AZD8186 and Paclitaxel in Advanced Gastric Cancer

Inclusion Criteria: 1. Have the willingness to sign a written informed consent document prior to any study specific procedures 2. Age ≥ 19 years of male and female 3. At each phase of the trial, subjects who meet the following requirements in the appropriate phase will be enrolled. A. Phase 1b: Subjects with a histologically confirmed metastatic solid tumor that have progressed after treatment with approved therapies or for which there is no standard effective therapy available. B. Phase 2b: Subjects with histologically confirmed locally advanced or metastatic gastric cancer that have progressed after treatment with first-line fluoropyrimidine-based chemotherapy, with PTEN loss by immunohistochemistry (IHC), PTEN gene abnormality (PTEN gene deletion or loss of function mutation) or Phosphatidylinositol-4,5-Bisphosphate 3-Kinase Catalytic Subunit Beta(PIK3CB) gene abnormality (amplification or gain of function mutation) identified by next generation sequencing (NGS). If the subject received adjuvant chemotherapy after curative gastric resection and lymph node dissection, adjuvant chemotherapy is considered to be the first-line palliative chemotherapy if the disease recurred during adjuvant chemotherapy or within 6 months after the completion of adjuvant chemotherapy. 4. Patients must have measurable disease based on RECIST 1.1 (Phase 2 part only). Measurable disease will not be required for enrollment in the phase1b part. Patients with evaluable lesion only (without measurable lesion) can be enrolled in the phase 1b part. 5. Eastern Cooperative Oncology Group(ECOG) performance status 0-1 6. Patients must have adequate organ and marrow function as defined below: A. Absolute neutrophil count (ANC) ≥ 1.5 x 109/L, B. Hemoglobin ≥ 9.0 g/dL, C. Platelet ≥ 100 x 109/L, D. Aspartate transaminase(AST) and/or alanine transaminase(ALT) ≤ 3 × upper limit of normal (ULN) \[Regardless of the presence of liver metastases, only subjects who have AST/ALT ≤ 3 × ULN can be enrolled in phase 1b part; In phase 2 part, subjects with AST and/or ALT ≤ 5 X ULN can be enrolled if they have liver metastases\] E. Total bilirubin: ≤ 1 × ULN; Subjects with a bile duct obstruction will be eligible if they meet the criteria after appropriate bile drainage; Patients with Gilbert syndrome should also be registered after confirming that the total bilirubin level is within the normal range through a follow-up screening test F. Serum creatinine clearance \>50 milliliter/min 7. Adequate cardiac function with corrected QT interval(QTc) \< 470 msec 8. Patients must be able to swallow and retain oral medications 9. Serum β-human chorionic gonadotropin (HCG) test negative within 14 days before the first administration (women of childbearing potential only). 10. Requirements for contraception must be followed. Exclusion Criteria: 1. Active central nervous system (CNS) lesions (ie, those with radiologically unstable or symptomatic brain lesions). For those who receive radiation or surgical treatment, the subject can be enrolled if the subject is maintained without evidence of CNS disease progression for more than 4 weeks. However, patients with a leptomeningeal metastases are excluded. 2. Treatment with any of the following: * Nitrosourea or mitomycin C within 6 weeks of the first dose of study treatment * Any cytotoxic chemotherapy from a previous treatment regimen within 14 days. If the subject received an investigational drug from another clinical trial, the subject can be enrolled after 2 weeks of last administration and more than 5 x half-life of the investigational drug. If monoclonal antibody therapy was given, the subject can be enrolled after four weeks after the last dose. * Strong or moderate inducers or inhibitors of CYP3A4 within 2 weeks before the first dose of study treatment * Radiotherapy with a wide field of radiation within 4 weeks or radiotherapy with a limited field of radiation for palliation within 2 weeks of the first dose of study treatment. * Any previous exposure to a Phosphatidylinositol 3-kinase (PI3K) inhibitor (including selective or pan PI3K inhibitors), Akt, mammilian target of rapamycin (mTOR) inhibitors. 3. History of allogeneic bone marrow transplantation or organ transplantation 4. History of another primary cancer (excluding gastric cancer): Exceptions are: * Adequately treated non-melanoma skin cancer (basal cell or squamous cell carcinoma), curatively treated in situ cancer of the cervix, completely resected thyroid cancer without distant metastasis in which all treatment has been completed (Appropriate wound healing is required prior to clinical trial enrollment) * Other curatively treated solid tumors except for gastric cancer with no evidence of disease recurrence at least 36 months before participating in this trial 5. Clinically significant cardiovascular disease including but not limited to: * Acute coronary syndrome within the 6 months prior to the initiation of study drug (including myocardial infarction or unstable angina, Coronary Artery Bypass Graft surgery, percutaneous coronary intervention and stenting) * Current heart failure or past history of heart failure * Current or past history of clinically significant cardiac arrhythmia (eg, complete left bundle branch block, third degree heart block) * Any risk factors that prolong QTc or increase the probability of arrhythmia, including medication (eg: heart failure, hypokalemia, congenital long QT syndrome, history of Torsades de Pointes) 6. Persistent uncontrolled hypertension as defined by: systolic \>180 mmHg or diastolic \>100 mmHg despite medical treatment 7. Seropositivity of HIV, or known active hepatitis B and/or active hepatitis C infection. Hepatitis B carriers may be enrolled if prophylactic use of an antiviral agent with minimal interaction with CYP3A4 is administered to inhibit hepatitis B virus (HBV) activation (eg. Entecavir, adefovir) 8. Impairment of gastrointestinal function or gastrointestinal disorders (eg. untreated ulcerative disorders; uncontrolled nausea, vomiting, or diarrhea; absorption disorder syndrome; small bowel resection; ileostomy). Patients with ileostomy will not allowed to be enrolled, but patients with colostomy can be enrolled to this study. 9. As judged by the Investigator, all other symptoms and associated disease for which the investigator determined that participation in this study is contraindicated (e.g. Infection/inflammation; severe liver dysfunction; bilateral diffuse interstitial lung disease; uncontrolled renal disease; unstable heart and lung disease; hemorrhagic disease; intestinal obstruction; unable to swallow oral pills; social and psychological problems, etc) 10. Pregnant or lactating women. 11. Medical, psychiatric, cognitive, or other conditions that may interfere with the ability of the subject to understand the study information, provide the informed consent, follow the protocol process, or complete the clinical trial 12. Hypersensitivity to paclitaxel