In profiling studies, the analysis of a single dataset often leads to unsatisfactory results because of the small sample size. Multi-dataset analysis utilizes information across multiple independent datasets and outperforms single-dataset analysis. Among the available multi-dataset analysis methods, integrative analysis methods aggregate and analyze raw data and outperform meta-analysis methods, which analyze multiple datasets separately and then pool summary statistics. In this study, we conduct integrative analysis and marker selection under the heterogeneity structure, which allows different datasets to have overlapping but not necessarily identical sets of markers. Under certain scenarios, it is reasonable to expect some similarity of identified marker sets -- or equivalently, similarity of model sparsity structures -- across multiple datasets. However, the existing methods do not have a mechanism to explicitly promote such similarity. To tackle this problem, we develop a sparse boosting method. This method uses a BIC/HDBIC criterion to select weak learners in boosting and encourage sparsity. A new penalty is introduced to promote the similarity of model sparsity structures across datasets. The proposed method has an intuitive formulation and is broadly applicable and computationally affordable. In numerical studies, we analyze right censored survival data under the AFT (accelerated failure time) model. Simulation shows that the proposed method outperforms alternative boosting and penalization methods with more accurate marker identification. The analysis of three breast cancer prognosis datasets shows that the proposed method can identify marker sets with increased similarity across datasets and improved prediction performance.