as formula (6). The variance of the residuals to the intermediate model was assumed to be similar as that in the mitochondrial model.
$$S{R}_{.975}=\frac{residual{s}_{.975}}{{\sigma}_{mito}}$$(6) 
f.
The microarray probes with standardised residuals less than 2 were included for later robust regression analysis. The line estimated from this regression analysis represents the methylation regression line (Figure 2d).

g.
The scale estimate σ_{meth} of the methylation regression line was estimated using only those microarray probes below the line, with the most extreme 5% removed.

h.
The standardised residuals of all the microarray probes to the methylated regression line were calculated as formula (7). The log likelihood ratio (LR) of all the microarray probes was estimated by formula (8) for further analysis.
$$S{R}_{meth}=\frac{residual{s}_{meth}}{{\sigma}_{meth}}$$(7)LR = SR^{2}_{ mito } SR^{2}_{ meth }
Determination of log likelihood ratio cutoffs
Two inconsistency rates (IR_{meth} and IR_{unmeth}) and two consistency rates (CR_{meth} and CR_{unmeth}) between dyeswap arrays were used to determine the log like likelihood ratio threshold. IR_{meth} (formula 9) represents the rate of the microarray probes identified as methylated in one array but as unmethylated in the other one, while IR_{unmeth} (formula 10) is the rate of the microarray probes identified as unmethylated in one array but as methylated in the other one. CR_{meth} (formula 11) and CR_{unmeth} (formula 12) are the rates for the spots identified as methylated (CR_{meth}) and unmethylated (CR_{unmeth}) in both dyeswap arrays (Figure 7).
b The log likelihood ratio thresholds (LR_{meth} and LR_{unmeth}) for methylated and unmethylated microarray probes, which kept the IR rates low (at or close to 1%) and the CR rates high (at or close to 140%), were used as the cutoffs for methylated and unmethylated loci. IR tends to rise with the increase of CR slowly, but starts to increase dramatically when the CR goes above 140%, at which point the inconsistency rate is generally about 1%. We have therefore used CR > 140% and IR < 1% as the criteria for determining the methylation cutoffs.
Identification of robust regression outliers
Each microarray probe was scored based on the cutoffs of likelihood ratios for methylation and unmethylation on dyeswap arrays using the weighted methylation scoring scheme shown in Figure 3. The microarray probes consistently identified as methylated candidates on dyeswap arrays were scored of 1; similarly unmethylated microarray probes were scored of 1. The rest of the microarray probes were assigned a weighted score based on their location on the plot.
A robust regression model [28] was constructed with the averaged scores in one class of samples as the explanatory variable, and the corresponding scores in the other class of samples as the dependent variable. The degree of trimming was determined according to Barnett et al. [29] when estimating the variance of residuals to the robust linear regression model.
It was assumed that the standardised residuals (SRs) from the robust regression line followed a normal distribution N(μ, σ^{2}). μ and σ were estimated excluding outliers using the MADMedian Rule [30]. The p value for each SR cutoff was calculated as described by Simon et al [25]. This pvalue reflects the probability of observing a group of more extreme residuals from the fitted normal distribution. Microarray probes were identified as outliers if their SRs were larger than the cutoff for which the pvalue was less than 0.01.
Estimation of misclassification rate
The misclassification rate was estimated by drawing bootstrap samples 500 times with replacement from the two classes (sensitive and resistant) and carrying out hierarchical clustering based on the loci identified as differentially methylated using weighted scores for MLDA and log ratios without betweengroup normalisation for SAM and PAM, respectively. Clustering was carried out using Euclidean distance as the distance metric, and clusters were agglomerated using the average linkage criterion. The clustering tree was cut into two groups and the number of misclassified cell lines was counted. The misclassification rate was obtained from the averaged number of misclassified samples in 500 bootstraps divided by the total number of samples.
SAM and PAM analysis
The raw signal intensities of each channel were subtracted by the median signal intensities of corresponding channel of controls on HCGI12K array. After this correction, SAM in samr package and PAM in pamr package were applied using log ratios (digested/undigested) in R version 2.7.0. Betweengroup normalisation was not used in SAM and PAM to avoid overcorrection masking the differential methylation.
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Acknowledgements
This work was supported by a CRUK programme grant to RB, NIH R21 grant CA110475 to RB and TH, and an Ovarian Cancer Action project grant to RB, JMT and JG.
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WD conducted the statistical analysis and algorithm development supervised by JP and RB. The DMH data was produced by JMT in collaboration with TH and PY. RB, JP and KV conceived the study. JMT, JG and CZ conducted validation by MSP or pyrosequencing in RB's lab. WD, JP and RB prepared the manuscript with review by all authors. Funding was obtained by RB and TH.
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Dai, W., Teodoridis, J.M., Graham, J. et al. Methylation Linear Discriminant Analysis (MLDA) for identifying differentially methylated CpG islands. BMC Bioinformatics 9, 337 (2008). https://doi.org/10.1186/147121059337
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Keywords
 Standardise Residual
 Resistant Cell Line
 Mitochondrial Sequence
 Consistency Rate
 Microarray Probe