The radiation space environment includes particles such as protons and multiple species of heavy ions, with much of the exposure to these radiations occurring at extremely low average dose-rates. Limitations in databases needed to predict cancer hazards in human beings from such radiations are significant and currently do not provide confidence that such predictions are acceptably precise or accurate. In this article, we outline the need for animal carcinogenesis data based on a more sophisticated understanding of the dose-response relationship for induction of cancer and correlative cellular endpoints by representative space radiations. We stress the need for a model that can interrelate human and animal carcinogenesis data with cellular mechanisms. Using a broad model for dose-response patterns which we term the "subalpha-alpha-omega (SAO) model", we explore examples in the literature for radiation-induced cancer and for radiation-induced cellular events to illustrate the need for data that define the dose-response patterns more precisely over specific dose ranges, with special attention to low dose, low dose-rate exposure. We present data for multiple endpoints in cells, which vary in their radiosensitivity, that also support the proposed model. We have measured induction of complex chromosome aberrations in multiple cell types by two space radiations, Fe-ions and protons, and compared these to photons delivered at high dose-rate or low dose-rate. Our data demonstrate that at least three factors modulate the relative efficacy of Fe-ions compared to photons: (i) intrinsic radiosensitivity of irradiated cells; (ii) dose-rate; and (iii) another unspecified effect perhaps related to reparability of DNA lesions. These factors can produce respectively up to at least 7-, 6- and 3-fold variability. These data demonstrate the need to understand better the role of intrinsic radiosensitivity and dose-rate effects in mammalian cell response to ionizing radiation. Such understanding is critical in extrapolating databases between cellular response, animal carcinogenesis and human carcinogenesis, and we suggest that the SAO model is a useful tool for such extrapolation.