Regression analysis of a graphical proportional hazards model for informatively left-truncated current status data

In survival analysis, researchers commonly focus on variable selection issues in real–world data, particularly when complex network structures exist among covariates. Additionally, due to factors such as data collection costs and delayed entry, real-world data often exhibit censoring and truncation phenomena.This paper addresses left-truncated current status data by employing a copula-based approach to model the relationship between censoring time and failure time. Based on this, we investigate the problem of variable selection in the context of complex network structures among covariates. To this end, we integrate Markov Random Field (MRF) with the Proportional Hazards (PH) model, and extend the latter to more flexibly characterize the correlation structure among covariates. For solving the constructed model, we propose a penalized optimization method and utilize spline functions to estimate the baseline hazard function. Through numerical simulation experiments and case studies of clinical trial data, we comprehensively evaluate the effectiveness and performance of the proposed model and its parameter inference strategy. This evaluation not only demonstrates the robustness of the proposed model in handling complex disease data but also further verifies the high precision and reliability of the parameter estimation method.