A Poisson-multinomial mixture approach to grouped and right-censored counts. Issue 2 (17th January 2018)

• Record Type: Journal Article
• Authors: Fu, Qiang; Guo, Xin; Land, Kenneth C.
• Is Part Of: Communications in statistics. Volume 47:Issue 2(2018)
• Page Start: 427
• Page End: 447
• Publication Date: 2018-01-17
• Subjects: Grouped and right-censored count data -- mixed poisson models -- zero-inflated Poisson distribution -- multinomial distribution -- MLE-GRC; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1303736
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Although count data are often collected in social, psychological, and epidemiological surveys in grouped and right-censored categories, there is a lack of statistical methods simultaneously taking both grouping and right-censoring into account. In this research, we propose a new generalized Poisson-multinomial mixture approach to model grouped and right-censored (GRC) count data. Based on a mixed Poisson-multinomial process for conceptualizing grouped and right-censored count data, we prove that the new maximum-likelihood estimator (MLE-GRC) is consistent and asymptotically normally distributed for both Poisson and zero-inflated Poisson models. The use of the MLE-GRC, implemented in an R function, is illustrated by both statistical simulation and empirical examples. This research provides a tool for epidemiologists to estimate incidence from grouped and right-censored count data and lays a foundation for regression analyses of such data structure.