Missing covariates are commonly encountered when evaluating covariate effects on survival outcomes. Excluding missing data from the analysis may lead to biased parameter estimation and a misleading conclusion. The inverse probability weighting method is widely used to handle missing covariates. However, obtaining asymptotic variance in frequentist inference is complicated because it involves estimating parameters for propensity scores. In this paper, we propose a new approach based on an approximate Bayesian method without using Taylor expansion to handle missing covariates for survival data. We consider a stratified proportional hazards model so that it can be used for the non-proportional hazards structure. Two cases for missing pattern are studied: a single missing pattern and multiple missing patterns. The proposed estimators are shown to be consistent and asymptotically normal, which matches the frequentist asymptotic properties. Simulation studies show that our proposed estimators are asymptotically unbiased and the credible region obtained from posterior distribution is close to the frequentist confidence interval. The algorithm is straightforward and computationally efficient. We apply the proposed method to a stem cell transplantation data set.

在评估协变量对生存结果的影响时，通常会遇到缺少协变量的情况。从分析中排除缺失数据可能会导致参数估计有偏差和误导性结论。逆概率加权方法广泛用于处理缺失的协变量。然而，在频率论者推理中获得渐近方差是复杂的，因为它涉及估计倾向得分的参数。在本文中，我们提出了一种基于近似贝叶斯方法的新方法，无需使用泰勒展开来处理生存数据的缺失协变量。我们考虑分层比例风险模型，以便它可以用于非比例风险结构。研究了两种丢失模式的情况：单个丢失模式和多个丢失模式。所提出的估计量被证明是一致的和渐近正态的，这与常客渐近特性相匹配。仿真研究表明，我们提出的估计量是渐近无偏的，并且从后验分布获得的可信区域接近于频率派置信区间。该算法简单明了，计算效率高。我们将所提出的方法应用于干细胞移植数据集。