Extension of a Cox proportional hazards cure model when cure information is partially known

When there is evidence of long-term survivors, cure models are often used to model the survival curve. A cure model is a mixture model consisting of a cured fraction and an uncured fraction. Traditional cure models assume that the cured or uncured status in the censored set cannot be distinguished. But in many practices, some diagnostic procedures may provide partial information about the cured or uncured status relative to certain sensitivity and specificity. The traditional cure model does not take advantage of this additional information. Motivated by a clinical study on bone injury in pediatric patients, we propose a novel extension of a traditional Cox proportional hazards (PH) cure model that incorporates the additional information about the cured status. This extension can be applied when the latency part of the cure model is modeled by the Cox PH model. Extensive simulations demonstrated that the proposed extension provides more efficient and less biased estimations, and the higher efficiency and smaller bias is associated with higher sensitivity and specificity of diagnostic procedures. When the proposed extended Cox PH cure model was applied to the motivating example, there was a substantial improvement in the estimation.