Regeneron 1331 Kinetics Sub-Study HoFH

Eligibility criteria: -Eligibility will be made based on the data collected at the screening visit of the R1500-CL-1331 protocol. Subjects must meet all inclusion/exclusion criteria for eligibility of that study to be eligible to participate in this sub-study. Below is the eligibility criteria for R1500-CL-1331. Inclusion: * Men and women 18 years or older at the time of the screening visit * Diagnosis of HoFH by one of the following: 1. Documented mutation or mutations in both LDLR alleles 2. Documented presence of homozygous or compound heterozygous mutations in Apo B and/or PCSK9 3. Documented skin fibroblast LDLR activity \<20% of normal * Willing to consistently maintain his/her usual diet for the duration of the study * Willing and able to comply with clinic visits and study-related procedures * Provide signed informed consent Exclusion: * Background medical LMT (if applicable) that has not been stable for at least 4 weeks (6 weeks for fibrates) prior to the screening visit (week -2) (unless participating in the run-in period to stabilize) * Having undergone lipid apheresis within 4 weeks prior to the screening visit (week -2) (unless participating in the run-in period to wash out) * Presence of any clinically significant uncontrolled endocrine disease known to influence serum lipids or lipoproteins. Note: Patients on thyroid replacement therapy can be included if the dosage of thyroxine has been stable for at least 12 weeks prior to screening visit (week -2) * Use of systemic corticosteroids, unless used as replacement therapy for pituitary/adrenal disease with a stable regiment for at least 6 weeks prior to the screening visit (week -2) Note: Topical, intra-articular, nasal, inhaled, and ophthalmic steroid therapies are not considered as "systemic" and are allowed * History of a myocardial infarction, unstable angina leading to hospitalization, coronary bypass graft surgery, percutaneous coronary intervention, uncontrolled cardiac arrhythmia, carotid surgery or stenting, stroke, transient ischemic attack, carotid revascularization, endovascular procedure or surgical intervention for peripheral vascular disease within 3 months prior to the screening visit (week -2) * Known history of HIV and a CD4 count less than 350c/mL Note: Patients with a history of HIV can be included, as long as they: 1. have a CD4 count greater than 350c/mL; 2. have an undetectable viral load for at least 12 months prior to screening; 3. have no opportunistic infections or active tuberculosis for at least 12 months prior to screening; 4. are not receiving prophylaxis for opportunistic infections; and have been on stable antiretroviral therapy for at least 12 months prior to screening * Use of another investigational drug or therapy within 30 days or at least 5 half-lives (whichever is longer) prior to screening visit (week -2). Includes patients who were involved in a prior clinical trial and are not sure of their treatment assignment. * Previous participation in any clinical trial of REGN1500 * Conditions/situation such as: 1. Any clinically significant abnormality identified at the time of screening that, in the judgement of the investigator or any subinvestigator, would preclude safe completion of the study or constrain endpoints assessment; eg. major systemic diseases, patients with short life expectancy 2. Patient considered by the investigator or any subinvestigator as inappropriate for this study for any reason, eg: deemed unable to meet specific protocol requirements, such as scheduled visits. Deemed unable to tolerate injections as per the patient or the investigator. Investigator or any subinvestigator, pharmacist, study coordinator, other study staff or relative thereof directly involved in the conduct of the protocol, etc. Presence of any other conditions (eg, geographic or social), either actual or anticipated, that the investigator feels would restrict or limit the patient's participation for the duration of the study * Laboratory findings during screening period: 1. Positive test for Hepatitis B surface antigen and/or Hepatitis C antibody 2. Positive serum beta-human chorionic gonadotropin or urine pregnancy test in women of childbearing potential 3. Triglycerides greater than 400 mg/dL ( \>3.95 mmol/L) (1 repeat lab is allowed) 4. Estimated glomerular filtration rate \<30 mL/min/1.73m\^2 according to 4-variable Modification of Diet in Renal Disease Study equation (calculated by central lab) 5. Alanine amintransferase (ALT) or aspartate aminotransferase (AST) \>3 x the upper limit of normal (ULN) (1 repeat lab is allowed) 6. Creatine phosphokinase (CPK) \>3 x ULN (1 repeat lab is allowed) * Known hypersensitivity to monoclonal antibody therapeutics * History of hypersensitivity reaction to doxycycline or similar compound * Pregnant or breast-feeding women * Sexually active men, or women of childbearing potential, who are unwilling to utilize adequate contraception for at least 6 months after the last dose of study drug.