带有污染协变量和辅助生存信息的Cox模型的改进估计方法研究
Research on Improved Estimation Method of the Cox Model with Contaminated Covariable and Auxiliary Survival Information
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摘要: 在流行病学、生物医学和临床试验等领域的研究中,Cox模型是最受欢迎的半参数回归模型之一. 在建模过程中,观测到的协变量通常是被污染的, 污染因子可测, 但是污染函数未知,直接使用被污染的协变量进行参数估计, 可能会造成错误的统计推断.研究者往往发现疾病治疗的最佳时刻点, 如果忽略这些辅助生存信息,可能导致估计效率的降低.本文研究带有污染协变量和辅助生存信息的Cox模型的一种改进估计,通过核平滑方法校准受污染的协变量, 并通过分组提取辅助生存信息用于参数估计,然后使用广义矩估计方法解决超维方程组求解的问题.模拟分析和实证研究结果表明:基于协变量校准后的Cox模型的广义矩估计方法比偏似然估计方法、协变量未调整的Cox模型的广义矩估计方法的效果更好.Abstract: Cox model is one of the most popular semi-parametric regression models in epidemiology, biomedical science and clinical trials. In the modeling process, the observed covariates are usually contaminated, and the pollution factor can be measured, but the pollution function is unknown. Therefore, the direct use of the contaminated covariate for parameter estimation may lead to incorrect statistical inference. Researchers often find the best time for disease treatment, and omission of such survival information may lead to a decrease in the estimated effectiveness. In this paper, an improved estimation of the Cox model with contaminated covariates and auxiliary survival information is studied. Kernel smoothing method is used to calibrate the contaminated covariates, and auxiliary survival information is extracted by grouping for parameter estimation. Then, generalized moment estimation method is used to solve the problem of hyperdimensional equations. The results of simulation analysis and empirical study show that the generalized moment estimation method based on the Cox model with covariate calibration is better than the partial likelihood estimation method and the generalized moment estimation method based on the Cox model with the unadjusted covariates.