ASGN Model Parameter Estimation using MCMC

Description

Estimates parameters (alpha, mu, sigma2) for the ASGN model using Markov Chain Monte Carlo (MCMC) methods. This function can be used for both cancer and normal groups in the multi-stage DMR detection framework, and also as a standalone function for fitting skewed and potentially bimodal data.

Usage

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

Arguments

Details

This function implements a Metropolis-Hastings within Gibbs sampler to estimate the parameters of the ASGN distribution, which can model skewed and potentially bimodal data. The algorithm updates alpha and mu using Metropolis-Hastings steps and sigma2 using inverse Gamma sampling.

The ASGN (Alpha-skewed generalized normal) distribution is particularly useful for modeling methylation data that often exhibits skewness and bimodal issue.

Value

A list that may contain the following elements:

• posteriors: Vector of posterior means for alpha, mu, and sigma2 (always present)

• mcmc_samples: List containing full MCMC chains for alpha, mu, and sigma2 (only if return_mcmc = TRUE)

• summary: Data.frame containing parameter estimates with 95% credible intervals (only if return_summary = TRUE)

Author(s)

Zhexuan Yang, Duchwan Ryu, and Feng Luan

See Also

mmcmcBayes for the main DMR detection function, traceplot_asgn for MCMC diagnostic plots

Examples

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

result <- asgn_func(dt, return_mcmc = TRUE, return_summary = TRUE)
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

Identifies and analyzes overlapping regions between two sets of differentially methylated regions (DMRs) detected by different methods. Computes overlap percentages to assess consistency between detection approaches.

Usage

compare_dmrs(rst1, rst2)

Arguments

Details

This function performs comparison of genomic regions between two DMR detection results. It identifies both partial and complete overlaps between regions and calculates overlap percentage by total region size.

Value

A data frame with the following columns:

Returns NULL if no overlaps are found.

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 multi-stage MCMC Bayesian method for detecting differentially methylated regions (DMRs) between cancer and normal groups. It uses the ASGN model for parameter estimation and provides both Bayes Factor and p-value based testing.

Usage

mmcmcBayes(
  cancer_data,
  normal_data,
  stage = 1,
  max_stages = 3,
  num_splits = 10,
  test = "BF",
  mcmc = NULL,
  priors_cancer = NULL,
  priors_normal = NULL,
  bf_thresholds = NULL,
  pvalue_thresholds = NULL,
  return_mcmc = FALSE
)

Arguments

Details

This function implements a multistage MCMC Bayesian approach for DMR detection. It recursively splits genomic regions and applies Bayesian testing. This function supports both Bayes Factor and Anderson-Darling tests for significance assessment. The algorithm begins by analyzing entire chromosomal regions, then recursively splits significant regions into smaller sub-regions for analysis, stopping when either maximum stages reached or no significant differences are detected.

Value

A list containing DMR detection results and, if requested, MCMC samples.

Returns NULL if no significant DMRs are detected.

Author(s)

Zhexuan Yang, Duchwan Ryu, and Feng Luan

See Also

Helper functions in this package: asgn_func for parameter estimation, traceplot_asgn for MCMC diagnostics, compare_dmrs for result comparison

Examples

 

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

priors=list(alpha = 1,mu = 1,sigma2 = 1)

mcmc = list(nburn = 5000, niter = 10000, thin = 5) 

set.seed(2021)
rst <- mmcmcBayes(cancer_demo, normal_demo, 
                 stage = 1,max_stages = 2,num_splits = 5,
                 test = "BF", priors_cancer = NULL, priors_normal = NULL,
                 bf_thresholds = list(stage1 = 10, stage2 = 10.3, stage3 = 10.3),
                 return_mcmc = TRUE)
print(rst$dmrs)

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

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

Examples

data(normal_demo)
head(normal_demo)

Create Traceplots for MCMC Parameters

Description

Creates traceplots for MCMC parameters (alpha, mu, sigma2) to assess convergence. Users are responsible for setting up their preferred plot layout using par().

Usage

traceplot_asgn(mcmc_samples, param = "all", main = NULL)

Arguments

Value

No return value, creates base R plots

Examples

# Load the datasets
data(cancer_demo)
data(normal_demo)
rst <- mmcmcBayes(cancer_demo, normal_demo, 
                 stage = 1,max_stages = 2,num_splits = 5,
                 test = "BF", priors_cancer = NULL, priors_normal = NULL,
                 bf_thresholds = list(stage1 = 10, stage2 = 10.3, stage3 = 10.3),
                 return_mcmc = TRUE)

traceplot_asgn(rst$mcmc_samples$current_stage$cancer, param = "alpha", main = "Cancer Alpha")