Most existing optimization objectives considered in non-orthogonal multiple access (NOMA) power allocation schemes are non-delay-sensitive metrics. In order to apply NOMA to various Internet of Things scenarios, the delay must be considered. The effective capacity of users, which characterizes the capacity under specific expiration probabilities, can potentially be a performance metric of statistical delay quality of service (QoS). In this paper, we propose two novel dynamic power allocation schemes with statistical delay QoS guarantee in the uplink NOMA system with paired users. One of the schemes maximizes the sum effective capacity (SEC) of the strong and weak users, which is a non-convex nonlinear optimization problem and is solved by Lagrangian dual decomposition and successive convex approximation (SCA). The other one maximizes the effective energy efficiency (EEE) of uplink NOMA, which is a fractional optimization problem and is solved by integrating the Dinkelbach method, SCA, and Lagrangian dual decomposition. Numerical results show that the SEC and EEE can be significantly improved by the proposed schemes, compared to the existing NOMA and orthogonal multiple access power allocation schemes.