Profile likelihood estimation for the cox proportional hazards (PH) cure model and standard errors

In survival analysis, Cox PH cure model has attracted attention for decades. The profile likelihood approach is one of the well known estimation methods employed within the Cox PH cure modeling framework. Typically, the parameters in the profile likelihood are estimated using expectation maximization (EM) algorithm. However, there is a challenge in estimating the standard error (SE) of the estimator in the profile likelihood method. In this paper, we propose a new approach to show the asymptotic normality of the maximum profile likelihood estimator and obtain the closed form expression for the SE of the estimator. Real data example and simulation studyshowed that our method is more computationally efficient and performs better in estimating standard errors compared with the bootstrap methods in ‘smcure’ package (Cai et al. 2012).