In high-throughput cancer genomic studies, markers identified from the analysis of single datasets may have unsatisfactory properties because of low sample sizes. Integrative analysis pools and analyzes raw data from multiple studies, and can effectively increase sample size and lead to improved marker identification results. In this study, we consider the integrative analysis of multiple high-throughput cancer prognosis studies. In the existing integrative analysis studies, the interplay among genes, which can be described using the network structure, has not been effectively accounted for. In network analysis, tightly-connected nodes (genes) are more likely to have related biological functions and similar regression coefficients. The goal of this study is to develop an analysis approach that can incorporate the gene network structure in integrative analysis. To this end, we adopt AFT (accelerated failure time) models to describe survival. A weighted least squares approach, which has low computational cost, is adopted for estimation. For marker selection, we propose a new penalization approach. The proposed penalty is composed of two parts. The first part is a group MCP penalty, and conducts gene selection. The second part is a Laplacian penalty, and smoothes the differences of coefficients for tightly-connected genes. A group coordinate descent approach is developed to compute the proposed estimate. Simulation study shows satisfactory performance of the proposed approach when there exist moderate to strong correlations among genes. We analyze three lung cancer prognosis datasets, and demonstrate that incorporating the network structure can lead to the identification of important genes and improved prediction performance.