Semi‐Parametric Estimation of the Non‐Mixture Cure Model With Right‐Censored Data Under a Network Structure

ABSTRACT In studies with right‐censored data involving a cure fraction, it is conventional to model the cured and non‐cured groups separately. However, this modeling approach is unable to employ a single model to capture the latent relationship between covariates and failure time. Furthermore, when covariates possess an interdependent network structure, traditional cure models cannot capture the relationship between the network structure and the failure time. Therefore, this paper constructs a semi‐parametric cure model incorporating a network structure by integrating the exponential family graphical model and the non‐mixture cure model under right‐censored data. A Sieve maximum likelihood estimation method based on Bernstein polynomials is proposed for estimating unknown parameters and identifying the network structure. The robustness of the proposed method is validated through numerical simulations conducted under various settings. Finally, the proposed method is applied to the study of head and neck squamous cell carcinoma data, revealing the potential influence of the inter‐gene network structure on HNSCC progression.