Fitting Multi-Type Branching Process Models to Panel Data

• Activity Number: 618
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Jason Xu*+ and Vladimir Minin and Peter Guttorp
• Companies: and University of Washington and University of Washington
• Keywords: Branching processes ; Expectation Maximization (EM) ; Birth-death-shift models ; Missing Data ; Tuberculosis

Abstract

Continuous-time linear birth-shift-death (BSD) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. For instance, such processes can model disease trajectories within patients. Estimation of the effects of individual covariates on the birth, shift, and death rates of the process can then be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. First, we approximate the BSD process with a two-type branching process. Next, we derive an expectation maximization (EM) algorithm, using spectral techniques to reduce calculation of expected sufficient statistics in the E-step to one dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BSD process, and apply to general multi-type branching processes, where rates can depend on patient-specific covariates. We apply our method to study intrapatient time evolution of IS6110 copy number, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.