In a given CpG site from a single cell we will either have a C or a T
after bisulfite-based DNA conversion methods. We asume a Binomial model
and maximum likelihood estimation to obtain consistent
hydroxymethylation and methylation proportions with single nucleotide
resolution. MLML2R package allows the user to jointly
estimate hydroxymethylation and methylation consistently and
efficiently.
T reads are referred to as converted cytosine and C reads are referred to as unconverted cytosine. In case of Infinium Methylation arrays, we have intensities representing the unconverted (M) and converted (U) channels. The most used summary from these experiments is the proportion \(\beta=\frac{M}{M+U}\), commonly referred to as . Naively using the difference between betas from BS and oxBS as an estimate of 5-hmC (hydroxymethylated cytosine), and the difference between betas from BS and TAB as an estimate of 5-mC (methylated cytosine) can many times provide negative proportions and instances where the sum of uC (unmodified cytosine), 5-mC and 5-hmC proportions is greater than one due.
The function MLML takes as input the data from the
different bisulfite-based methods and returns the estimated proportion
of methylation, hydroxymethylation and unmethylation for a given CpG
site. Table 1 presents the arguments of the MLML and Table
2 lists the results returned by the function.
The function assumes that the order of the samples by rows and columns in the input matrices is consistent. In addition, all the input matrices must have the same dimension. In the provided examples, rows represent CpG loci and columns represent samples. Nonetheless transposed matrices can also be supplied.
| Arguments | Description |
|---|---|
U.matrix |
Converted cytosines (T counts or U channel) from standard BS-conversion (reflecting True 5-C). |
T.matrix |
Unconverted cytosines (C counts or M channel) from standard BS-conversion (reflecting 5-mC+5-hmC). |
G.matrix |
Converted cytosines (T counts or U channel) from TAB-conversion (reflecting 5-C + 5-mC). |
H.matrix |
Unconverted cytosines (C counts or M channel) from TAB-conversion (reflecting True 5-hmC). |
L.matrix |
Converted cytosines (T counts or U channel) from oxBS-conversion (reflecting 5-C + 5-hmC). |
M.matrix |
Unconverted cytosines (C counts or M channel) from oxBS-conversion (reflecting True 5-mC). |
| Value | Description |
|---|---|
mC |
maximum likelihood estimate for the proportion of methylation |
hmC |
maximum likelihood estimate for the proportion of hydroxymethylation |
C |
maximum likelihood estimate for the proportion of unmethylation |
methods |
the conversion methods used to produce the MLE |
We will use the dataset from Field (2015), which consists of eight DNA samples from the same DNA source treated with oxBS and BS and hybridized to the Infinium 450K array.
When data is obtained through Infinium Methylation arrays, we
recommend the use of the minfi package (Aryee et al. 2014), a well-established tool for
reading, preprocessing and analysing DNA methylation data from these
platforms. Although our example relies on minfi and other
Bioconductor tools, MLML2R does not depend on any packages.
Thus, the user is free to read and preprocess the data using any
software of preference and then import into R in matrix format the
intensities from the M and U channels (or C and T counts from
sequencing) reflecting unconverted and converted cytosines,
respectively.
To start this example we will need the following packages:
It is usually best practice to start the analysis from the raw data, which in the case of the 450K array is a file.
The raw files are deposited in GEO and can be downloaded by using the
getGEOSuppFiles. There are two files for each replicate,
since the 450k array is a two-color array. The files are downloaded in
compressed format and need to be uncompressed before they are read by
the read.metharray.exp function.
getGEOSuppFiles("GSE63179")
untar("GSE63179/GSE63179_RAW.tar", exdir = "GSE63179/idat")
list.files("GSE63179/idat", pattern = "idat")
files <- list.files("GSE63179/idat", pattern = "idat.gz$", full = TRUE)
sapply(files, gunzip, overwrite = TRUE)The files can now be read:
To access phenotype data we use the pData function. The
phenotype data is not yet available from the rgSet.
In this example the phenotype is not really relevant, since we have only one sample: male, 25 years old. What we do need is the information about the conversion method used in each replicate: BS or oxBS. We will access this information automatically from GEO:
if (!file.exists("GSE63179/GSE63179_series_matrix.txt.gz"))
download.file(
"https://ftp.ncbi.nlm.nih.gov/geo/series/GSE63nnn/GSE63179/matrix/GSE63179_series_matrix.txt.gz",
"GSE63179/GSE63179_series_matrix.txt.gz")
geoMat <- getGEO(filename="GSE63179/GSE63179_series_matrix.txt.gz",getGPL=FALSE)
pD.all <- pData(geoMat)
#Another option
#geoMat <- getGEO("GSE63179")
#pD.all <- pData(geoMat[[1]])
pD <- pD.all[, c("title", "geo_accession", "characteristics_ch1.1",
"characteristics_ch1.2","characteristics_ch1.3")]
pDThis phenotype data needs to be merged into the methylation data. The following commands guarantee we have the same replicate identifier in both datasets before merging.
sampleNames(rgSet) <- sapply(sampleNames(rgSet),function(x)
strsplit(x,"_")[[1]][1])
rownames(pD) <- pD$geo_accession
pD <- pD[sampleNames(rgSet),]
pData(rgSet) <- as(pD,"DataFrame")
rgSetThe rgSet is an object from RGChannelSet
class used for two color data (green and red channels). The input in the
MLML function are matrices with methylated and unmethylated
information from each conversion method. We can use the
MethylSet class, which contains the methylated and
unmethylated signals. The most basic way to construct a
MethylSet is using the function
preprocessRaw.
Here we chose the function preprocessNoob (Triche et al. 2013) for background correction,
dye bias normalization and construction of the MethylSet.
We encourage the user to consider other normalization methods such as
SWAN (Maksimovic et al. 2012), BMIQ (Teschendorff et al. 2012), RCP (Niu et al. 2016), Funnorm (Fortin et al. 2014), and others, as well as
combination of some of these methods, as suggested by Liu and Siegmund (2016).
The BS replicates are in columns 1, 3, 5, and 6 (information from
pD$title). The remaining columns are from the oxBS treated
replicates.
After the preprocessing steps we can use MLML from the
MLML2R package.
MChannelBS <- getMeth(MSet.noob)[,BSindex]
UChannelBS <- getUnmeth(MSet.noob)[,BSindex]
MChannelOxBS <- getMeth(MSet.noob)[,oxBSindex]
UChannelOxBS <- getUnmeth(MSet.noob)[,oxBSindex]When only two methods are available, the default option of
MLML function returns the exact constrained maximum
likelihood estimates using the the pool-adjacent-violators algorithm
(PAVA) (Ayer et al. 1955).
results_exact <- MLML(T.matrix = MChannelBS , U.matrix = UChannelBS,
L.matrix = UChannelOxBS, M.matrix = MChannelOxBS)
save(results_exact,file="results_exact_oxBS.rds")Maximum likelihood estimate via EM-algorithm approach (Qu et al. 2013) is obtained with the option . In this case, the default (or user specified) is considered in the iterative method.
results_em <- MLML(T.matrix = MChannelBS , U.matrix = UChannelBS,
L.matrix = UChannelOxBS, M.matrix = MChannelOxBS,
iterative = TRUE)The estimates are very similar for both methods:
We will use the dataset from Thienpont et al. (2016), which consists of 24 DNA samples treated with TAB-BS and hybridized to the Infinium 450K array from newly diagnosed and untreated non-small-cell lung cancer patients (12 normoxic and 12 hypoxic tumours). The dataset is deposited under GEO accession number GSE71398.
We will need the following packages:
Obtaining the data:
getGEOSuppFiles("GSE71398")
untar("GSE71398/GSE71398_RAW.tar", exdir = "GSE71398/idat")
list.files("GSE71398/idat", pattern = "idat")
files <- list.files("GSE71398/idat", pattern = "idat.gz$", full = TRUE)
sapply(files, gunzip, overwrite = TRUE)Reading the files:
The phenotype data is not yet available from the
rgSet.
We need to correctly identify the 24 DNA samples: 12 normoxic and 12 hypoxic non-small-cell lung cancer. We also need the information about the conversion method used in each replicate: BS or TAB. We will access this information automatically from GEO:
if (!file.exists("GSE71398/GSE71398_series_matrix.txt.gz"))
download.file(
"https://ftp.ncbi.nlm.nih.gov/geo/series/GSE71nnn/GSE71398/matrix/GSE71398_series_matrix.txt.gz",
"GSE71398/GSE71398_series_matrix.txt.gz")
geoMat <- getGEO(filename="GSE71398/GSE71398_series_matrix.txt.gz",getGPL=FALSE)
pD.all <- pData(geoMat)
#Another option
#geoMat <- getGEO("GSE71398")
#pD.all <- pData(geoMat[[1]])
pD <- pD.all[, c("title", "geo_accession", "source_name_ch1",
"tabchip or bschip:ch1","hypoxia status:ch1",
"tumor name:ch1","batch:ch1","platform_id")]
pD$method <- pD$`tabchip or bschip:ch1`
pD$group <- pD$`hypoxia status:ch1`
pD$sample <- pD$`tumor name:ch1`
pD$batch <- pD$`batch:ch1`This phenotype data needs to be merged into the methylation data. The following commands guarantee we have the same replicate identifier in both datasets before merging.
sampleNames(rgSet) <- sapply(sampleNames(rgSet),function(x)
strsplit(x,"_")[[1]][1])
rownames(pD) <- as.character(pD$geo_accession)
pD <- pD[sampleNames(rgSet),]
pData(rgSet) <- as(pD,"DataFrame")
rgSetThe following command produces a quality control report, which helps to identify failed samples:
After looking at the quality control report, we notice a problematic sample: GSM1833667. This sample and its corresponding pair in the TAB experiment, GSM1833691, were removed from subsequent analysis.
The input in the MLML function accepts as input a
MethylSet, which contains the methylated and unmethylated
signals. We used the function preprocessNoob (Triche et al. 2013) for background correction,
dye bias normalization and construction of the
MethylSet.
BSindex <- which(pD$method=="BSchip")[-which(pD$geo_accession
%in% c("GSM1833667","GSM1833691"))]
TABindex <- which(pD$method=="TABchip")[-which(pD$geo_accession
%in% c("GSM1833667","GSM1833691"))]
MSet.noob <- preprocessNoob(rgSet)
MChannelBS <- getMeth(MSet.noob)[,BSindex]
UChannelBS <- getUnmeth(MSet.noob)[,BSindex]
MChannelTAB <- getMeth(MSet.noob)[,TABindex]
UChannelTAB <- getUnmeth(MSet.noob)[,TABindex]We can now use MLML from the MLML2R
package.
One needs to carefully check if the columns across the different input matrices represent the same sample. In this example, all matrices have the samples consistently represented in the columns: sample 1 in the first column, sample 2 in the second, and so forth.
When any two of the methods are available, the default option of
MLML function returns the exact constrained maximum
likelihood estimates using the the pool-adjacent-violators algorithm
(PAVA) (Ayer et al. 1955).
results_exact <- MLML(T.matrix = MChannelBS , U.matrix = UChannelBS,
G.matrix = UChannelTAB, H.matrix = MChannelTAB)Maximum likelihood estimate via EM-algorithm approach (Qu et al. 2013) is obtained with the option . In this case, the default (or user specified) is considered in the iterative method.
results_em <- MLML(T.matrix = MChannelBS , U.matrix = UChannelBS,
G.matrix = UChannelTAB, H.matrix = MChannelTAB,
iterative = TRUE)The estimates for 5-hmC proportions are very similar for both methods:
The estimates for 5-mC proportions are very similar for both methods:
We will use the dataset from Li et al. (2016), which consists of three human lung normal-tumor pairs (six samples). Each sample was divided into two replicates: one treated with BS and the other with oxBS, which were then sequenced using the Illumina HiSeq 2000 (Homo sapiens) platform. The preprocessed dataset is available at GEO accession GSE70090. The details of the preprocessing procedures are described in Li et al. (2016).
Obtaining the data:
library(GEOquery)
getGEOSuppFiles("GSE70090")
untar("GSE70090/GSE70090_RAW.tar", exdir = "GSE70090/data")Decompressing the files:
dataFiles <- list.files("GSE70090/data", pattern = "txt.gz$", full = TRUE)
sapply(dataFiles, gunzip, overwrite = TRUE)We need to identify the different samples from different methods (BS-conversion, oxBS-conversion), we will use the file names do extract this information.
files <- list.files("GSE70090/data")
filesfull <- list.files("GSE70090/data",full=TRUE)
tissue <- sapply(files,function(x) strsplit(x,"_")[[1]][2]) # tissue
id <- sapply(files,function(x) strsplit(x,"_")[[1]][3]) # sample id
tmp <- sapply(files,function(x) strsplit(x,"_")[[1]][4])
convMeth <- sapply(tmp, function(x) strsplit(x,"\\.")[[1]][1]) # DNA conversion method
group <- ifelse(id %in% c("N1","N2","N3","N4"),"normal","tumor")
id2 <- paste(tissue,id,sep="_")
GSM <- sapply(files,function(x) strsplit(x,"_")[[1]][1]) # GSM
pheno <- data.frame(GSM=GSM,tissue=tissue,id=id2,convMeth=convMeth,
group=group,file=filesfull,stringsAsFactors = FALSE)Selecting only the three human lung normal-tumor pairs:
library(data.table)
phenoLung <- pheno[pheno$tissue=="lung",]
# order to have all BS samples and then all oxBS samples
phenoLung <- phenoLung[order(phenoLung$convMeth,phenoLung$id),]Preparing the data for input in the MLML function:
### BS
files <- phenoLung$file[phenoLung$convMeth=="BS"]
C_BS <- do.call(cbind,lapply(files,function(fn)
fread(fn,data.table=FALSE,select=c("methylated_read_count"))))
TotalBS <- do.call(cbind,lapply(files,function(fn)
fread(fn,data.table=FALSE,select=c("total_read_count"))))
T_BS <- TotalBS - C_BS
### oxBS
files <- phenoLung$file[phenoLung$convMeth=="oxBS"]
C_OxBS <- do.call(cbind,lapply(files,function(fn)
fread(fn,data.table=FALSE,select=c("methylated_read_count"))))
TotalOxBS <- do.call(cbind,lapply(files,function(fn)
fread(fn,data.table=FALSE,select=c("total_read_count"))))
T_OxBS <- TotalOxBS - C_OxBS
# since rownames and colnames are the same across files:
tmp <- fread(files[1], data.table=FALSE, select=c("chr","position"))
CpG <- paste(tmp[,1],tmp[,2],sep="-")
rownames(C_BS) <- CpG
rownames(T_BS) <- CpG
colnames(C_BS) <- phenoLung$id[phenoLung$convMeth=="BS"]
colnames(T_BS) <- phenoLung$id[phenoLung$convMeth=="BS"]
rownames(C_OxBS) <- CpG
rownames(T_OxBS) <- CpG
colnames(C_OxBS) <- phenoLung$id[phenoLung$convMeth=="oxBS"]
colnames(T_OxBS) <- phenoLung$id[phenoLung$convMeth=="oxBS"]
Tm = as.matrix(C_BS)
Um = as.matrix(T_BS)
Lm = as.matrix(T_OxBS)
Mm = as.matrix(C_OxBS)Only CpGs with coverage of at least 10 across all samples and all conversion procedures (BS and oxBS) were considered in the following results (\(7685557\) CpGs).
TotalBS <- Tm+Um
TotalOxBS <- Lm+Mm
library(matrixStats)
tmp1 <- rowMins(TotalBS,na.rm=TRUE) # minimum coverage across samples from BS for each CpG
tmp2 <- rowMins(TotalOxBS,na.rm=TRUE) # minimum coverage across samples from oxBS for each CpG
aa <-which(tmp1>=10 & tmp2>=10)
# CpGs with coverage at least 10 across all samples for both methods (BS and oxBS)
length(aa)We can now use MLML from the MLML2R
package.
library(MLML2R)
results_exact <- MLML(T.matrix = Tm[aa,],
U.matrix = Um[aa,],
L.matrix = Lm[aa,],
M.matrix = Mm[aa,])
results_em <- MLML(T.matrix = Tm[aa,],
U.matrix = Um[aa,],
L.matrix = Lm[aa,],
M.matrix = Mm[aa,],
iterative = TRUE)Comparing the estimates for 5-hmC proportions from iterative and non
iterative option from MLML function:
The estimates for 5-mC proportions are also very similar for both methods:
To illustrate the package when all the three methods are available or when any combination of only two of them are available, we will simulate a dataset.
We will use a sample of the estimates of 5-mC, 5-hmC and uC of the previous oxBS+BS array example shown in Section 2.1 as the true proportions, as shown in Figure 4.
Two replicate samples with 1000 CpGs will be simulated. For CpG \(i\) in sample \(j\):
\[T_{i,j} \sim Binomial(n=c_{i,j},p=p_m+p_h)\] \[M_{i,j} \sim Binomial(n=c_{i,j}, p=p_m)\] \[H_{i,j} \sim Binomial(n=c_{i,j},p=p_h)\] \[U_{i,j}=c_{i,j}-T_{i,j}\] \[L_{i,j}=c_{i,j}-M_{i,j}\] \[G_{i,j}=c_{i,j}-H_{i,j}\] where the random variables are defined in Table 1, and \(c_{i,j}\) represents the coverage for CpG \(i\) in sample \(j\).
The following code produce the simulated data:
load("results_exact_oxBS.rds") # load estimates from previous example
set.seed(112017)
index <- sample(1:dim(results_exact$mC)[1],1000,replace=FALSE) # 1000 CpGs
Coverage <- round(MChannelBS+UChannelBS)[index,1:2] # considering 2 samples
temp1 <- data.frame(n=as.vector(Coverage),
p_m=c(results_exact$mC[index,1],
results_exact$mC[index,1]),
p_h=c(results_exact$hmC[index,1],
results_exact$hmC[index,1]))
MChannelBS_temp <- c()
for (i in 1:dim(temp1)[1])
{
MChannelBS_temp[i] <- rbinom(n=1, size=temp1$n[i],
prob=(temp1$p_m[i]+temp1$p_h[i]))
}
UChannelBS_sim2 <- matrix(Coverage - MChannelBS_temp,ncol=2)
MChannelBS_sim2 <- matrix(MChannelBS_temp,ncol=2)
MChannelOxBS_temp <- c()
for (i in 1:dim(temp1)[1])
{
MChannelOxBS_temp[i] <- rbinom(n=1, size=temp1$n[i], prob=temp1$p_m[i])
}
UChannelOxBS_sim2 <- matrix(Coverage - MChannelOxBS_temp,ncol=2)
MChannelOxBS_sim2 <- matrix(MChannelOxBS_temp,ncol=2)
MChannelTAB_temp <- c()
for (i in 1:dim(temp1)[1])
{
MChannelTAB_temp[i] <- rbinom(n=1, size=temp1$n[i], prob=temp1$p_h[i])
}
UChannelTAB_sim2 <- matrix(Coverage - MChannelTAB_temp,ncol=2)
MChannelTAB_sim2 <- matrix(MChannelTAB_temp,ncol=2)
true_parameters_sim2 <- data.frame(p_m=results_exact$mC[index,1],
p_h=results_exact$hmC[index,1])
true_parameters_sim2$p_u <- 1-true_parameters_sim2$p_m-true_parameters_sim2$p_hWhen only two methods are available, the default option returns the exact constrained maximum likelihood estimates using the the pool-adjacent-violators algorithm (PAVA) (Ayer et al. 1955).
library(MLML2R)
results_exactBO1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2)Maximum likelihood estimate via EM-algorithm approach (Qu et al. 2013) is obtained with the option . In this case, the default (or user specified) is considered in the iterative method.
results_emBO1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
iterative=TRUE)When only two methods are available, we highly recommend the default
option iterative=FALSE since the difference in the
estimates obtained via EM and exact constrained is very small, but the
former requires more computational effort:
## [1] "Mean absolute difference: 0.0001259144" library(microbenchmark)
mbmBO1 = microbenchmark(
EXACT = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2),
EM = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
iterative=TRUE),
times=10)
mbmBO1## Unit: microseconds
## expr min lq mean median uq max neval
## EXACT 205.804 213.508 245.0447 238.967 263.783 338.783 10
## EM 5890.063 6010.398 8120.9069 7185.748 8309.203 17995.819 10Comparison between approximate exact constrained and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.005980957"Comparison between EM-algorithm and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.005396121"Using PAVA:
results_exactBT1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2)Using EM-algorithm:
results_emBT1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,
iterative=TRUE)Comparison between PAVA and EM:
## [1] "Mean absolute difference: 3.196297e-07" mbmBT1 = microbenchmark(
EXACT = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2),
EM = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,
iterative=TRUE),
times=10)
mbmBT1## Unit: microseconds
## expr min lq mean median uq max neval
## EXACT 180.337 187.430 563.7811 206.220 221.583 2034.621 10
## EM 4208.262 4276.119 4772.5930 4318.477 4820.356 6522.855 10Comparison between approximate exact constrained and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.0030728"Comparison between EM-algorithm and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.002319746"Using PAVA:
results_exactOT1 <- MLML(L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2)Using EM-algorithm:
results_emOT1 <- MLML(L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,
iterative=TRUE)Comparison between PAVA and EM:
## [1] "Mean absolute difference: 1.435988e-07" mbmOT1 = microbenchmark(
EXACT = MLML(L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2),
EM = MLML(L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,
iterative=TRUE),
times=10)
mbmOT1## Unit: microseconds
## expr min lq mean median uq max neval
## EXACT 173.354 180.196 207.728 185.827 199.943 384.188 10
## EM 2147.922 2183.179 2439.487 2220.599 2248.601 4310.232 10Comparison between approximate exact constrained and true 5-hmC proportion used in simulation:
## [1] "Mean absolute difference: 0.0030728"Comparison between EM-algorithm and true 5-hmC proportion used in simulation:
## [1] "Mean absolute difference: 0.003072645"When data from the three methods are available, the default otion in
the MLML function returns the constrained maximum
likelihood estimates using an approximated solution for Lagrange
multipliers method.
results_exactBOT1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2)Maximum likelihood estimate via EM-algorithm approach (Qu et al. 2013) is obtained with the option . In this case, the default (or user specified) is considered in the iterative method.
results_emBOT1 <- MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,iterative=TRUE)We recommend the default option iterative=FALSE since
the difference in the estimates obtained via EM and the approximate
exact constrained is very small, but the former requires more
computational effort:
## [1] "Mean absolute difference: 6.665856e-07" mbmBOT1 = microbenchmark(
EXACT = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2),
EM = MLML(T.matrix = MChannelBS_sim2,
U.matrix = UChannelBS_sim2,
L.matrix = UChannelOxBS_sim2,
M.matrix = MChannelOxBS_sim2,
G.matrix = UChannelTAB_sim2,
H.matrix = MChannelTAB_sim2,
iterative=TRUE),
times=10)
mbmBOT1## Unit: microseconds
## expr min lq mean median uq max neval
## EXACT 498.401 510.744 548.9055 520.7275 539.508 787.461 10
## EM 1169.134 1192.298 1441.0482 1217.5295 1283.097 3291.930 10Comparison between approximate exact constrained and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.002708598"Comparison between EM-algorithm and true hydroxymethylation proportion used in simulation:
## [1] "Mean absolute difference: 0.002045009"