Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of...

Area of Science:

• Computational Biology
• Epidemiology
• Stochastic Modeling

Background:

• Continuous-time birth-death-shift (BDS) processes are vital for modeling evolutionary dynamics, particularly transposable elements in molecular epidemiology.
• Estimating covariate effects on BDS rates from discrete, uneven patient data poses significant computational challenges.
• Transposable elements like IS6110 are key genetic markers for tracking Mycobacterium tuberculosis infection clusters.

Purpose of the Study:

• To develop an efficient and robust computational method for inferring BDS process rates from discretely and unevenly observed data.
• To apply this method to study the intrapatient evolutionary dynamics of the IS6110 transposable element.

Main Methods:

• Proposed a multi-type branching process approximation to BDS processes.
• Developed an expectation maximization algorithm utilizing spectral techniques for efficient calculation of expected sufficient statistics.
• Reduced complex calculations to low-dimensional integration for robust rate inference.

Main Results:

• The developed expectation maximization algorithm provides an efficient and robust optimization routine for inferring BDS process rates.
• The methodology was rigorously tested and validated through simulation studies.
• Successfully applied the method to analyze the intrapatient time evolution of the IS6110 transposable element.

Conclusions:

• The proposed multi-type branching process approximation and expectation maximization algorithm offer a powerful tool for analyzing BDS processes in challenging observational settings.
• This method has broad applicability to multi-type branching processes with covariate-dependent rates.
• The study provides valuable insights into the evolutionary dynamics of IS6110 in Mycobacterium tuberculosis infections.