Event history analysis with time-dependent covariates via landmarking supermodels and boosted trees

TL;DR

This paper introduces a flexible, nonparametric method for dynamic event prediction using landmarking supermodels and boosted trees, effectively capturing complex covariate effects without restrictive assumptions.

Contribution

It develops a novel approach combining landmarking supermodels with gradient boosted trees for high-dimensional, time-dependent covariates in event history analysis, with theoretical guarantees.

Findings

Method performs well in diverse simulation settings.

Computationally efficient via standard gradient boosting software.

Applied successfully to primary biliary cirrhosis data.

Abstract

We propose a nonparametric method for dynamic prediction in event history analysis with high-dimensional, time-dependent covariates. The approach estimates future conditional hazards by combining landmarking supermodels with gradient boosted trees. Unlike joint modeling or Cox landmarking models, the proposed estimator flexibly captures interactions and nonlinear effects without imposing restrictive parametric assumptions or requiring the covariate process to be Markovian. We formulate the approach as a sieve M-estimator and establish weak consistency. Computationally, the problem reduces to a Poisson regression, allowing implementation via standard gradient boosting software. A key theoretical advantage is that the method avoids the temporal inconsistencies that arise in landmark Cox models. Simulation studies demonstrate that the method performs well in a variety of settings, and its practical value is illustrated through an analysis of primary biliary cirrhosis data.