When it comes to improving cancer therapies, one challenge is to identify key biological parameters that prevent immune escape and maintain an equilibrium state characterized by a stable subclinical tumor mass, controlled by the immune cells. Based on a space and size structured partial differential equation model, we developed numerical methods that allow us to predict the shape of the equilibrium at low cost, without running simulations of the initial-boundary value problem. In turn, the computation of the equilibrium state allowed us to apply global sensitivity analysis methods that assess which and how parameters influence the residual tumor mass. This analysis reveals that the elimination rate of tumor cells by immune cells far exceeds the influence of the other parameters on the equilibrium size of the tumor. Moreover, combining parameters that sustain and strengthen the antitumor immune response also proves more efficient at maintaining the tumor in a long-lasting equilibrium state. Applied to the biological parameters that define each type of cancer, such numerical investigations can provide hints for the design and optimization of cancer treatments.