Reduction tree to determine estimators from the multivariate interval censored data

• Published in: Journal of physics. Conference series 2019-04, Vol.1211 (1), p.12026
• Main Authors: Fatekurohman, M, Kusmayadi, T A, Antika, D P
• Format: Article
• Language: English
• Subjects: Distribution functions; Graph theory; Graphical representations; Intersections; Maximum likelihood estimators; Multivariate analysis; Reduction
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1211/1/012026

In this paper methods for finding the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of time to event data will be presented. The basic approach is to use graph theory (in particular reduction tree), to simplify the problem. The Multivariate interval censored data can be represented by its intersection graph. The idea behind the reduction tree approach is based on the fact that when censored data can be partitioned into several groups such that observations from different groups do not intersect, we may compute the NPMLE with the data in each group separately. Each group can be further simplified when sorne observations in the group intersect all other observations: with respect to the group, such observations have no incidence on the NPMLE computation. Once these observations are, in effect, removed from the group, the group may be further partitioned.The process can go on recursively, forming the reduction tree. In the three dimension, the support area intersection of beams, where X absis the time of infection, Y ordinat the time of onset and Z the time of death. The results obtained by the leaves from the reduction tree are not unique and are maximum cliques.