Huang Chiung-Yu, Wang Mei-Cheng
Division of Biostatistics, School of Public Health, University of Minnesota, 420 Delaware Street S.E., Minneapolis, Minnesota 55455, USA.
Biometrics. 2005 Jun;61(2):392-402. doi: 10.1111/j.1541-0420.2005.00328.x.
This article considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In the literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data on the first pair of censored bivariate recurrence times. These methods are inefficient in the model considered here because recurrence times of higher orders are not used. Asymptotic properties of the proposed estimators are established. Numerical studies demonstrate the estimators perform well with practical sample sizes. We apply the proposed method to the South Verona, Italy, psychiatric case register (PCR) data set for illustration of the methods and theory.
本文考虑了这样一种统计模型，其中两种不同类型的事件，如疾病的诊断和疾病的缓解，随时间交替发生，并且观察到存在右删失。我们提出了双变量复发时间联合分布和首次复发时间边际分布的非参数估计量。一般来说，由于可识别性问题，第二次复发时间的边际分布无法估计，但第二次复发时间的条件分布可以非参数估计。在文献中，已经开发了基于第一对删失双变量复发时间的数据来估计双变量复发时间联合分布的统计方法。这些方法在此处考虑的模型中效率不高，因为未使用更高阶的复发时间。建立了所提出估计量的渐近性质。数值研究表明，这些估计量在实际样本量下表现良好。我们将所提出的方法应用于意大利南维罗纳精神病病例登记册（PCR）数据集，以说明方法和理论。
