Many drugs are used during the provision of intensive care for the preterm newborn infant. Recommendations for drug dosing in newborns depend upon data from population based pharmacokinetic research. There is a need to be able to modify drug dosing in response to the preterm infant's response to the standard dosing recommendations. The real-time integration of physiological data with drug dosing data would facilitate individualised drug dosing for these immature infants. This paper proposes the use of a novel computational framework that employs real-time, temporal data analysis for this task. Deployment of the framework within the cloud computing paradigm will enable widespread distribution of individualized drug dosing for newborn infants.