A scalable approach for continuous time Markov models with covariates.

Area of Science:

• Computational Statistics
• Biostatistics
• Mathematical Biology

Background:

• Continuous time Markov models (CTMM) are essential for analyzing time-to-event data.
• Existing CTMM fitting methods face scalability challenges with large datasets due to computational costs.
• High computational cost arises from repeated matrix exponential calculations for each observation.

Purpose of the Study:

• To propose an optimized technique for fitting CTMM with covariates.
• To address the scalability issues of existing CTMM fitting methods.
• To enable feasible fitting of large-scale biological and medical data.

Main Methods:

• Utilized stochastic gradient descent (SGD) for optimization.
• Implemented differentiation of the matrix exponential via Padé approximation.
• Developed two novel methods for standard error computation using Padé and power series expansions.

Main Results:

• The proposed optimization technique significantly improves the feasibility of fitting large-scale CTMM.
• Demonstrated improved performance compared to existing CTMM fitting methods through simulations.
• Successfully applied the method to the large-scale multiple sclerosis NO.MS dataset.

Conclusions:

• The novel optimization technique enhances the scalability of CTMM fitting.
• This approach facilitates the analysis of large, complex datasets in various scientific fields.
• The method provides a robust framework for incorporating covariates in CTMM analyses.