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We introduce a new framework for fairness study of Power-Domain Non-Orthogonal Multiple Access (PD-NOMA) with fairness factor definitions to analyse pair and system behaviour. Aiming at both pair-wise and system-level fairness as key performance goals, first, we present a power allocation scheme to maximize sum bit rate within each pair. We demonstrate analytically that it is possible to enhance both users' bit rates in the pair over their Orthogonal Multiple Access (OMA) equivalent rates without impacting fairness. Additionally, at system level, we complement our work proposing two prioritization algorithms to enhance fairness through the NOMA paring process. Simulations show that the schemes are effective to maximize the system fairness when it is measured with, either the users' or the pairs' bit rates.