Safety and Tolerability of Trametinib in Combination With Docetaxel in Japanese Subjects With Non-small Cell Lung Cancer

Inclusion Criteria Subjects eligible for enrolment in the study must meet all of the following criteria: * Provided signed written informed consent. * 20 years old or older (at the time consent is obtained). * Histologically or cytologically confirmed NSCLC. * Diagnosed of Stage IV, or postoperative recurrence. * Tumor progression after receiving one prior platinum-based chemotherapy. Targeted therapies (gefitinib, crizotinib, etc) with no significant hematological toxicities will not be counted. * Performance status score of ≤1 according to the Eastern Cooperative Oncology Group (ECOG) scale. * Able to swallow and retain orally administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels. * All prior treatment-related toxicities must be CTCAE v4.0 \<=Grade 1 (except alopecia) at the time of enrollment. * Women of childbearing potential must have a negative serum pregnancy test within 7 days of the first dose of study treatment and agree to use effective contraception throughout the treatment period, and for 4 months after the last dose of study treatment. * Men must agree to use effective contraception throughout the treatment period of docetaxel. * Adequate organ baseline function defined as Hematology: absolute neutrophil count\>=1.5 x 10\^9/Liter (L), hemoglobine\>=9 gramms/decilitre, platelet\>==100 x 10\^9/L, Prothrombine time/international normalized ratio and activated partial thromboplastine time\<=1.5 x upper limit of normal (ULN) Hepatic: albumin\>=2.5 grams/decilitre, total bilirubine \<=ULN, aspartate aminotransferase and alanine aminotransferase \<=1.5 x ULN if alkaline phosphatase is \>=ULN or \<=2.5 ULN if alkaline phosphatase is \<ULN. Renal: creatinine\<=1.5 x ULN or calculated creatinine clearance \>=50 millilter (mL)/minute. Cardiac:left ventricular ejector factor\>=lower limit of normal by echocardiogram. * Negative for Hepatitis B surface (HBs) antigen, Hepatitis virus B core (HBc) antibody, HBs antibody and Hepatitis C Virus (HCV) antibody. If HBs antigen is negative and both or either of HBc and HBs antibody is positive, Hepatitis B Virus (HBV) DNA should be measured. Exclusion Criteria * Anti-cancer therapy (including chemotherapy, radiation therapy, immunotherapy, biologic therapy, hormonal therapy, major surgery, tumor embolization or investigational therapy) within the last three weeks, with the following exceptions: six weeks for prior nitrosourea or mitomycin C and two weeks for anti-cancer therapy given continuously or on a weekly basis with limited potential for delayed toxicity. * Previously treated with docetaxel * Previously treated with MEK inhibitor * Current use of a prohibited medication * Suspected of or currently have clinically significant infectious disease. * Hypersensitivity to polysorbate 80. * Hypersensitivity to filgrastim or growth factor * History or current evidence/risk of retinal vein occlusion (RVO) or central serous retinopathy (CSR): History of RVO or CSR, or predisposing factors to RVO or CSR (e.g., uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes) Visible retinal pathology as assessed by ophthalmologic exam that is considered a risk factor for RVO or CSR such as: Evidence of new optic disc cupping, Evidence of new visual field defects on automated perimetry, Intraocular pressure \>21 millimeter of mercury (mmHg) as measured by tonography. * Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression. Subjects who require treatment for these conditions should be excluded. * History of another malignancy. Exception: Subjects who have been disease-free for 5 years, or subjects with a history of completely resected non-melanoma skin cancer or in situ carcinoma are eligible. * Any serious and/or unstable pre-existing medical (aside from malignancy exception above), psychiatric disorder, or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures. * History of interstitial lung disease or pneumonitis * Evidence of severe or uncontrolled systemic diseases (e.g., unstable or uncompensated respiratory, hepatic, renal, metabolic, or cardiac disease). * History or evidence of cardiovascular risk including any of the following: LVEF\<LLN A QT interval corrected for heart rate using the Bazett's formula \>=480 millisecond. History or evidence of current clinically significant uncontrolled arrhythmias. Exception: Subjects with controlled atrial fibrillation for \>30 days prior to study treatment are eligible. Currently treated subject should be excluded. History of acute coronary syndromes (including myocardial infarction and angina), coronary angioplasty, or stenting within 6 months prior to randomization. Subjects currently treated with anticoagulant. History or evidence of current \>= Class II congestive heart failure as defined by New York Heart Association. Treatment refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mmHg which cannot be controlled by anti-hypertensive therapy. Subjects with intra-cardiac defibrillators or permanent pacemakers. Known cardiac metastases. * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to dimethyl sulfoxide (DMSO). * Lactating female * Known Human Immunodeficiency Virus (HIV) infection