Optimal subsampling for semi‐parametric accelerated failure time models with massive survival data using a rank‐based approach

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi-parametric AFT models with rank-based estimation have received limited attention. The challenges arise from the non-smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well-defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non-smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two-step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program.