Abstract

Cure models are popularly used to analyze failure time data where some individuals could eventually experience and others might never experience an event of interest. However in many studies, there are diagnostic procedures available to provide further information about whether a subject is cured. Wu et al. (2014) proposed a method, called the {\it extended} cure model, that incorporated such additional diagnostic cured status information into the classical cure model analysis. Through extensive simulations, they demonstrated that the extended cure models provide more efficient and less biased estimations,  and higher efficiency and smaller bias are associated with higher sensitivity and specificity of the diagnostic procedure used. In this paper, we provide theoretical justifications of this positive association for some special cases. More specifically we shows that the maximum likelihood estimators (MLEs) of the parameters for an extended exponential cure model are asymptotically more efficient than the MLEs for the corresponding classical exponential cure model.

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