We consider a mixture cure rate model with a cure fraction to account for the proportion of subjects that are medically cured. When the risk factors are grouped, we are interested in identifying the groups and individual risk factors that are important to the survival probability or the cure rate. For the non-cured proportion, we adopt a class of semiparametric transformation models, and for the cured proportion, we utilize a logistic model. We propose an expectation-maximization (EM) algorithm based bi-level variable selection method to select and estimate the important groups and individual risk factors within a group simultaneously. Simulation studies are conducted to examine the finite sample properties of the proposed methods, and real data examples are used for illustration.