An Extended Semi-Parametric Accelerated Failure Time Cure Model for Partial Cure Information Known

Cure model is a useful model for analyzing failure time data when there is evidence of long-term survivors. In traditional cure models, it is assumed that the cured or uncured status in the censored set cannot be distinguished. However, in many occasions, data of some diagnostic procedures, with some sensitivity and specificity, may have provided partial information about the cured or uncured status in the censored set. Failure to use such data would be wasteful and result in efficiency loss. Wu et al. in 2014 proposed an extended cure model. It incorporates such additional diagnostic information into traditional Proportional Hazards (PH) cure model analysis. In this work, we extended a semi-parametric Accelerated-Failure-Time (AFT) cure model to incorporate the additional diagnostic information because AFT model may be more appropriate than PH models in some applications and it provides intuitive and easy-to-understand interpretation through postulating direct relationship between failure-times and covariates. Through simulations, we showed that the proposed extended semi-parametric AFT cure model provided more efficient and less biased estimations than traditional semi-parametric AFT cure model; higher efficiency and smaller bias were associated with higher sensitivity and specificity of the diagnostic procedures. The proposed method was illustrated using a clinical data example.