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

• Activity Number: 168
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jason Xu* and Vladimir Minin and Peter Guttorp
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Branching Processes ; Birth-death-shift Models ; Expectation Maximization ; Molecular Epidemiology ; Missing Data

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. Estimating 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 an unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, using spectral techniques to reduce calculation of expected sufficient statistics to low dimensional integration. These methods apply broadly to discretely observed 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 IS6100 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.