Analysis of Zero Inflated Longitudinal Data Using Proc Nlmixed

Commonly used parametric models may lead to erroneous inference when analyzing count or continuous data with excess of zeroes. For non-clustered data, the most commonly used models to address the issue of excess zeroes are zero inflated Poisson (ZIP), zero inflated negative binomial (ZINB), hurdle Poisson (HP) and hurdle negative binomial (HNB). Our goal is to expand these for modeling longitudinal data by developing a unified PROC NLMIXED based SAS® macro that allows for a grid search of parameter initial values to facilitate convergence. The motivating data set comes from a longitudinal study in an African American population with poorly controlled type 2 diabetes conducted at the Veterans Administration (VA) and Medical University of South Carolina (MUSC) medical centers between 2009 and 2012. A total of 256 subjects were followed for one year and measures were taken at baseline and at month 3, 6 and 12 post baseline after the subjects were randomly assigned to four treatment groups: Telephone-delivered diabetes knowledge/information, Telephone-delivered motivation/behavioral skills training intervention, Telephone-delivered diabetes knowledge/information and motivation/behavioral intervention and Usual Care. The main goal of the study was to determine the efficacy of the treatment groups in relation to the usual care group in reducing the levels of hemoglobin A1c at 12 months. We used these data to demonstrate the application of this unified SAS macro that has the capability to fit the above two part/mixture models for zero inflated and correlated count data. The macro facilitates model comparison based on fit statistics, parameter estimates with corresponding standard errors and graphs. Moreover, the proposed unified macro address the issue of convergence by finding good initial starting values for the parameters and performing a grid search for the best estimation of the standard errors corresponding to the random effects.