Abstract

We develop the quadratic inference function method to the parameter estimation of the marginal models with general relative risk form and common baseline hazard function for multivariate failure time data. The usual exponential relative risk form is relaxed to an non-negative twice differentiable form. The proposed estimator, under some regularity conditions, is shown to be consistent and asymptotically normal with a covariance matrix that can be consistently estimated. In addition, a test statistic based on the quadratic inference function for the parameter inference has been provided. The simulation results show that the proposed method taking the correlation between the failure times into the estimation procedure gains more efficiency than the method using the independent structure when the correlation cannot be ignored, and can easily deal with the situation when the cluster size is large. The proposed method is illustrated by analysis of a real data from the Diabetic Retinopathy Study.

摘要

我们开发了二次推理函数方法来对具有一般相对风险形式和多变量故障时间数据的共同基线危险函数的边际模型进行参数估计。通常的指数相对风险形式被放宽为非负二次可微形式。在某些规律性条件下，所提出的估计量被证明与可以一致估计的协方差矩阵是一致的且渐近正态的。此外，还提供了基于二次推断函数的参数推断检验统计量。仿真结果表明，当相关性不可忽略时，将故障次数之间的相关性纳入估计过程的方法比使用独立结构的方法具有更高的效率，并且可以轻松应对集群规模较大的情况。通过分析糖尿病视网膜病变研究的真实数据来说明所提出的方法。