Speech recordings are being more frequently used to detect and monitor disease, leading to privacy concerns. Beyond cryptography, protection of speech can be addressed by approaches, such as perturbation, disentanglement, and re-synthesis, that eliminate sensitive information of the speaker, leaving the information necessary for medical analysis purposes. In order for such privacy protective approaches to be developed, clear and systematic specifications of assumptions concerning medical settings and the needs of medical professionals are necessary. In this paper, we propose a Scenario of Use Scheme that incorporates an Attacker Model, which characterizes the adversary against whom the speaker's privacy must be defended, and a Protector Model, which specifies the defense. We discuss the connection of the scheme with previous work on speech privacy. Finally, we present a concrete example of a specified Scenario of Use and a set of experiments about protecting speaker data against gender inference attacks while maintaining utility for Parkinson's detection.