Study of Vorinostat and Gefitinib in Relapsed/ or Refractory Patients With Advanced Non-small Cell Carcinoma (NSCLC)

Inclusion Criteria: * Histologic or cytologic diagnosis of NSCLC, Stage IV or selected stage IIIB (with positive pleural effusion or multiple ipsilateral lung nodules) according to the American Joint Committee on Cancer (AJCC). * Previously treated with at least one platinum-based chemotherapy. * Before study entry, a minimum of 28 days must have elapsed since any prior chemotherapy. * Prior radiation therapy is allowed as long as the irradiated area is not the only source of measurable disease. * No other forms of cancer therapy, such as radiation, immunotherapy for at least 2 weeks before the enrollment in study. * Performance status of 0-2 on the ECOG criteria. * At least one unidimensionally measurable lesion meeting Response Evaluation Criteria in Solid Tumors (Revised RECIST guideline version 1.1) * Estimated life expectancy of at least 8 weeks. * Patient compliance that allow adequate follow-up. * Adequate hematologic (WBC count 4,000/mm3, platelet count 150,000/mm3), hepatic (bilirubin level 1.5 mg/dL, AST/ALT 80 IU/L), and renal (creatinine concentration 1.5 mg/dL) function. * Informed consent from patient or patient's relative. * Males or females at least 18 years of age. * If female: childbearing potential either terminated by surgery, radiation, or menopause, or attenuated by use of an approved contraceptive method (intrauterine device \[IUD\], birth control pills, or barrier device) during and for 3 months after trial. If male, use of an approved contraceptive method during the study and 3 months afterwards. Females with childbearing potential must have a urine negative hCG test within 7 days prior to the study enrollment. * Patients with brain metastasis are allowed unless there were clinically significant neurological symptoms or signs Exclusion Criteria: * Presence of small-cell lung cancer alone or with NSCLC * Unresolved chronic toxic effects from previous anticancer therapy: but patient could be enrolled, if they have recovered from any treatment-related toxicities NCI CTCAE grade ≤2 * Inability to swallow tablets * Second primary malignancy (except in situ carcinoma of the cervix or adequately treated basal cell carcinoma of the skin or prior malignancy treated more than 5 years ago without recurrence). * More than three previous chemotherapy regimens for NSCLC * Previous treatment with any EGFR-TKI * Patients who have been exposed to any prior HDAC inhibitor, with the exception of exception of valpronic acid used for treating seizures, provided there is a 30-day washout period * Patients with active HIV or hepatitis B or C infection * Concomitant use of phenytoin, carbamazepine, rifampicin, barbiturates, cyclosporine A, valpronic acid, Phenobarbital, ketoconazole, coumarin-derivative anticoagulants or St John's wort; severe or uncontrolled systemic disease; clinically active interstitial lung disease (except uncomplicated lymphangitic carcinomatosis) pregnancy; and breastfeeding. * MI within preceding 6 months or symptomatic heart disease, including unstable angina, congestive heart failure or uncontrolled arrhythmia * Serious concomitant infection including postobstructive pneumonia * Major surgery other than biopsy within the past two weeks.