Fit an Alpha-Skewed Generalized Normal (ASGN) Distribution by MCMC

Description

asgn_func() fits an alpha-skewed generalized normal (ASGN) distribution to univariate numeric data using an MCMC algorithm. The ASGN family provides a flexible parametric model that can accommodate skewness and, for certain parameter values, bimodal density shapes.

Usage

asgn_func(
  data,
  priors = NULL,
  mcmc = list(nburn = 5000, niter = 10000, thin = 1),
  seed = NULL
)

Arguments

Details

The input data may be any univariate numeric sample (vector or a one-column matrix). In the mmcmcBayes workflow, data is typically a vector of sample-wise regional mean M-values (one value per sample). However, asgn_func() is not specific to DNA methylation and can be used more generally for fitting skewed or potentially bimodal continuous data.

Value

A list with the following elements:

• posteriors: Vector of posterior means for alpha, mu, and sigma2.

• summary: Data frame containing parameter estimates and 95% credible intervals with columns parameter, estimate, lower_ci, and upper_ci.

If there are fewer than two non-missing observations, a default value posteriors = c(1, 0, 1) is returned, and summary is omitted.

Author(s)

Zhexuan Yang, Duchwan Ryu, and Feng Luan

References

Mahmoudi, E., Jafari, H., & Meshkat, R. (2019). Alpha-skew generalized normal distribution and its applications. Applications and Applied Mathematics: An International Journal (AAM), 14, 784-804.

See Also

mmcmcBayes for the main DMR detection function,

Examples

# Generate sample data
set.seed(2021)
dt <- rgamma(1000, shape = 2, rate = 1)
dt <- as.matrix(dt, ncol=1)

result <- asgn_func(dt)
print(result$summary)

Cancer Methylation Demo Data

Description

A demonstration dataset containing methylation M-values for cancer samples. Used for testing and examples in the mmcmcBayes package.

Usage

cancer_demo

Format

A data frame with CpG sites and methylation values.

Source

The first 5000 CpG sites of Chromosome 6 of 450K dataset.

Examples

data(cancer_demo)
head(cancer_demo)

Compare Differentially Methylated Regions (DMRs) from Two Methods

Description

compare_dmrs() identifies overlapping regions between two sets of differentially methylated regions (DMRs), typically obtained from two different detection methods. It reports pairwise overlaps and a simple overlap percentage that can be used to assess consistency between methods.

Usage

compare_dmrs(rst1, rst2)

Arguments

Details

This function compares genomic regions between two DMR result objects. For each region in rst1, it searches for regions in rst2 on the same chromosome that have any overlap in CpG index range (partial or complete).

CpG identifiers in Start_CpG and End_CpG are assumed to contain an embedded numeric component that reflects their ordering along the genome (e.g., "cg00017002"). Internally, these IDs are converted to numeric values by stripping non-digit characters; rows for which this conversion fails are removed before comparison.

For each overlapping pair of regions, the function computes

• the size of the overlapping segment (in CpG index units), and

• an overlap percentage, defined as

  \text{overlap\_size} / \max(\text{length\_method1}, \text{length\_method2}) \times 100,

  where length_method1 and length_method2 are the lengths of the two regions in CpG index units.

The overlap percentage is therefore symmetric in the two methods and can be interpreted as “how much of the larger region is covered by the overlap.”

Value

A data frame with one row per overlapping pair of regions and the columns:

• Chromosome: chromosome name of the overlapping regions.

• Start_CpG_Method1: start CpG ID from rst1.

• End_CpG_Method1: end CpG ID from rst1.

• Start_CpG_Method2: start CpG ID from rst2.

• End_CpG_Method2: end CpG ID from rst2.

• Overlap_Percentage: overlap percentage relative to the larger of the two regions (in CpG index units), rounded to two decimals.

Returns NULL if no overlaps are found or if, after cleaning, one of the inputs has no usable rows.

Author(s)

Zhexuan Yang, Duchwan Ryu, and Feng Luan

See Also

Related functions in this package: mmcmcBayes for DMR detection using multi-stage MCMC, asgn_func for parameter estimation with ASGN distribution

Examples

# Create sample DMR results
dmr_method1 <- data.frame(
  Chromosome = c("chr1", "chr1", "chr2"),
  Start_CpG = c("cg0001", "cg0050", "cg0100"),
  End_CpG = c("cg0020", "cg0070", "cg0150")
)

dmr_method2 <- data.frame(
  Chromosome = c("chr1", "chr2", "chr2"),
  Start_CpG = c("cg0005", "cg0120", "cg0090"),
  End_CpG = c("cg0025", "cg0160", "cg0110")
)

# Compare overlapping regions
overlaps <- compare_dmrs(dmr_method1, dmr_method2)

Multi-stage MCMC Bayesian Method for DMR Detection

Description

This function implements a multistage MCMC Bayesian method for detecting differentially methylated regions (DMRs) between two groups (typically cancer and normal). The method operates on methylation measurements on the M-values.

For each candidate region and for each group, the function summarizes the region at the sample level by averaging M-values across CpG sites within the region. These sample-wise means are using an alpha-skewed generalized normal (ASGN) distribution. A Bayes factor (BF) comparing the two groups is then used within a multistage region-splitting scheme to identify the DMRs.

Usage

mmcmcBayes(
  cancer_data,
  normal_data,
  stage = 1,
  max_stages = 3,
  num_splits = 50,
  mcmc = NULL,
  priors_cancer = NULL,
  priors_normal = NULL,
  bf_thresholds = c(0.5, 0.8, 1.05)
)

Arguments

Details

The inputs cancer_data and normal_data must have the same set of CpG sites in the same order. Each row corresponds to a CpG site, and the first two columns are required to be:

• CpG_ID: character CpG identifier.

• Chromosome: chromosome label (integer or character).

All remaining columns are assumed to be numeric M-values for individual samples in the respective group (e.g., "M_sample1", "M_sample2", ...).

For each group, a sample wise mean M-values are computed and passed to asgn_func to obtain posterior mean of the ASGN parameters. A Bayes factor (BF) comparing the two groups is then computed for the current region. If the BF exceeds a stage-specific threshold, the region is either accepted as a DMR (at the final stage) or split into subregions and analyzed at the next stage. This continues until either max_stages is reached or no subregion passes the BF thresholds.

The values used in the examples are intentionally small to ensure fast execution and are not intended as recommended settings for real analyses.

Value

A data frame with one row per detected DMR and the following columns:

• Chromosome: chromosome label.

• Start_CpG: CpG ID where the region starts.

• End_CpG: CpG ID where the region ends.

• CpG_Count: number of CpG sites in the region.

• Decision_Value: final Bayes factor for the region.

• Stage: stage at which the region was detected.

If no regions pass the BF thresholds, NULL is returned.

Author(s)

Zhexuan Yang, Duchwan Ryu, and Feng Luan

See Also

asgn_func for ASGN parameter estimation, plot_dmr_region for visualizing individual DMR profiles, summarize_dmrs for summarizing detected regions, compare_dmrs for comparing DMR sets.

Examples

# Load the datasets
data(cancer_demo)
data(normal_demo)

mcmc <- list(nburn = 1000, niter = 2000, thin = 1)

set.seed(2021)

rst <- mmcmcBayes(cancer_demo, normal_demo,
                 stage = 1,
                 max_stages = 2,
                 num_splits = 5,
                 mcmc = mcmc,
                 priors_cancer = NULL,
                 priors_normal = NULL,
                 bf_thresholds = c(0.5, 0.8, 1.05))

print(rst)

Normal Methylation Demo Data

Description

A demonstration dataset containing methylation M-values for normal samples. Used for testing and examples in the mmcmcBayes package.

Usage

normal_demo

Format

A data frame with CpG sites and methylation values.

Source

Derived from the first 5000 CpG sites of Chromosome 6 of the 450K dataset (processed and reduced for example use only).

Examples

data(normal_demo)
head(normal_demo)

Plot mean methylation profiles for a selected DMR

Description

Visualize a single DMR detected by mmcmcBayes() by plotting the mean M-values across CpG sites in the region for the cancer and normal groups.

Usage

plot_dmr_region(
  dmr_table,
  cancer_data,
  normal_data,
  dmr_index = 1,
  main = NULL,
  ...
)

Arguments

Details

This function takes the DMR table returned by mmcmcBayes() together with the original cancer_data and normal_data matrices used in the analysis. It selects one DMR by index and computes, for each CpG site in the region, the mean M-value across cancer samples and across normal samples. These two mean profiles are then plotted against the CpG index within the region.

The input data frames cancer_data and normal_data are expected to have the same CpG sites in the same order, with at least the columns CpG_ID and Chromosome, followed by one column per sample containing M-values. Sample columns are identified automatically as those whose names start with "M_sample".

CpG sites whose mean M-value is NA or non finite in either group are removed prior to plotting. The x axis index therefore refers to the filtered CpG positions within the selected region.

Value

The function is called for its side effect of creating a plot. It returns (invisibly) a list containing the CpG IDs in the region and the mean profiles for cancer and normal groups.

Examples

data(cancer_demo)
data(normal_demo)

set.seed(2021)
mcmc <- list(nburn = 1000, niter = 2000, thin = 1)

dmr_res <- mmcmcBayes(
  cancer_demo, normal_demo,
  stage         = 1,
  max_stages    = 2,
  num_splits    = 5,
  mcmc          = mcmc,
  priors_cancer = NULL,
  priors_normal = NULL,
  bf_thresholds = c(0.5, 0.8, 1.05)
)

plot_dmr_region(dmr_res, cancer_demo, normal_demo, dmr_index = 1)

Summarize DMR results from mmcmcBayes

Description

Convenience function to summarize the DMR table returned by mmcmcBayes(). It reports the number of detected regions, summaries of region sizes and decision values, and counts by chromosome and (optionally) by stage.

Usage

summarize_dmrs(dmr_table)

Arguments

Details

The function is designed to work with the data frame returned by mmcmcBayes(). At minimum, the input dmr_table is expected to contain the columns Chromosome, CpG_Count, and Decision_Value. If a Stage column is present, counts by stage are also reported.

If dmr_table is NULL or has zero rows, a summary object with n_dmrs = 0 is returned and all other components are NULL.

Value

An object of class "mmcmcBayes_dmr_summary", which is a list with elements:

• n_dmrs: Total number of detected DMRs.

• size_summary: Named numeric vector of summary statistics for CpG_Count (min, 1st quartile, median, mean, 3rd quartile, max), or NULL if CpG_Count is not available.

• decision_summary: Named numeric vector of summary statistics for Decision_Value (min, 1st quartile, median, mean, 3rd quartile, max), or NULL if Decision_Value is not available.

• by_chromosome: A data frame with counts of DMRs per chromosome, or NULL if Chromosome is not available.

• by_stage: A data frame with counts of DMRs per stage, if a Stage column is present; otherwise NULL.

Examples

data(cancer_demo)
data(normal_demo)

mcmc <- list(nburn = 1000, niter = 2000, thin = 1)

set.seed(2021)
dmr_res <- mmcmcBayes(
  cancer_demo, normal_demo,
  stage         = 1,
  max_stages    = 2,
  num_splits    = 5,
  mcmc          = mcmc,
  priors_cancer = NULL,
  priors_normal = NULL,
  bf_thresholds = c(0.5, 0.8, 1.05)
)

summary_res <- summarize_dmrs(dmr_res)
summary_res