As the high throughput technologies rapidly develop, multiple types of genomic data become available within and across different studies. It has become a challenging task in modern statistical research to use all types of genomic data to infer some disease-prone genetic information. In this paper, we propose an integrative analysis of multiple types of genomic data from different investigation centers for different sets of samples, clinical covariates and survival data under a framework of an accelerated failure time with frailty (AFTF) model. The proposed integrative approach aims to find relevant features and make inference for patients' survival time. A weighted least square function plus a sparse group LASSO penalty is developed as the objective function to estimate and select the relevant features simultaneously. Extensive simulation studies are conducted to assess the performance of the proposed method with two types of genomic data, DNA methylation data and copy number variation data, on 600 genes and three clinical covariates. The proposed method is applied to the analysis of the Cancer Genome Atlas (TCGA) data on Glioblastoma (GBM), a lethal brain cancer.
