A New Approach for Handling Longitudinal Count Data with Zero‐Inflation and Overdispersion: Poisson Geometric Process Model

Abstract

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

A review of the extensions of the geometric process, applications, and challenges

“…For instance, Bartolucci et al apply the GP to analyse the cardiovascular studies. Wan and Chan use the Poisson GP model to analyse the longitudinal count data with zero inflation and overdispersion. Yedida et al conduct a warranty cost analysis using alternating quasi‐renewal processes.…”

Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions

“…Chan and Leung (2010) initiated the binary GP model to study the trends of methadone treatment outcomes. And, Wan and Chan (2009) introduced the generalized mixture Poisson GP (GMPGP) model to analyze the new tumour counts of the bladder cancer patients which is extended from the PGP model initiated by Wan (2006).…”

“…In this paper, we seek a new direction to model overdispersed longitudinally time series of counts due to the presence of outliers. Our proposed model is an extension of the generalized mixture Poisson geometric process (GMPGP) model proposed by Wan and Chan (2009) which is developed from the geometric process (GP) model originated by Lam (1988a,b). The GMPGP model is a two-component mixture model with a mean function to analyze the covariate effect and a ratio function to describe the time effect.…”

“…Meanwhile, the mixture effects in both mean and ratio functions can capture the population heterogeneity and overdispersion in the data. See Wan (2006) and Wan and Chan (2009) for more details. In this paper, we introduce a robust mixture Poisson geometric process (RMPGP) model using some heavy-tailed distributions in scale mixture representation.…”

Binary geometric process model for the modeling of longitudinal binary data with trend

“…This model has been applied predominately to the modeling of deteriorating systems and to reliability and maintenance problem in the study of optimal replacement or repairable models (Lam 1988a(Lam ,b, 1992aLam and Zhang 1996;Lam et al 2002). In recent years, new methods of inference for the GP model have been derived and successfully applied to different areas (Wan and Chan 2009;Chan et al 2010a,b). In statistical inference, Lam (1992b) proposed some nonparametric (NP) methods of inference including the least square of errors (LSE).…”