The paper introduces several model structures for data-driven characterization of drug-to-effect curves for patients experiencing pain. The purpose is to link opioid input to the pain level effect in the body. Fractional order impedance models are proposed and evaluated to characterize comprehensive dynamics. Data used for identification is recorded in patients following surgery and experiencing postoperative pain. In this work, we use the prototype Anspec-PRO monitor based on skin impedance with persistent excitation and 2D or 3D output representation. Notwithstanding dynamic complexity, understanding feedback paths in physiological pain pathways is fundamental. This particular prototype allows real-time characterization of frequency-dependent impedance, enabling online identification. The mathematical assessment of experienced pain is an important step towards modeling surgical disturbance effects within the depth of anesthesia paradigm.