Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements

TL;DR

This paper introduces an efficient EM algorithm with spectral techniques for inferring birth, death, and shift rates in discretely observed birth-death-shift processes, with applications to genetic element evolution in epidemiology.

Contribution

It develops a novel spectral EM approach for BDS processes, enabling robust inference from discretely observed data, applicable to multi-type branching processes with covariates.

Findings

Validated method through simulation studies.

Successfully applied to study transposable element evolution.

Improved computational efficiency and robustness.

Abstract

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements - important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a mutli-type branching process approximation to BDS processes and develop a corresponding expectation maximization (EM) algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply more broadly to multi-type branching processes where rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a frequently used element during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.