Considerable evidence suggests that inflammation may play a role in the neurodegenerative process of Alzheimer's disease (AD), and the use of non-steroidal anti-inflammatory drugs may be associated with reduced occurrence of AD. ADAPT is a randomized trial that will test the ability of the non-steroidal anti-inflammatory medications naproxen and celecoxib to delay or prevent the onset of AD and age-related cognitive decline. This long-term trial will run for 5 to 7 years.