Souto Arias Luis A, Cirillo Pasquale, Oosterlee Cornelis W
Mathematical Institute, Utrecht University, Utrecht, The Netherlands.
ZHAW School of Law and Management, Zurich University of Applied Sciences, Zurich, Switzerland.
R Soc Open Sci. 2023 Mar 8;10(3):221223. doi: 10.1098/rsos.221223. eCollection 2023 Mar.
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.
我们提出了一种用于双变量左截断和右删失观测值的非参数估计器，它结合了期望最大化算法和强化瓮过程。由此产生的期望强化算法允许以先验分布的形式纳入专家知识，因此属于贝叶斯模型类别。在数据由于抽样过程中的偏差（如左截断和右删失的情况）而不完整的应用中，这可能是相关的。通过这种新方法，还可以恢复截断变量的分布，从而更深入地了解这些偏差，并在诸如现患队列研究等应用中发挥重要作用。使用人工数据集和实证数据集对估计器进行了数值测试，并与其他方法（如Copula模型和Kaplan-Meier估计器）进行了比较。
