Fitting Birth-Death Processes to Panel Data with Applications to Bacterial DNA Fingerprinting

Area of Science:

• Biostatistics
• Computational Biology
• Epidemiology

Background:

• Continuous-time linear birth-death-immigration (BDI) processes model population dynamics in ecology and epidemiology.
• In clinical settings, BDI processes can track individual disease trajectories and estimate covariate effects on birth/death rates.
• Analyzing patient panel data (unevenly spaced time points) for BDI models presents significant optimization challenges.

Purpose of the Study:

• To propose a novel Expectation-Maximization (EM) algorithm for fitting linear BDI models with covariates to panel data.
• To develop a computationally efficient and robust method for analyzing complex population dynamics.

Main Methods:

• Derived a closed-form expression for the joint generating function of BDI process statistics.
• Reduced the E-step of the EM algorithm and Fisher information calculation to one-dimensional integration.
• Implemented the algorithm in an open-source R package for practical application.

Main Results:

• Successfully applied the method to DNA fingerprinting data of *Mycobacterium tuberculosis*.
• Analyzed the intrapatient time evolution of the IS6110 genetic marker.
• Identified previously undocumented differences in IS6110 birth-death rates across three major *M. tuberculosis* lineages.

Conclusions:

• The novel EM algorithm provides an efficient and robust tool for fitting linear BDI models to panel data.
• Findings on IS6110 dynamics offer crucial insights for epidemiologists using DNA fingerprinting for *M. tuberculosis* surveillance.
• This work bridges statistical modeling with molecular epidemiology for improved understanding of infectious disease dynamics.