A Clinical Study of the Efficacy of Natalizumab on Reducing Disability Progression in Participants With Secondary Progressive Multiple Sclerosis

Key Inclusion Criteria (Part 1):

* Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information in accordance with national and local subject privacy regulations.
* SPMS defined as relapsing-remitting disease followed by progression of disability independent of or not explained by multiple sclerosis (MS) relapses for at least 2 years.
* EDSS score of 3.0 to 6.5, inclusive.
* Multiple Sclerosis Severity Score of 4 or higher.
* Documented confirmed evidence of disease progression independent of clinical relapses over the 1 year prior to enrollment as defined in the Study Reference Guide.

Key Exclusion Criteria (Part 1):

* Relapsing remitting multiple sclerosis (RRMS) or primary progressive MS as defined by the revised McDonald Committee criteria.
* Clinical relapse (within 3 months) prior to randomization.
* T25FW test of \>30 seconds during the screening period.
* Any value below the lower limit of normal for blood levels of leukocytes, lymphocytes, or neutrophils.
* Considered by the Investigator to be immunocompromised based on medical history, physical examination, laboratory testing, or any other testing required by local guidelines, or due to prior immunosuppressive or immunomodulating treatment.
* Subjects for whom MRI is contraindicated (i.e., have pacemakers or other contraindicated implanted metal devices, are allergic to gadolinium, or have claustrophobia that cannot be medically managed).
* History of any clinically significant (as determined by the Investigator) cardiac, endocrinologic, hematologic, hepatic, immunologic, metabolic, urologic, pulmonary, neurologic (other than MS), dermatologic, psychiatric, and renal, or other major disease that would preclude participation in a clinical study.
* History of malignant disease, including solid tumors and hematologic malignancies (with the exception of basal cell and squamous cell carcinomas of the skin that have been completely excised and are considered cured).
* Known history of or positive test result for human immunodeficiency virus.
* Positive test result for hepatitis C virus (test for hepatitis C virus antibody or hepatitis B virus (test for hepatitis B surface antigen and/or hepatitis B core antibody).
* History of transplantation or any anti-rejection therapy.
* Presence of any infectious disease (e.g., cellulitis, abscess, pneumonia, septicemia) within 30 days prior to screening.
* History of progressive multifocal leukoencephalopathy or other opportunistic infections.

Treatment History (Part 1)

* Any prior treatment with cell-depleting therapies, including total lymphoid irradiation, cladribine, rituximab, alemtuzumab, or bone marrow ablation.
* Any prior treatment with natalizumab.
* Treatment with mitoxantrone, cyclophosphamide, cyclosporine, azathioprine, methotrexate, mycophenolate mofetil, T cell or T cell receptor vaccination, fingolimod, daclizumab, or cytapheresis within 6 months prior to randomization.
* Treatment with intravenous or oral corticosteroids, intravenous immunoglobulin, or plasmapheresis for treatment of MS within the 3 months prior to randomization.
* Treatment with glatiramer acetate or any interferon beta preparations within 4 weeks prior to randomization.
* Treatment with 4-aminopyridine within 30 days prior to randomization, unless a stable dose has been maintained for at least 30 days prior to randomization and will be continued for the course of this study.

Key Inclusion Criteria (Part 2):

* Subjects must have participated in and completed Part 1 per protocol, and have documented assessment attempts for EDSS, T25FW, and 9HPT prior to first open-label dosing.

Key Exclusion Criteria (Part 2):

* Subjects with any significant change in clinical status, including laboratory tests that, in the opinion of the Investigator, would make them unsuitable to participate in this extension study. The Investigator must re-review the subject's medical fitness for participation and consider any diseases that would preclude treatment.
* Subjects who discontinued study treatment in Part 1 OR had fewer than 20 infusions in Part 1 OR missed 2 or more consecutive infusions in Part 1.

NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.