Mixture Cure Semiparametric Accelerated Failure Time Models With Partly Interval‐Censored Data

In practical survival analysis, the situation of no event for a patient can arise even after a long period of waiting time, which means a portion of the population may never experience the event of interest. Under this circumstance, one remedy is to adopt a mixture cure Cox model to analyze the survival data. However, if there clearly exhibits an acceleration (or deceleration) factor among their survival times, then an accelerated failure time (AFT) model will be preferred, leading to a mixture cure AFT model. In this paper, we consider a penalized likelihood method to estimate the mixture cure semiparametric AFT models, where the unknown baseline hazard is approximated using Gaussian basis functions. We allow partly interval-censored survival data which can include event times and left-, right-, and interval-censoring times. The penalty function helps to achieve a smooth estimate of the baseline hazard function. We will also provide asymptotic properties to the estimates so that inferences can be made on regression parameters and hazard-related quantities. Simulation studies are conducted to evaluate the model performance, which includes a comparative study with an existing method from the smcure R package. The results show that our proposed penalized likelihood method has acceptable performance in general and produces less bias when faced with the identifiability issue compared to smcure. To illustrate the application of our method, a real case study involving melanoma recurrence is conducted and reported. Our model is implemented in our R package aftQnp which is available from https://github.com/Isabellee4555/aftQnP.