  With the rapid development of data collection and aggregation technologies in
many scientific disciplines, it is becoming increasingly ubiquitous to conduct
large-scale or online regression to analyze real-world data and unveil
real-world evidence. In such applications, it is often numerically challenging
or sometimes infeasible to store the entire dataset in memory. Consequently,
classical batch-based estimation methods that involve the entire dataset are
less attractive or no longer applicable. Instead, recursive estimation methods
such as stochastic gradient descent that process data points sequentially are
more appealing, exhibiting both numerical convenience and memory efficiency. In
this paper, for scalable estimation of large or online survival data, we
propose a stochastic gradient descent method which recursively updates the
estimates in an online manner as data points arrive sequentially in streams.
Theoretical results such as asymptotic normality and estimation efficiency are
established to justify its validity. Furthermore, to quantify the uncertainty
associated with the proposed stochastic gradient descent estimator and
facilitate statistical inference, we develop a scalable resampling strategy
that specifically caters to the large-scale or online setting. Simulation
studies and a real data application are also provided to assess its performance
and illustrate its practical utility.
