Hamiltonian Monte Carlo is a powerful tool for constructing a Markov chain that is invariant to a given target probability distribution. Hamiltonian dynamics are used to drive the movement of the chain. However, differentiability limits its applicability to continuous probability spaces only. In this work we exploit a modification of the standard procedure, known as Discontinuous Hamiltonian Monte Carlo, to compare two different scores used in rhinology to assess the stage of illness in patients with severe chronic rhinosinusitis in a follow-up study.