Rosiglitazone (RSG) has been tested and is approved as a treatment for type II diabetes mellitus, a disease that occurs when the body ineffectively uses glucose. RSG XR, the investigational drug, is an extended-release form of RSG. This study tests whether RSG XR safely provides benefit to people with mild to moderate Alzheimer's disease (AD). RSG XR is a new approach to AD therapy and this study tests whether one's genes alter the effectiveness of RSG XR. Glucose is used by cells to make energy that they need to live. Changes in the ability of cells to use of glucose can lead to diseases like diabetes. Glucose levels may be lower in the brains of AD patients, and their brain cells may also use glucose less well than in unaffected people. The proper function of brain cells may be critical to memory and thought. If brain cells use glucose poorly, this might impact AD. Drugs that help brain cells properly use glucose may help a person maintain normal memory and thinking. Data suggesting that RSG may help AD patients was first seen in a small study at the Univ. of Washington and then from a larger international GSK study. In the first study, those receiving RSG once daily for 6 months scored better on 3 tests of memory and thought than those who did not receive RSG. In the GSK study, those that benefited most from therapy with RSG XR had a specific genetic pattern. They lacked the gene that caused them to produce apolipoprotein E e4 (APOE e4). Subjects who have the APOE e4 gene may have two copies, one from each parent, or they may have only one APOE e4 gene meaning that they inherited either the APOE e2 or APOE e3 version of the gene from one parent. Subjects with one copy of the APOE e4 gene remained fairly stable while those with two copies of APOE e4 continued to worsen during the 6-month treatment. This study will directly test the effect of RSG XR on people who either have or lack the APOE e4 gene.