Kernel Machines for Current Status Data

TL;DR

This paper introduces a kernel machine method for estimating failure time expectations in survival analysis with current status data, providing theoretical guarantees and demonstrating competitive performance through simulations and real data analysis.

Contribution

It develops a novel kernel machine approach with theoretical convergence guarantees for current status data, a challenging censored data type in survival analysis.

Findings

Method achieves convergence to the true expectation.

Performs comparably or better than existing methods in simulations.

Provides finite sample bounds and oracle inequalities.

Abstract

In survival analysis, estimating the failure time distribution is an important and difficult task, since usually the data is subject to censoring. Specifically, in this paper we consider current status data, a type of data where all of the observations are censored. The format of the data is such that the failure time is restricted to knowledge of whether or not the failure time exceeds a random monitoring time. We propose a flexible kernel machine approach for estimation of the failure time expectation as a function of the covariates, with current status data. In order to obtain the kernel machine decision function, we minimize a regularized version of the empirical risk with respect to a new loss function. Using finite sample bounds and novel oracle inequalities, we prove that the obtained estimator converges to the true conditional expectation for a large family of probability measures. Finally, we present a simulation study and an analysis of real-world data that compares the performance of the proposed approach to existing methods. We show empirically that our approach is comparable to current state of the art, and in some cases is even better.