This paper considers the problem of transmitting data packets from sensors recording health information in a wireless body area network (WBAN). We model a resource-constrained paradigm in which measuring the channel interference incurs a non-trivial power cost. Each data packet has a deadline before the health information it contains is no longer relevant and the packet is dropped from the queue. In each time time slot the sensor must arbitrate whether to measure the channel interference and incur the associated cost, or rely on a previous measurement that may be inaccurate. Once the interference estimate is determined, the sensor may attempt to transmit a health packet to the central controller. The transmission power is chosen to minimize the costs associated with the power consumption, the cost of packet delays in the backlog buffer, and the cost of information loss from dropping packets. We formulate the dual channel-measurement/transmission-power control problem, and prove a performance bound on the overall expected cost incurred from using aging channel measurements.