A Study of Ramucirumab and Docetaxel in Participants With Solid Tumors

Inclusion Criteria: * Participant has histologic or cytologic documentation of a malignant solid tumor * Participant has an advanced solid tumor that is resistant to standard therapy or for which no standard therapy is available * Participant has had 0-1 prior taxane-containing treatment regimens (including taxane monotherapy), which must have been completed at least 6 months before the first dose of study medication. Prior bevacizumab is allowed. * Participant has resolution to Grade ≤ 1 (except where otherwise stated in this eligibility criteria) by the National Cancer Institute Common Terminology Criteria for Adverse Events, Version 4.0 (NCI-CTCAE v 4.0) of all clinically significant toxic effects of prior chemotherapy, surgery, radiotherapy, or hormonal therapy * Participant has an Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0-2 * Participant has adequate hematologic function (absolute neutrophil count \[ANC\] ≥ 1500 cells/liter (cells/L), hemoglobin ≥ 10 grams/deciliter (g/dL), and platelet count ≥ 100,000 cells/microliter (cells/mcL)\]. Blood transfusion is allowed but must be completed 48 hours before study drug administration. * Participant has adequate hepatic function (bilirubin ≤ 1.5 times the upper limit of normal \[x ULN\], aspartate transaminase \[AST\] and alanine transaminase \[ALT\] ≤ 1.5 x ULN) * Participant has serum creatinine ≤ 1.5 x ULN. If serum creatinine \> 1.5 x ULN, the calculated creatinine clearance \[CrCl\] should be ≥ 40 milliliters/minute (mL/min) * Participant's urinary protein is \<2+ on dipstick or routine urinalysis (UA) at study entry * Participant must have adequate coagulation function as defined by an international normalized ratio (INR) of ≤ 1.5 and a partial thromboplastin time (PTT) or an activated PTT (aPTT) ≤ 1.5 x ULN * Women with childbearing potential must have a negative serum or urine pregnancy test. Eligible participants of reproductive potential (both sexes) agree to use adequate method of contraception during the study period and for 12 weeks after the last dose of study medication. Exclusion Criteria: * Has a known allergy or hypersensitivity to any of the treatment components * Are currently enrolled in, or discontinued within the last 14 days from, a clinical trial involving an investigational product or non-approved use of a drug or device, or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Has received a therapeutic monoclonal antibody within 42 days prior to first dose of study medication * Has received radiotherapy within 14 days prior to first dose of study medication * Has received cytotoxic chemotherapy within 21 days prior to first dose of study medication * Is receiving concurrent treatment with another anticancer therapy, including chemotherapy, immunotherapy, hormonal therapy (except for androgen deprivation therapy for prostate cancer), radiation therapy, chemoembolization, targeted or other investigational anticancer therapy * Is receiving chronic therapy with nonsteroidal anti-inflammatory agents or other antiplatelet agents. (Aspirin use at doses up to 325 milligrams/day (mg/day) and analgesic agents with no or low bleeding risk are permitted.) * Has a history of uncontrolled hereditary or acquired bleeding or thromboembolic disorders * Has experienced any arterial thromboembolic event, including myocardial infarction (MI), unstable angina, stroke or transient ischemic attack (TIA), within 6 months prior to first dose of study medication * Has a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism during the 3 months prior to first dose of study medication * Has experienced a Grade 3 or 4 hemorrhagic event within 3 months prior to first dose of study medication * Has experienced peripheral neuropathy ≥ Grade 2 at any time prior to study entry * Has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection, Crohn's disease, ulcerative colitis, or chronic diarrhea * History of gastrointestinal perforation and/or fistulae within 6 months prior to randomization * Has an ongoing or active infection requiring treatment with intravenous antibiotics * Has a serious or nonhealing wound, peptic ulcer, or bone fracture within 28 days prior to first dose of study medication * Has uncontrolled hypertension despite standard medical management * Has symptomatic congestive heart failure, symptomatic or poorly controlled cardiac arrhythmia, or any other serious, uncontrolled medical disorders, which in the opinion of the investigator would make the participant ineligible for participation in the study * Has known brain or leptomeningeal metastases * Has known positive status for human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome-related illness * Has known active drug or alcohol abuse * Has pulmonary lymphangitic involvement that results in pulmonary dysfunction requiring active treatment, including the use of oxygen * Has had major surgery within 28 days prior to first dose of study medication or subcutaneous venous access device implantation within 7 days prior to first dose of study medication * Has an elective or planned major surgery during the course of the trial * If the primary cancer is non-small-cell lung cancer (NSCLC), there is radiographic evidence of intratumor cavitation, major blood vessel invasion or encasement by cancer, or proximity of cancer to major airways * Has received prior ramucirumab (IMC-1121B) therapy * Is receiving concomitant therapy with clinically relevant inhibitors or inducers of cytochrome P450 3A4 and 3A5 and/or isoenzymes * Has cirrhosis at a level of Child-Pugh B (or worse), or cirrhosis and a history of hepatic encephalopathy, or ascites resulting from cirrhosis and requiring ongoing treatment with diuretics and/or paracentesis