Estimation of reinforced urn processes under left-truncation and right-censoring

We propose a non-parametric estimator for bivariate left-truncated and right-censored observations that combines the expectation-maximization algorithm and the reinforced urn process. The resulting expectation-reinforcement algorithm allows for the inclusion of experts' knowledge in the form of...

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Bibliographic Details
Published in:Royal Society open science 2023-03, Vol.10 (3), p.221223-221223
Main Authors: Souto Arias, Luis A, Cirillo, Pasquale, Oosterlee, Cornelis W
Format: Article
Language:English
Subjects:
bivariate survival function
expectation–maximization
left-truncation
Mathematics
reinforced urn process
right-censoring
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Summary:We propose a non-parametric estimator for bivariate left-truncated and right-censored observations that combines the expectation-maximization algorithm and the reinforced urn process. The resulting expectation-reinforcement algorithm allows for the inclusion of experts' knowledge in the form of a prior distribution, thus belonging to the class of Bayesian models. This can be relevant in applications where the data is incomplete, due to biases in the sampling process, as in the case of left-truncation and right-censoring. With this new approach, the distribution of the truncation variables is also recovered, granting further insight into those biases, and playing an important role in applications like prevalent cohort studies. The estimators are tested numerically using artificial and empirical datasets, and compared with other methodologies such as copula models and the Kaplan-Meier estimator.
ISSN:2054-5703
2054-5703
DOI:10.1098/rsos.221223