Department of Statistics, Mathematical Analysis and Operational Research, University of Santiago de Compostela, Santiago de Compostela, Spain.
Department of Statistics and Operations Research, University of Granada, Granada, Spain.
Biom J. 2023 Jan;65(1):e2000353. doi: 10.1002/bimj.202000353. Epub 2022 Jul 5.
This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on two real data sets one from biomedical research and one from veterinary medicine.
本文探讨了在具有随机效应的 Cox 比例风险模型中检验协变量效应的函数形式。我们假设由于右删失，响应是聚类的且不完整。在零假设（参数协变量效应）和备择假设（非参数效应）下，使用完全边际似然进行模型估计。在备择假设下，使用正交展开估计非参数协变量效应。检验统计量是似然比统计量，其分布使用自举方法进行逼近。通过模拟研究了所提出的检验程序的性能。该方法还应用于两个真实数据集，一个来自生物医学研究，另一个来自兽医。
