Facial phenotyping for medical prediagnosis has recently been successfully exploited as a novel way for the preclinical assessment of a range of rare genetic diseases, where facial biometrics is revealed to have rich links to underlying genetic or medical causes. In this paper, we aim to extend this facial prediagnosis technology for a more general disease, Parkinson's Diseases (PD), and proposed an Artificial-Intelligence-of-Things (AIoT) edge-oriented privacy-preserving facial prediagnosis framework to analyze the treatment of Deep Brain Stimulation (DBS) on PD patients. In the proposed framework, a novel edge-based privacy-preserving framework is proposed to implement private deep facial diagnosis as a service over an AIoT-oriented information theoretically secure multi-party communication scheme, while data privacy has been a primary concern toward a wider exploitation of Electronic Health and Medical Records (EHR/EMR) over cloud-based medical services. In our experiments with a collected facial dataset from PD patients, for the first time, we proved that facial patterns could be used to evaluate the facial difference of PD patients undergoing DBS treatment. We further implemented a privacy-preserving information theoretical secure deep facial prediagnosis framework that can achieve the same accuracy as the non-encrypted one, showing the potential of our facial prediagnosis as a trustworthy edge service for grading the severity of PD in patients.