A Poisson-multinomial mixture approach to grouped and right-censored counts

Qiang Fu, Xin Guo and Kenneth C. Land

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 2, 427-447

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1303736

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