Cancer screening programs have been implemented in many different countries for many years to collect information of the fatal diseases, to provide early diagnosis, to support medical research, and to help governments making policies. However, few of those programs have utilized latest data science technologies, therefore not be able to generate the maximum benefits from those programs. To overcome this problem and improve the quality of cancer screening programs, this paper firstly (i) reviews the typical architecture and IT technologies used in current screening programs and recognizes their limitations; then (ii) introduces recent developments in data science that could be implemented in screening programs; finally (iii) proposes the structure of General Medical Screening Framework (GMSF), which could be developed to host future cancer screening programs that will advance data coverage, data accuracy, data usage and lower in the costs. The structure of GMSF and its key elements are described in this paper and some practical approaches to build GMSF are discussed. This work might initialize a series or research to bring the latest IT technologies, particularly data science technologies, into cancer screening programs, and significantly increase the efficiency and reduce the cost of future cancer screening programs.