Sun Yifei, Chiou Sy Han, Marr Kieren A, Huang Chiung-Yu
Department of Biostatistics, Columbia University Mailman School of Public Health, 722 W168th St., New York, New York 10032, U.S.A.
Department of Mathematical Sciences, University of Texas at Dallas, 800 W. Campbell Road, Richardson, Texas 75080, U.S.A.
Biometrika. 2022 Mar;109(1):195-208. doi: 10.1093/biomet/asab008. Epub 2021 Feb 12.
Single-index models have gained increased popularity in time-to-event analysis owing to their model flexibility and advantage in dimension reduction. We propose a semiparametric framework for the rate function of a recurrent event counting process by modelling its size and shape components with single-index models. With additional monotone constraints on the two link functions for the size and shape components, the proposed model possesses the desired directional interpretability of covariate effects and encompasses many commonly used models as special cases. To tackle the analytical challenges arising from leaving the two link functions unspecified, we develop a two-step rank-based estimation procedure to estimate the regression parameters with or without informative censoring. The proposed estimators are asymptotically normal, with a root- convergence rate. To guide model selection, we develop hypothesis testing procedures for checking shape and size independence. Simulation studies and a data example on a hematopoietic stem cell transplantation study are presented to illustrate the proposed methodology.
单指标模型因其模型灵活性和降维优势，在生存时间分析中越来越受欢迎。我们通过用单指标模型对复发事件计数过程的规模和形状成分进行建模，提出了一个用于该过程速率函数的半参数框架。通过对规模和形状成分的两个链接函数施加额外的单调约束，所提出的模型具有协变量效应所需的方向可解释性，并包含许多常用模型作为特殊情况。为了解决因两个链接函数未指定而产生的分析挑战，我们开发了一种基于秩的两步估计程序，用于在有或无信息删失的情况下估计回归参数。所提出的估计量是渐近正态的，具有根收敛速率。为了指导模型选择，我们开发了用于检验形状和规模独立性的假设检验程序。给出了模拟研究和造血干细胞移植研究的数据示例，以说明所提出的方法。
