CoxianPhaseTypeR

CoxianPhaseTypeR is an R package designed for fitting Coxian Phase-Type (Coxian-PH) distributions to time-to-event data using the Expectation-Maximization (EM) algorithm. The package facilitates parameter estimation, probability density function (PDF) evaluation, survival probability computation, and model selection criteria, making it a valuable tool for survival analysis and other applications requiring phase-type distributions.

Features

• Flexible Model Fitting: Fit Coxian-PH models with an arbitrary number of phases.
• Parameter Estimation: Utilize the EM algorithm for efficient parameter estimation.
• Model Evaluation: Compute log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) for model comparison.
• Simulation Tools: Generate synthetic data from specified Coxian-PH distributions for testing and validation.
• Visualization: Plot fitted distributions and survival functions for intuitive analysis.

Installation

You can install the stable version of CoxianPhaseTypeR from CRAN:

install.packages("CoxianPhaseTypeR")

For the latest development version, install directly from GitHub:

# Install devtools if not already installed
install.packages("devtools")

# Install from GitHub
devtools::install_github("DulanDias/CoxianPhaseTypeR")

Usage

Here's a basic example demonstrating how to simulate data, fit a Coxian-PH model, and evaluate its performance:

# Load the package
library(CoxianPhaseTypeR)

# Simulate survival data from a 2-phase Coxian-PH model
set.seed(123)  # For reproducibility
data <- simulate_coxian(n = 100, lambda = c(2.0, 1.5), mu = c(1.0, 0.8))

# Fit a Coxian-PH model with 2 phases
fit <- fit_coxian(data, num_phases = 2)

# Print estimated parameters
print(fit)

# Evaluate model performance using Log-Likelihood, AIC, and BIC
model_fit <- compute_model_fit(fit)
print(model_fit)

# Determine the optimal number of phases by iterating from m = 1 to 5
best_model <- determine_optimal_phases(data, max_phases = 5)

# Print the best-fitting model
print(best_model)

Functions

• simulate_coxian(): Simulates survival data from a specified Coxian-PH distribution.
• fit_coxian(): Fits a Coxian-PH model to observed data using the EM algorithm.
• compute_model_fit(): Calculates log-likelihood, AIC, and BIC for a fitted model.
• determine_optimal_phases(): Identifies the optimal number of phases by fitting models with varying phase counts and selecting the best based on model selection criteria.
• plot_coxian(): Visualizes the fitted Coxian-PH distribution.
• plot_survival_fit(): Plots the survival function of the fitted model against empirical survival data.

Comparison with Other R Packages

While several R packages support general phase-type modeling, CoxianPhaseTypeR offers a specialized and structured implementation for Coxian-PH distributions, particularly for models with more than two phases. It provides:

• A dedicated EM algorithm optimized for Coxian-PH estimation.
• Automated model selection tools to determine the optimal number of phases.
• Integrated simulation and visualization functions tailored for Coxian models.
• Scalability for multi-phase models beyond ( m = 2 ), which existing packages may not efficiently support.

References

• Ross, S. M. (2014). Introduction to Probability Models (11th ed.). Academic Press.
• Bladt, M., & Nielsen, B. F. (2005). Matrix-Exponential Distributions in Applied Probability. Springer.
• Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific.

License

This package is licensed under the MIT License. See the LICENSE file for details.

Contributing

Contributions are welcome! Please open an issue or submit a pull request on GitHub.