The purpose of this study is determine if 2 cycles of SGN-35 can be used instead of ICE prior to autologous stem cell transplant (ASCT) for relapsed and refractory HL. There are 2 steps to treating patients with relapsed or refractory HL. The first step is to shrink the lymphoma with chemotherapy. The chemotherapy regimen commonly used is called ICE. ICE is a combination of chemotherapy drugs: ifosfamide, carboplatin, and etoposide. The second step of treatment is to give high doses of chemotherapy and radiation therapy followed by infusion of stem cells. This is called an ASCT. This study will focus on the first step of treatment for relapsed and refractory HL.

ICE chemotherapy can cause many side effects. We believe that there are patients who can receive less toxic treatments and still do well. We have learned from past studies that [18F]FDG-PET scans (which we will call "PET scans") can be used to predict who will do well after ASCT. PET scans are tests used to measure the metabolic activity of the disease. Patients without abnormal activity on their PET scan (negative PET scan) before ASCT are much more likely to be cured than those with activity on their PET scan (positive PET scan).

In this study, instead of beginning with ICE chemotherapy, the patient will receive a new drug called Brentuximab vedotin (SGN-35). SGN-35 is a type of drug called an antibody drug conjugate. SGN-35 has 2 parts; a part that targets cancer cells (the antibody) and a cell killing part (the chemotherapy). The antibody part of SGN-35 sticks to a target called CD30. CD30 is an important molecule on some cancer cells (including Hodgkin lymphoma) and some normal cells of the immune system. The cell killing part of SGN-35 is a chemotherapy called monomethyl auristatin E (MMAE).

It can kill cells that the antibody part of SGN-35 sticks to.

Compared to ICE chemotherapy, SGN-has fewer side effects and does not require inpatient admission for treatment. We aim to determine whether patients can avoid treatment with ICE prior to ASCT. We will use the results of the PET scan to determine whether the patient needs additional chemotherapy before ASCT. If the PET scan is negative, the patient will be referred to ASCT and not receive ICE chemotherapy. If the PET scan is positive, the physician will discuss further treatment options with the patient.

Inclusion Criteria:

• Histologic diagnosis of cd30 positive classical Hodgkin's lymphoma.
• Primary refractory or relapsed disease proven by biopsy or fine needle aspiration (cytology) of an involved site. Pathology must be reviewed at MSKCC.
• Relapse or refractory disease following doxorubicin or nitrogen mustard containing front-line therapy
• Fluorodeoxyglucose (FDG)-avid disease by FDG-PET/CT and measurable disease of at least 1.5 cm by spiral CT, as assessed by the site radiologist.
• Cardiac ejection fraction of greater than 45%, measured since last chemotherapy.
• Hemoglobin-adjusted diffusing capacity for carbon monoxide of greater than 50% on pulmonary function testing, measured since last chemotherapy
• Serum creatinine < or = to 1.5 mg/dl; if creatinine >1.5 mg/dl then the measured 12- or 24-hour creatinine clearance must be >60 ml/minute.
• ANC>1000/μl and Platelets>50,000/μl
• Total bilirubin < 2.0 mg/dl in the absence of a history of Gilbert's disease.
• Females of childbearing age must be on an acceptable form of birth control.
• Age between 12 and 72
• HIV I and II negative.

Exclusion Criteria:

• Received more than 1 prior treatment (combined modality therapy represents 1 treatment) for Hodgkin Lymphoma
• Hepatitis B surface antigen positive or hepatitis B core antibody positive.
• Known pregnancy or breast-feeding.
• Medical illness unrelated to Hodgkin's Lymphoma, which, in the opinion of the attending physician and/or principal investigator, makes participation in this study inappropriate.
• Peripheral neuropathy > grade 2

2 years

Cohort 1: FDG-PET Abnormal and Cohort 2: Expansion Cohort: FDG-PET Abnormal received the same intervention. Cohort 1: FDG-PET Normalization and Cohort 2, Expansion Cohort: FDG-PET Normalization received the same intervention