Estimation Of The Linear Transformation Cure Model With Shape Restrictions

With the development of modern medical technology,survival data with a non-negligible cure fraction are commonly encountered in clinical studies.Cure models are reasonable in analyzing such data and therefore drawing researchers' attention nowadays.In this paper,we consider the flexible linear transformation cure model.By deriving the explicit function expression between the transformation function in the model and the baseline hazard function,we are able to estimate the baseline hazard function of practical meaning.And by adopting the Bernstein polynomial approximation,we can conveniently add shape constraints to the baseline hazard function according to different types of data,which can help improve the performance of the estimation.Besides,we focus on the widely applicable right-censored data,and adopt the method of sieve maximum likelihood estimation to obtain the optimal sieve estimator,which,under some regularity conditions,leads to some very appealing asymptotic properties,including the strong consistency,the convergence rate and the asymptotic normality.Finally,we conduct extensive simulation studies to evaluate the performance of the proposed estimator,and apply the proposed estimation method to the bone marrow transplantation dataset.