Variable selection in a flexible parametric mixture cure model with interval‐censored data

In standard survival analysis, it is generally assumed that every individual will experience someday the event of interest. However, this is not always the case, as some individuals may not be susceptible to this event. Also, in medical studies, it is frequent that patients come to scheduled interviews and that the time to the event is only known to occur between two visits. That is, the data are interval‐censored with a cure fraction. Variable selection in such a setting is of outstanding interest. Covariates impacting the survival are not necessarily the same as those impacting the probability to experience the event. The objective of this paper is to develop a parametric but flexible statistical model to analyze data that are interval‐censored and include a fraction of cured individuals when the number of potential covariates may be large. We use the parametric mixture cure model with an accelerated failure time regression model for the survival, along with the extended generalized gamma for the error term. To overcome the issue of non‐stable and non‐continuous variable selection procedures, we extend the adaptive LASSO to our model. By means of simulation studies, we show good performance of our method and discuss the behavior of estimates with varying cure and censoring proportion. Lastly, our proposed method is illustrated with a real dataset studying the time until conversion to mild cognitive impairment, a possible precursor of Alzheimer's disease. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.