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.

Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept

Associated longitudinal response variables are faced with variations caused by repeated measurements over time along with the association between the responses. To model a longitudinal ordinal outcome using generalized linear mixed models, integrating over a normally distributed random intercept in the proportional odds ordinal logistic regression does not yield a closed form. In this paper, we combined a longitudinal count and an ordinal response variable with Bridge distribution for the random intercept in the ordinal logistic regression submodel. We compared the results to that of a normal distribution. The two associated response variables are combined using correlated random intercepts. The random intercept in the count outcome submodel follows a normal distribution. The random intercept in the ordinal outcome submodel follows Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modelling approaches. To illustrate the performance of the model, a simulation study was conducted. Based on the simulation results, assuming a Bridge distribution for the random intercept of ordinal logistic regression results in accurate estimation even if the random intercept is normally distributed. Moreover, considering the association between longitudinal count and ordinal responses resulted in estimation with lower standard error in comparison to univariate analysis. In addition to the same interpretation for the parameter in marginal and conditional estimates thanks to the assumption of a Bridge distribution for the random intercept of ordinal logistic regression, more efficient estimates were found compared to that of normal distribution.