Privacy protection in electronic healthcare applications is an important consideration due to the sensitive nature of personal health data. Internet of Health Things (IoHT) networks have privacy requirements within a healthcare setting. However, these networks have unique challenges and security requirements (integrity, authentication, privacy and availability) must also be balanced with the need to maintain efficiency in order to conserve battery power, which can be a significant limitation in IoHT devices and networks. Data are usually transferred without undergoing filtering or optimization, and this traffic can overload sensors and cause rapid battery consumption when interacting with IoHT networks. This consequently poses restrictions on the practical implementation of these devices. As a solution to address the issues, this paper proposes a privacy-preserving two-tier data inference framework - this can conserve battery consumption by reducing the data size required to transmit through inferring the sensed data and can also protect the sensitive data from leakage to adversaries. Results from experimental evaluations on privacy show the validity of the proposed scheme as well as significant data savings without compromising the accuracy of the data transmission, which contributes to energy efficiency of IoHT sensor devices.