Efficient Estimation Of The Partially Linear Non-mixture Cure Model With Auxiliary Subgroup Survival Information

The impacts of biomarkers on disease outcome are complex in clinical studies.Then the assumption that the covariate effects were linear seems too restrictive or impractical at times.Besides,with the rapid increase of available data,statistical approaches to integrate the extra information from differently obtainable sources or types are increasingly popular tools in medical studies.In this paper,we propose the semiparametric estimation for the partially linear nonmixture cure model which is an extension of the promotion time cure model by incorporating nonlinear covariate effects.The sieve empirical maximum likelihood method based on Bernstein polynomials is developed to combine the subgroup auxiliary survival information under right censored time-to-event data.And we present the asymptotic properties for the proposed estimator of regression parameters.Simulation studies show that the estimator we derived is more efficient than the traditional maximum likelihood method without synthesizing the auxiliary subgroup survival probabilities.We analyze the breast cancer data example to demonstrate our theory and method.