Integrating Multisource Block-Wise Missing Data in Model Selection

For multisource data, blocks of variable information from certain sources are likely missing. Existing methods for handling missing data do not take structures of block-wise missing data into consideration. In this article, we propose a multiple block-wise imputation (MBI) approach, which incorporates imputations based on both complete and incomplete observations. Specifically, for a given missing pattern group, the imputations in MBI incorporate more samples from groups with fewer observed variables in addition to the group with complete observations. We propose to construct estimating equations based on all available information, and integrate informative estimating functions to achieve efficient estimators. We show that the proposed method has estimation and model selection consistency under both fixed-dimensional and high-dimensional settings. Moreover, the proposed estimator is asymptotically more efficient than the estimator based on a single imputation from complete observations only. In addition, the proposed method is not restricted to missing completely at random. Numerical studies and ADNI data application confirm that the proposed method outperforms existing variable selection methods under various missing mechanisms. Supplementary materials for this article are available online.

针对多源数据，特定来源的可变信息块大概率存在缺失。现有缺失数据处理方法未考虑分块缺失数据的结构特征。本文提出一种多重分块插补（multiple block-wise imputation, MBI）方法，该方法整合了基于完整观测与不完整个体的插补策略。具体而言，对于给定的缺失模式组，MBI的插补过程除使用完全观测组的样本外，还引入了观测变量更少的分组中的更多样本。本文提出基于所有可用信息构建估计方程，并整合信息性估计函数以获得高效估计量。研究表明，所提方法在固定维数与高维两种设定下均具备估计与模型选择一致性。此外，所提估计量的渐近效率优于仅基于完全观测进行单次插补得到的估计量。进一步地，本方法不受完全随机缺失（missing completely at random, MCAR）机制的限制。数值模拟实验与ADNI数据应用验证表明，在多种缺失机制下，所提方法的表现优于现有变量选择方法。本文的补充材料可在线获取。