Survival analysis for proportional odds model with network structure

In medical research, factors such as loss to follow-up can lead to the precise occurrence time of the event of interest for study subjects being unobserved, resulting in right-censored data. The covariates within such data often exhibit complex network structures. Consequently, our study constructs a proportional odds model that incorporates network structures, drawing from both the proportional odds model and the exponential family graphical model. We employ the Sieve maximum likelihood method to estimate unknown parameters while simultaneously identifying the network structure. To validate the effectiveness of the proposed method, we conducted numerical simulations under various settings. The results indicate that the method achieves high accuracy in parameter estimation and network structure identification. Finally, the proposed method was applied to a study on type 2 diabetic retinopathy to explore potential factors influencing the development of retinopathy.