The non-equilibrium fluctuation dissipation theorem is applied to predict how critically ill patients respond to treatment, based upon data currently collected by standard hospital monitoring devices. This framework is demonstrated on a common procedure in critical care: the spontaneous breathing trial. It is shown that the responses of groups of similar patients to the spontaneous breathing trial can be predicted by the non-equilibrium fluctuation dissipation approach. This mathematical framework, when fully formed and applied to other clinical interventions, may serve as part of the basis for personalized critical care.