Pre-Smoothing methods for transition probabilities in Complex Non-Markovian Multi-State Models

Abstract

Multi-state models are essential tools in longitudinal data analysis, enabling the estimation of transition probabilities that provide predictive insights into clinical outcomes across stages of disease progression or recovery. Conventional approaches to inference in these models often rely on the Markov assumption, which simplifies computation but may not hold in complex real-world settings. To address this limitation, we extend the landmark Aalen-Johansen estimator by incorporating presmoothing techniques, offering a robust alternative for estimating transition probabilities in non-Markovian multi-state models, including those with multiple states and reversible transitions. The proposed method effectively reduces estimation variability and mitigates biases arising from the selection of arbitrary landmark times. Through empirical evaluation using three real-world datasets with distinct multi-state structures, we demonstrate that the presmoothed estimator achieves enhanced precision and stability, particularly in the presence of high noise or small sample sizes. To facilitate its application, we provide an R package, presmoothedTP, which implements all the proposed methods.