Exenatide Weekly Injections as an Adjunctive Treatment in Patients With Schizophrenia

The specific aims include: Primary aim: 1\. Examine the efficacy of exenatide weekly injection in improving negative symptoms as measured by the Scale for the Assessment of Negative Symptoms (SANS) total score. Secondary aims: 1\. Examine the efficacy of exenatide in improving cognition as measured by the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) Consensus Cognitive Battery (MCCB) composite score. Tertiary/Exploratory aims: 1. Examine exenatide's effect on schizophrenia symptoms as measured by the Positive and Negative Syndrome Scale (PANSS) total score. 2. Examine the efficacy of exenatide in improving social function as measured by the Instrumental Activities of Daily Living Scale (IADL) and the Heinrich Carpenter Quality of Life Scale (QLS). 3. Examine exenatide's effect on neuro-protection as measured by the change in hippocampal volume. 4. Examine exenatide's effects on inflammatory markers including serum levels of high sensitivity C-reactive Protein (CRP), Interleukin 6 (IL-6), and tumor necrosis factor (TNF-α). 5. Examine the potential moderator role of baseline serum levels of C-reactive Protein (CRP), Interleukin 6 (IL-6), tumor necrosis factor (TNF-α), and baseline hippocampal volume for exenatide's effects on negative and cognitive symptoms. 6. Examine the potential mediator role of changes from baseline in serum levels of C-reactive Protein (CRP), Interleukin 6 (IL-6), tumor necrosis factor (TNF-α), and hippocampal volume for exenatide's effects on negative and cognitive symptoms. 7. Examine the efficacy of exenatide in reducing body weight and improving glucose metabolism as measured by fasting plasma glucose and HbA1c. 8. Examine the safety and tolerability of exenatide as measured by changes in the side effects questionnaire (SEQ, SEQabbrev), EKG and vital signs