Ionizing radiation induces DNA damage to cycling cells which, if left unrepaired or misrepaired, can cause cell inactivation or heritable, viable mutations. The latter can lead to cell transformation, which is thought to be an initial step of cancer formation. Consequently, the study of radiation-induced cell transformation promises to offer insights into the general properties of radiation carcinogenesis. As for other end points, the effectiveness in inducing cell transformation is elevated for radiation qualities with high linear energy transfer (LET), and the same is true for cancer induction. In considering DNA damage as a common cause of both cell death and transformations, a worthwhile approach is to apply mathematical models for the relative biological effectiveness (RBE) of cell killing to also assess the carcinogenic potential of high-LET radiation. In this work we used an established RBE model for cell survival and clinical end points, the local effect model (LEM), to estimate the transformation probability and the carcinogenic potential of ion radiation. The provided method consists of accounting for the competing processes of cell inactivation and induction of transformations or carcinogenic events after radiation exposure by a dual use of the LEM. Correlations between both processes inferred by the number of particle impacts to individual cells were considered by summing over the distribution of hits that individual cells receive. RBE values for cell transformation in vitro were simulated for three independent data sets, which were also used to gauge the approach. The simulations reflect the general RBE systematics both in magnitude and in energy and LET dependence. To challenge the developed method, in vivo carcinogenesis was investigated using the same concepts, where the probability for cancer induction within an irradiated organ was derived from the probability of finding carcinogenic events in individual cells. The predictions were compared with experimental data of carcinogenesis in Harderian glands of mice. Again, the developed method shows the same characteristics as the experimental data. We conclude that the presented method is helpful to predictively assess RBE for both neoplastic cell transformation and tumor induction after ion exposure within a wide range of LET values. The theoretical concept requires a non-linear component in the photon dose response for carcinogenic end points as a precondition for the observed enhanced effects after ion exposure, thus contributing to a long debate in epidemiology. Future work will use the method for assessing cancer induction in radiation therapy and exposure scenarios frequently discussed in radiation protection.