The relative biological effectiveness (RBE) is a central quantity in particle radiobiology and depends on many physical and biological factors. The local effect model (LEM) allows one to predict the RBE for radiobiologic experiments and particle therapy. In this work the sensitivity of the RBE on its determining factors is elucidated based on monitoring the RBE dependence on the input parameters of the LEM. The relevance and meaning of all parameters are discussed within the formalism of the LEM. While most of the parameters are fixed by experimental constraints, one parameter, the threshold dose Dt, may remain free and is then regarded as a fit parameter to the high LET dose response curve. The influence of each parameter on the RBE is understood in terms of theoretic considerations. The sensitivity analysis has been systematically carried out for fictitious in vitro cell lines or tissues with α/β = 2 Gy and 10 Gy, either irradiated under track segment conditions with a monoenergetic beam or within a spread out Bragg peak. For both irradiation conditions, a change of each of the parameters typically causes an approximately equal or smaller relative change of the predicted RBE values. These results may be used for the assessment of treatment plans and for general uncertainty estimations of the RBE.