The primary purpose of this study is to evaluate the long-term safety and tolerability of ezetimibe (SCH 058235/MK-0653) 10 mg dosed daily and co-administered with either atorvastatin or simvastatin for up to 24 months in participants with homozygous familial hypercholesterolemia (FH).

Following completion of the 12-week, double-blind, efficacy and safety parent study (P01030/MK-0653-018; NCT03884452) participants will be offered entry into this open-label, 24-month extension study.

Inclusion Criteria:

• Has successfully completed the 12-week double-blind, efficacy and safety study of ezetimibe (Study P01030/MK-0653-018). Entry into this protocol must occur at the time of completion of Study P01030/MK-0653-018.
• All women must have a negative pregnancy test prior to study entry. Women of child bearing potential must agree to practice an effective barrier method of birth control for the duration of the study. In addition, participants administered a statin must agree to practice an effective barrier method of birth control for 30 days following the last dose of statin administered.
• Postmenopausal women who are receiving postmenopausal hormonal therapy or raloxifene must be maintained on a stable estrogen (ERT), estrogen/progestin (HRT) or raloxifene regimen during study period.
• Is willing to observe the National Cholesterol Education Program (NCEP) Step I diet for the duration of the study.
• Is willing to participate in the study and to complete all assessments.
• Patients or in the case of children, their parents or legal guardians, must agree to give written informed consent.

Exclusion Criteria:

• Participants who discontinued prematurely from Study P01030/MK-0653-018.
• Participants who are in a situation or have any condition which, in the opinion of the Investigator, may interfere with optimal participation in the study.
• Pregnant or lactating women.
• Participants who are known to be human immunodeficiency virus (HIV) positive.
• Participants who are taking any prohibited concomitant medications. Prohibited medications include:
• Fibric Acid Derivatives;
• Oral corticosteroids;
• (Cardiovascular drugs such as beta blockers, calcium channel blockers, angiotensin-converting enzyme [ACE] inhibitors, nitrates or alpha-adrenergic blockers or thiazide diuretics will be allowed, provided the dose will remain constant throughout the duration of the study. Acetylsalicylic acid administered as a platelet aggregation inhibitor or analgesic is permitted.);
• Treatment with psyllium or other fiber-based laxatives unless treated with a stable regimen treatment throughout the duration of the study period;
• Treatment with cyclosporine;
• Treatment with orlistat;
• Treatment with troglitazone (Rezulin®) or other thiazolidinedione antidiabetic agents, unless treated with a stable regimen throughout the duration of the study period;
• Treatment with agents with known drug interactions with simvastatin or atorvastatin including antifungal azoles (e.g. itraconazole and ketoconazole), macrolide antibiotics (e.g. erythromycin and clarithromycin) and nefazodone; In addition, treatment with other agents that may interfere with or induce the CYP3A4 isoenzyme of the cytochrome P450 system should be avoided, although they are not necessarily prohibited medications.;
• Treatment with medications which interact with simvastatin through uncertain mechanisms, including amiodarone and verapamil, are prohibited in participants administered simvastatin in this protocol.
• (Participants receiving LDL-C apheresis may continue on this therapy provided that they are on a stable regimen throughout the duration of the study and lipid levels for study visits are drawn just prior to an apheresis treatment session.);
• Participants on a stable regimen of resin therapy (as defined by the dose taken during the P01030/MK-0653-018 study) may continue that therapy provided that the daily dose of study treatment is taken ≥4 hours prior to the administration of the resin or ≥4 hours following any resin dose. In addition, the dose of resin should be taken no less than 4 hours before and no less than 4 hours after administration of study treatment.