Backward estimation of stochastic processes with failure events as time origins

TL;DR

This paper introduces a nonparametric method for estimating the mean of backward stochastic processes aligned at failure events, accounting for truncation and censoring, with applications to medical data.

Contribution

It proposes a novel one-sample nonparametric estimator for backward processes, incorporating prevalent cohort data and analyzing its large sample properties.

Findings

Estimator performs well with simulated data

Application to SEER-Medicare data illustrates practical utility

Including prevalent data enlarges the identifiable region

Abstract

Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER--Medicare linked data set is used to illustrate the proposed methodologies.