In cancer research, genomic studies have been extensively conducted, searching for markers associated with prognosis. Because of the "large d, small n" characteristic, results generated from the analysis of a single dataset can be unsatisfactory. Integrative analysis simultaneously analyzes multiple datasets and can be more effective than the analysis of single datasets and classic meta-analysis. In many existing integrative analyses, the homogeneity model has been assumed, which postulates that different datasets share the same set of markers. In practice, datasets may have been generated in studies that differ in patient selection criteria, profiling techniques, and many other aspects. Such differences may make the homogeneity model too restricted. Here we explore the heterogeneity model, which assumes that different datasets may have different sets of markers. With multiple cancer prognosis datasets, we adopt the AFT (accelerated failure time) models to describe survival. A weighted least squares approach is adopted for estimation. For marker selection, penalization-based methods are examined. These methods have intuitive formulations and can be computed using effective group coordinate descent algorithms. Analysis of three lung cancer prognosis datasets with gene expression measurements demonstrates the merit of heterogeneity model and proposed methods.