加速失效模型下大规模生存数据的分布式模型平均

Distributed Model Averaging for Large-Scale Survival Data under Accelerated Failure Time Models

摘要: 大规模分布式数据的出现，给传统统计分析带来了巨大挑战，也使得分布式统计分析近年来成为统计研究中的热点问题。分布式模型平均方法虽能有效处理大规模数据中的模型不确定性问题，但据作者了解，现有文献仅研究了完全数据的场景，尚未涉及生存数据的分布式模型平均。针对大规模分布式右删失生存数据，利用逆概率删失加权技术，本文提出了加速失效模型下的两种分布式Mallows类型的模型平均方法。两种方法分别采用单轮型估计算法与替代最小二乘的迭代型估计算法进行备选模型的回归系数估计，但在权重选择上均统一采用局部最优权重的简单平均策略。本文通过数值模拟实验验证了所提方法的有效性，并将所提方法用到了实际数据分析。结果表明，所提方法在保持与基于全数据方法相近预测精度的同时，显著提升了计算效率。

Abstract: The emergence of massive distributed data imposes significant challenges to traditional statistical approaches, and also makes distributed statistical learning a hot topic in recent years. Although distributed model averaging methods can effectively handle model uncertainty in these large-scale datas, to the best of our knowledge, existing relevant literature has only investigated the scenarios with complete data and has not yet covered survival data. For the massive distributed survival data with rightly censoring responses, we propose two distributed Mallows-type model averaging methods using the technique of inverse probability of censoring weighting under the accelerated failure time model. These two methods differ in the estimation of the coefficient vector of candidate models—one employs a one-round algorithm while the other uses an iterative algorithm based on surrogate least squares—but both adopt a simple averaging strategy based on locally optimal weights for weight aggregation. The effectiveness of the proposed methods is validated through numerical simulation studies, and the methods are also applied to a real data analysis. The results show that the proposed approaches maintain the prediction accuracy similar to that of full-data methods and yield a marked improvement in computational time.