Semiparametric Estimation For Doubly Censored Data With A Cured Subgroup

Doubly censored data is an important data type in the field of survival analysis.Such data arise when the failure time of interest is between two relevant events while both event times of them are interval-censored.We call these two relevant events the initial event and the subsequent event respectively.The analysis would not be effective if there exist some insusceptible subjects who are not at risk to the subsequent event.So the cure model emerged.However,most of the researches about the cure model base on either right-censored data or interval-censored data.For the doubly censored data,the cure model has not been extensively discussed.In this context,our paper considers the semiparametric estimation for doubly censored data with a cured subgroup.First of all,we introduce the model setting and derive the likelihood function under the additive hazards model.Secondly,the sieve spaced are constructed by using Bernstein polynomials to approximate the baseline hazard function,and the asymptotic properties of the estimator are established simultaneously.Thirdly,for convenience of computation,we develop an EM algorithm with multiple imputation to deal with the complex likelihood.Finally,to evaluate the finite sample performance,we conduct extensive simulation studies and apply our proposed method to analyzing the AIDS incubation time.