This study focuses on patients with severe traumatic brain injury (TBI). The purpose of the study is to compare two ways of treating patients with brain injury. Participants will be randomly assigned to one of two groups. One group will receive medical care based on monitoring of pressure in the brain (intracranial pressure or ICP) alone. The other group will receive medical care based on ICP and the amount of oxygen in the brain. In both strategies, doctors will monitor and modify the medical care provided in order to try to improve some measure of the brain's health. It is not yet known which measure of the brain's health, intracranial pressure or oxygen level, is more important. The study results will help determine whether using both methods is better than using one method alone for the treatment of TBI. Both methods are used in standard care, and monitoring devices are approved by the U.S. Food and Drug Administration (FDA).