Study of Gemcitabine, Carboplatin, and Panitumumab (GCaP) as Neoadjuvant Chemotherapy in Patients With Muscle-Invasive Bladder Cancer

Inclusion Criteria: * Histologically confirmed muscle invasive transitional cell carcinoma of the bladder at MSKCC (Note: urothelial carcinoma invading into the prostatic stroma with no histologic muscle invasion is allowed, provided the extent of disease is confirmed via imaging and/or EUA.) * Clinical stage T2-T4a N0/X M0 disease. * Medically appropriate candidate for radical cystectomy as per MSKCC attending urologic oncologist * Karnofsky Performance Status ≥ 80% * Age ≥ 18 years of age * Required Initial Laboratory Values: Absolute neutrophil count ≥ 1500 cells/mm3 * Platelets ≥ 100,000 cells/mm3 * Hemoglobin ≥ 9.0g/dL * Bilirubin ≤ 1.5 the upper limit of normal (ULN) for the institution * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN for the institution * Alkaline phosphatase ≤ 2.5 x ULN for the institution * Serum magnesium \> 1.4 mEq/L * Serum creatinine ≤ 2.0 mg/dL * Cisplatin ineligibility based on one or more of the following criteria: Estimated glomerular filtration rate (eGFR) 30-59 ml/min/1.73m2 using the CKD-EPI equation:(http://nephron.org/MDRD\_GFR.cgi) : eGFR = 141 x min(Scr/k, 1)a x max(Scr/k, 1)-1.209 x 0.993Age x 1.018 \[if female\] x 1.159 \[if black\] Scr is serum creatinine, k is 0.7 for females and 0.9 for males, a is -0.329 for females and -0.411 for males, min indicates the minimum of Scr/k or 1, and max indicates the maximum of Scr/k or 1. * Grade 2 sensory neuropathy * Grade 2 hearing loss * Patients must provide a pretreatment saliva sample for genomic analysis. Exclusion Criteria: * Prior systemic chemotherapy (prior intravesical therapy is allowed) * Serious intercurrent medical or psychiatric illness. * Prior radiation therapy to the bladder. * Concomitant use of any other investigational drugs * Any of the following within the 6 months prior to study drug administration: myocardial infarction, grade 2 or greater peripheral vascular disease, arterial thrombotic event, visceral arterial ischemia, cerebrovascular ischemia, transient ischemic attack, percutaneous transluminal angioplasty or stent, or unstable angina. Symptomatic and/or serious uncontrolled arrhythmia * Symptomatic congestive heart failure (NYHA class III or IVI) * History of interstitial lung disease e.g. pneumonitis or pulmonary fibrosis or evidence of interstitial lung disease on baseline chest CT scan. * History of any medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with the study participation or investigational product(s) administration or may interfere with the interpretation of the results. * Major surgery requiring general anesthesia within 21 days or minor surgery within 14 days of study enrollment. Subjects must have recovered from surgery related toxicities. * Pulmonary embolism, deep vein thrombosis, or other significant venous event ≤ 8 weeks before enrollment * Known allergy or hypersensitivity to any component of the study treatment(s) * Active infection requiring systemic treatment or any uncontrolled infections ≤14 days prior to enrollment. * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness. * Concurrent treatment on another clinical trial. Supportive care trials, surgical clinical trials or non-treatment trials, e.g. QOL, are allowed. * Ongoing treatment with therapeutic doses of warfarin (low dose warfarin up to 2 mg po daily for thromboembolic prophylaxis is allowed). * Pregnancy or breast-feeding. Patients must be surgically sterile or be postmenopausal, or must agree to use effective contraception during the period of therapy and for two (2) months following the last dose of panitumumab. The definition of effective contraception will be based on the judgment of the principal investigator or a designated associate. Male patients must be surgically sterile or agree to use effective contraception.