With increasing availability of massive survival data, researchers need valid statistical inferences for survival modeling whose computation is not limited by computer memories. Existing works focus on relative risk models using the online updating and divide-and-conquer strategies. The subsampling strategy has not been available due to challenges in developing the asymptotic properties of the estimator under semiparametric models with censored data. This article tackles optimal subsampling algorithms to fast approximate the maximum likelihood estimator for parametric accelerate failure time models with massive survival data. We derive the asymptotic distributions of the subsampling estimator and the optimal sampling probabilities that minimize the asymptotic mean squared error of the estimator. A feasible two-step algorithm is proposed where the optimal sampling probabilities in the second step are estimated based on a pilot sample in the first step. The asymptotic properties of the two-step estimator are established. The performance of the estimator is validated in a simulation study. A real data analysis illustrates the usefulness of the methods.

Massive survival data are increasingly common in many research fields, and subsampling is a practical strategy for analyzing such data. Although optimal subsampling strategies have been developed for Cox models, little has been done for semiparametric accelerated failure time (AFT) models due to the challenges posed by non-smooth estimating functions for the regression coefficients. We develop optimal subsampling algorithms for fitting semi-parametric AFT models using the least-squares approach. By efficiently estimating the slope matrix of the non-smooth estimating functions using are sampling approach, we construct optimal subsampling probabilities for the observations. For feasible point and interval estimation of the unknown coefficients, we propose a two-step method, drawing multiple subsamples in the second stage to correct for overe stimation of the variance in higher censoring scenarios. We validate the performance of our estimators through a simulation study that compares single and multiple subsampling methods, and apply the methods to analyze the survival time of lymphoma patients in the Surveillance, Epidemiology, and End Results program.

No abstract