Analysis of bivariate zero inflated count data with missing responses

Bivariate zero-inflated Poisson regression models have recently been used in various medical and biological settings to model excess zeros. However, there has not been any definite approach to deal with the same in the event of missing responses. The model itself is complex and as the responses are paired, missing values can occur in either or both coordinates. We propose a flexible Monte Carlo expectation maximization based approach to handle bivariate zero inflated count data with missing responses. We report the results of a simulation study designed to evaluate the performance of the proposed approach. To illustrate the application of our model and methodology, we consider a bivariate data concerning the demand for health care in Australia.

[1]  LIKELIHOOD-BASED INFERENCE WITH NONIGNORABLE MISSING RESPONSES AND COVARIATES IN MODELS FOR DISCRETE LONGITUDINAL DATA , 2006 .

[2]  G. C. Wei,et al.  A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms , 1990 .

[3]  J. Booth,et al.  Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm , 1999 .

[4]  M. Kenward,et al.  Informative Drop‐Out in Longitudinal Data Analysis , 1994 .

[5]  Getachew A. Dagne,et al.  Hierarchical Bayesian Analysis of Correlated Zero‐inflated Count Data , 2004 .

[6]  Michelle Shardell,et al.  Weighted estimating equations for longitudinal studies with death and non‐monotone missing time‐dependent covariates and outcomes , 2008, Statistics in medicine.

[7]  Ingram Olkin,et al.  A Family of Bivariate Distributions Generated by the Bivariate Bernoulli Distribution , 1985 .

[8]  Pravin K. Trivedi,et al.  Regression Analysis of Count Data , 1998 .

[9]  James M. Robins,et al.  Semiparametric Regression for Repeated Outcomes With Nonignorable Nonresponse , 1998 .

[10]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[11]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[12]  Richard J. Cook,et al.  A robust pairwise likelihood method for incomplete longitudinal binary data arising in clusters , 2011 .

[13]  S. Lipsitz,et al.  Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable , 2001 .

[14]  K. Chan,et al.  Monte Carlo EM Estimation for Time Series Models Involving Counts , 1995 .

[15]  Richard J. Cook,et al.  Weighted Generalized Estimating Functions for Longitudinal Response and Covariate Data That Are Missing at Random , 2010 .

[16]  Lang Wu,et al.  Simultaneous inference and bias analysis for longitudinal data with covariate measurement error and missing responses. , 2011, Biometrics.

[17]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[18]  Jye-Chyi Lu,et al.  Multivariate zero-inflated Poisson models and their applications , 1999 .

[19]  Wei Liu,et al.  Simultaneous Inference for Semiparametric Nonlinear Mixed‐Effects Models with Covariate Measurement Errors and Missing Responses , 2007, Biometrics.

[20]  Roderick J. A. Little,et al.  Modeling the Drop-Out Mechanism in Repeated-Measures Studies , 1995 .

[21]  D. Karlis,et al.  Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R , 2005 .

[22]  Xue-Dong Chen,et al.  Computational Statistics and Data Analysis Model Selection for Zero-inflated Regression with Missing Covariates , 2022 .

[23]  Joseph G Ibrahim,et al.  Theory and Inference for Regression Models with Missing Responses and Covariates. , 2008, Journal of multivariate analysis.

[24]  J. Robins,et al.  Analysis of semiparametric regression models for repeated outcomes in the presence of missing data , 1995 .

[25]  Joseph G Ibrahim,et al.  Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects Models , 2003, Biometrics.