Optimal distributed subsampling for accelerated failure time models with massive censored data

The availability of massive data stored across multiple locations is increasing in many fields. The data at each site often exhibits large-scale features. Current research primarily focuses on such datasets that consist of uncensored observations. As a popular model in survival analysis, the AFT model provides an intuitive explanation of survival times, making the model results easier to understand in practical applications. In this paper, we develop a distributed subsampling procedure specifically designed for accelerated failure time (AFT) model. The consistency and asymptotic normality of the resulting estimator are proved. A two-step algorithm is provided to address practical implementation issues and to determine both the optimal subsampling probabilities and allocation sizes. We conduct numerical simulation studies to evaluate the performance of our method and apply it to a lymphoma dataset.