Inclusion Criteria:
* Patients must be aged at least 50 at the time of initial invitation, and at least one of the following inclusion criteria must be satisfied:
* History of MI; or
* Cerebrovascular atherosclerotic disease (i.e. history of presumed ischaemic stroke or carotid revascularization); or
* Peripheral arterial disease (i.e. history of non-coronary revascularization, including aortic aneurysm repair or graft); or
* Diabetes mellitus with other evidence of symptomatic coronary heart disease (i.e. treatment or hospitalization for angina, or a history of coronary revascularization or acute coronary syndrome).
Exclusion Criteria:
* None of the following must be satisfied:
* Acute MI, acute coronary syndrome or stroke within 4 weeks prior to Screening Visit or during Run-in (but such individuals may be entered later, if appropriate);
* Planned coronary revascularization procedure within the next 6 months (such individuals may be entered later, if appropriate);
* Definite history of chronic liver disease, or abnormal liver function (i.e. alanine transaminase (ALT) \>2x the upper limit of normal (ULN)). Note: Individuals with a history of acute hepatitis are eligible provided this ALT limit is not exceeded;
* Severe renal insufficiency (i.e. creatinine \>200 µmol/L \[2.3 mg/dL\], dialysis or functioning renal transplant);
* Evidence of active inflammatory muscle disease (e.g. dermatomyositis, polymyositis), or creatine kinase (CK) \>3x ULN;
* Previous significant adverse reaction to a statin or anacetrapib;
* Current treatment with any of the following lipid-lowering treatments:
(i) a regimen considered to produce substantially greater LDL cholesterol reduction than atorvastatin 80 mg daily for individuals in non-Asian countries or 20 mg daily for those in North East Asia; or (ii) fibric acid derivative ("fibrate", including gemfibrozil); or (iii) niacin (nicotinic acid) at doses above 100 mg daily
* Concurrent treatment with a medication that is contraindicated with anacetrapib or atorvastatin:
(i) any potent CYP3A4 inhibitor, such as:
1. macrolide antibiotics (erythromycin, clarithromycin, telithromycin);
2. systemic imidazole or triazole antifungals (e.g. itraconazole, posaconazole);
3. protease inhibitors (e.g. atazanavir);
4. nefazodone
(ii) ciclosporin
(iii) daptomycin
(iv) systemic use of fusidic acid
Note: Individuals who are taking such drugs temporarily may be re-screened when they discontinue them, if considered appropriate;
* Known to be poorly compliant with clinic visits or prescribed medication;
* Medical history that might limit the individual's ability to take trial treatments for the duration of the study (e.g. severe respiratory disease; history of cancer or evidence of spread within last 5 years, other than non-melanoma skin cancer; or recent history of alcohol or substance misuse);
* Women of child-bearing potential (unless using adequate contraception);
* Current participation in a clinical trial with an unlicensed drug or device.
Individuals will also be excluded at the Screening visit if it is considered unlikely that they will achieve total cholesterol \<3.5 mmol/L (135 mg/dL) on the highest atorvastatin dose available in their region (atorvastatin 80 mg daily in non-Asian countries or 20 mg daily in North East Asia).
In addition, individuals will be excluded at the Randomization visit if any of the following are true:
* Total cholesterol above 4 mmol/L \[155 mg/dL\]
* Non-compliant with run-in treatment (\<90% scheduled run-in medication taken)
* Individual is no longer willing to be randomized into the 4-5 year trial
* The individual's doctor is of the view that their patient should not be randomized.
