Incomplete information on explanatory variables is commonly encountered in studies of possibly censored event times. A popular approach to deal with partially observed covariates is multiple imputation, where a number of completed data sets, that can be analyzed by standard complete data methods, are obtained by imputing missing values from an appropriate distribution. We show how the combination of multiple imputations from a compatible model with suitably estimated parameters and the usual Cox regression estimators leads to consistent and asymptotically Gaussian estimators of both the finite-dimensional regression parameter and the infinite-dimensional cumulative baseline hazard parameter. We also derive a consistent estimator of the covariance operator. Simulation studies and an application to a study on survival after treatment for liver cirrhosis show that the estimators perform well with moderate sample sizes and indicate that iterating the multiple-imputation estimator increases the precision.

中文翻译：

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具有缺失协变量数据的 Cox 回归的频繁多重插补的大样本结果

在可能的删失事件时间的研究中，通常会遇到关于解释变量的不完整信息。处理部分观察到的协变量的一种流行方法是多重插补，其中可以通过标准完整数据方法分析的许多完整数据集是通过从适当的分布中插补缺失值来获得的。我们展示了来自兼容模型的多重插补与适当估计的参数和通常的 Cox 回归估计量的组合如何导致有限维回归参数和无限维累积基线风险参数的一致和渐近高斯估计量。我们还推导出协方差算子的一致估计量。