A closed loop method and apparatus for controlling the administration of an hypnotic drug to a patient. Electroencephalographic (EEG) signal data is obtained from the patient. At least one measure of the complexity of the EEG signal data is derived from the data. The complexity measure may comprise the entropy of the EEG signal data. The EEG signal data complexity measure is used as the feedback signal in a control loop for an anesthetic delivery unit to control hypnotic drug administration to the patient in a manner that provides the desired hypnotic level in the patient. An EEG signal complexity measure obtained from the cerebral activity of the patient can be advantageously used in conjunction with a measure of patient electromyographic (EMG) activity to improve the response time of hypnotic level determination and of the feedback control of drug administration. A pharmacological transfer function may be used, along with pharmacokinetic and pharmacodynamic models.