Variable selection for longitudinal zero-inflated power series transition model

In modeling many longitudinal count clinical studies, the excess of zeros is a common problem. To take into account the extra zeros, the zero-inflated power series (ZIPS) models have been applied. These models assume a latent mixture model consisting of a count component and a degenerated zero component that has a unit point mass at zero. Usually, the current response measurement in a longitudinal sequence is a function of previous outcomes. For example, in a study about acute renal allograft rejection, the number of acute rejection episodes for a patient in current time is a function of this outcome at previous follow-up times. In this paper, we consider a transition model for accounting the dependence of current outcome on the previous outcomes in the presence of excess zeros. New variable selection methods for the ZIPS transition model using least absolute shrinkage and selection operator (LASSO), minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) penalties are proposed. An expectation-maximization (EM) algorithm using the penalized likelihood is applied for both parameters estimations and conducting variable selection. Some simulation studies are performed to investigate the performance of the proposed approach and the approach is applied to analyze a real dataset.