Xu Da, Zhao Hui, Sun Jianguo
Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, 130012, China.
Department of Statistics, Central China Normal University, Wuhan, 430079, China.
Lifetime Data Anal. 2018 Jan;24(1):94-109. doi: 10.1007/s10985-017-9397-0. Epub 2017 Jun 12.
Interval-censored failure time data and panel count data are two types of incomplete data that commonly occur in event history studies and many methods have been developed for their analysis separately (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006; Sun and Zhao in The statistical analysis of panel count data. Springer, New York, 2013). Sometimes one may be interested in or need to conduct their joint analysis such as in the clinical trials with composite endpoints, for which it does not seem to exist an established approach in the literature. In this paper, a sieve maximum likelihood approach is developed for the joint analysis and in the proposed method, Bernstein polynomials are used to approximate unknown functions. The asymptotic properties of the resulting estimators are established and in particular, the proposed estimators of regression parameters are shown to be semiparametrically efficient. In addition, an extensive simulation study was conducted and the proposed method is applied to a set of real data arising from a skin cancer study.
区间删失失效时间数据和成组计数数据是事件史研究中常见的两类不完全数据，并且已经分别开发了许多方法对其进行分析（孙在《区间删失失效时间数据的统计分析》。施普林格出版社，纽约，2006年；孙和赵在《成组计数数据的统计分析》。施普林格出版社，纽约，2013年）。有时，人们可能会对它们进行联合分析感兴趣或有必要进行联合分析，例如在具有复合终点的临床试验中，而在文献中似乎不存在既定的方法。在本文中，为联合分析开发了一种筛最大似然方法，在所提出的方法中，使用伯恩斯坦多项式来逼近未知函数。建立了所得估计量的渐近性质，特别是所提出的回归参数估计量被证明是半参数有效的。此外，进行了广泛的模拟研究，并将所提出的方法应用于一组来自皮肤癌研究的真实数据。
