Extended version of zero-inflated negative binomial distribution with application to HIV exposed infant count data

Abstract

Routine HIV exposed infants (HEI) data that is collected monthly depicts many HIV positive zeros due to prevention of mother-to-child transmission (PMTCT) policy. However, since implementation of PMTCT differs both geographically and facility-by-facility, there is likelihood of structured zero for HEI positive numbers (optimum PMTCT) and non-structured zero (sub-optimum PMTCT). Hence standard zero-inflated models may not be appropriate. This project seeks to extend the zero-inflated Negative Binomial (ZINB) model by incorporating Shanker distribution. Extensive simulations were conducted by varying parameters in the model, i.e. dispersion, shape and sample size. Results were compared using BC. The model was tested using HEI data sampled from six high HIV burden counties in Kenya. Both simulation and real HEI data results show that the model yielded better performance.