Efficient estimation for the non-mixture cure model with current status data

Medical advances including the neoadjuvant anti-PD-1 immunotherapy play a role in promoting clinical outcomes such as improved overall and progression-free survival probabilities. This paper considers the regression analysis of current status data with a cured subgroup in the population using a semiparametric non-mixture cure model. We propose a sieve maximum likelihood estimation for the model with the Bernstein polynomials. Moreover, an expectation-maximization (EM) algorithm is developed under the non-mixture cure model to calculate the estimators for both parametric and non-parametric components. Under some mild conditions, the asymptotic properties of the estimators are established, including the strong consistency, the convergence rate and the asymptotic normality. Simulation studies are conducted to investigate the finite sample performance of the proposed estimators. A real dataset from the tumorigenicity experiment is analysed for illustration.