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<br>

# Identifying differentially methylated probes

The first step is the identification of differentially methylated CpGs (DMCs) carried out by function `get.diff.meth`. 

In the `Supervised` mode, we compare the DNA methylation level of each distal CpG for all samples in Group 1 compared to all samples Group 2, using an unpaired one-tailed t-test. In the `Unsupervised` mode, the samples of each group (Group 1 and Group 2) are ranked by their DNA methylation beta values for the given probe, and those samples in the lower quintile (20\% samples with the lowest methylation levels) of each group are used to identify if the probe is hypomethylated in Group 1 compared to Group 2. The reverse applies for the identification of hypermethylated probes. It is important to highlight that in the `Unsupervised` mode, each probe selected may be based on a different subset the samples, and thus probe sets from multiple molecular subtypes may be represented. In the `Supervised` mode, all tests are based on the same set of samples.

The 20\% is a parameter to the `diff.meth` function called `minSubgroupFrac`. For the unsupervised analysis, this is set to 20\% as in Yao et al. [@yao2015inferring], because we wanted to be able to detect a specific molecular subtype among samples; these subtypes often make up only a minority of samples, and 20\% was chosen as a lower bound for the purposes of statistical power (high enough sample numbers to yield t-test p-values that could overcome multiple hypotheses corrections, yet low enough to be able to capture changes in individual molecular subtypes occurring in 20\% or more of the cases.) This number can be set as an input to the `diff.meth` function and should be tuned based on sample sizes in individual studies. 
In the `Supervised` mode, where the comparison groups are implicit in the sample set and labeled, the `minSubgroupFrac` parameter is set to 100\%.  An example would be a cell culture experiment with 5 replicates of the untreated cell line, and another 5 replicates that include an experimental treatment.


To identify hypomethylated DMCs, a one-tailed t-test is used to rule out the null hypothesis: $\mu_{group1} \geq \mu_{group2}$, where $\mu_{group1}$ is the mean methylation within the lowest group 1 quintile (or another percentile as specified by the `minSubgroupFrac` parameter) and $\mu_{group2}$ is the mean within the lowest group 2 quintile. Raw p-values are adjusted for multiple hypothesis testing using the Benjamini-Hochberg method, and probes are selected when they had adjusted p-value less than $0.01$ (which can be configured using the `pvalue` parameter). For additional stringency, probes are only selected if the methylation difference: $\Delta = \mu_{group1} - \mu_{group2}$ was greater than $0.3$. The same method is used to identify hypermethylated DMCs, except we use the *upper* quintile, and the opposite tail in the t-test is chosen.


![Source: Yao, Lijing, et al. "Inferring regulatory element landscapes and transcription factor networks from cancer methylomes." Genome biology 16.1 (2015): 105.](figures/paper_diff_meth.jpg) [@yao2015inferring,@yao2015demystifying]


# Function arguments

<div class="panel panel-info">
<div class="panel-heading">Main get.diff.meth arguments </div>
<div class="panel-body">
| Argument | Description |
|------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| data | A `multiAssayExperiment` with DNA methylation and Gene Expression data. See `createMAE` function. |
| diff.dir |  A character can be "hypo", "hyper" or "both", showing differential methylation dirction.  It can be "hypo" which is only selecting hypomethylated probes (one tailed test);  "hyper" which is only selecting hypermethylated probes (one tailed test);  or "both" which are probes differenly methylated (two tailed test). |
| minSubgroupFrac |  A number ranging from 0 to 1,specifying the fraction of extreme samples from group 1 and group 2  that are used to identify the differential DNA methylation.  The default is 0.2 because we typically want to be able to detect a specific (possibly unknown) molecular subtype among tumor; these subtypes often make up only a minority of samples, and 20\% was chosen as a lower bound for the purposes of statistical power. If you are using pre-defined group labels, such as treated replicates vs. untreated replicated, use a value of 1.0 (***Supervised*** mode) |
| pvalue | A number specifies the significant P value (adjusted P value by BH) cutoff for selecting significant hypo/hyper-methylated probes. Default is 0.01 |
| group.col | A column defining the groups of the sample. You can view the available columns using: `colnames(MultiAssayExperiment::colData(data))`. |
| group1 | A group from group.col. ELMER will run group1 vs group2. That means, if direction is hyper, get probes hypermethylated in group 1 compared to group 2. |
| group2 | A group from group.col. ELMER will run group1 vs group2. That means, if direction is hyper, get probes hypermethylated in group 1 compared to group 2. |
| sig.dif | A number specifies the smallest DNA methylation difference as a cutoff for selecting significant hypo/hyper-methylated probes. Default is 0.3. |
</div>
</div>

# Example of use
```{r,eval=TRUE, message=FALSE, warning = FALSE, results = "hide"}
mae <- get(load("mae.rda"))
sig.diff <- get.diff.meth(data = mae, 
                          group.col = "definition",
                          group1 =  "Primary solid Tumor",
                          group2 = "Solid Tissue Normal",
                          minSubgroupFrac = 0.2, # if supervised mode set to 1
                          sig.dif = 0.3,
                          diff.dir = "hypo", # Search for hypomethylated probes in group 1
                          cores = 1, 
                          dir.out ="result", 
                          pvalue = 0.01)
```

```{r,eval=TRUE, message=FALSE, warning = FALSE}
head(sig.diff)  %>% datatable(options = list(scrollX = TRUE))
# get.diff.meth automatically save output files. 
# - getMethdiff.hypo.probes.csv contains statistics for all the probes.
# - getMethdiff.hypo.probes.significant.csv contains only the significant probes which
# is the same with sig.diff
# - a volcano plot with the diff mean and significance levels
dir(path = "result", pattern = "getMethdiff")  
```


```{r,eval=TRUE, message=FALSE, warning = FALSE,echo=FALSE}
group1 <-  "Primary solid Tumor"
group2 <- "Solid Tissue Normal"
out <- readr::read_csv(dir(path = "result", pattern = "getMethdiff.hypo.probes.csv",full.names = TRUE))
TCGAbiolinks:::TCGAVisualize_volcano(x = as.data.frame(out)[,grep("Minus",colnames(out),value = T)],
                                         y = out$adjust.p, 
                                         title =  paste0("Volcano plot - Probes ",
                                                        "hypomethylated in ", group1, " vs ", group2,"\n"),
                                         filename = NULL,
                                         label =  c("Not Significant",
                                                    paste0("Hypermethylated in ",group1),
                                                    paste0("Hypomethylated in ",group1)),
                                         ylab =  expression(paste(-Log[10],
                                                                  " (FDR corrected P-values) [one tailed test]")),
                                         xlab =  expression(paste(
                                           "DNA Methylation difference (",beta,"-values)")
                                         ),
                                         x.cut = 0.3, 
                                         y.cut = 0.01)
```


# Bibliography
