### Study design and study population

The GIRaFH study was a retrospective, multicenter, cohort study. The study design and study population have been described elsewhere [4]. Briefly, lipid clinics in the Netherlands submit DNA samples from clinically suspected FH patients to a central laboratory for LDL-receptor mutation analysis [7]. We randomly selected hypercholesterolemic patients from this DNA-bank database. These patients had been referred from 27 lipid clinics throughout the Netherlands. A total of 2400 FH patients were included in this study. The FH diagnostic criteria were based on internationally established criteria [8].

Phenotypic data (including detailed information on cardiovascular events) were acquired by reviewing patient's medical records by a trained team of data collectors [9]. Guidelines for data collection from medical records were constructed for the purpose of the study and have been published [9]. Written informed consent was obtained from all living patients. The Ethics Institutional Review Board of each participating hospital approved the protocol.

### Determination of smoking-history

Upon review of the patient's medical records, sufficient data on lifetime smoking status was available in the medical records of 68 percent of the patients. Questionnaires were mailed to all participants in order to supplement the smoking data. In addition to the number of cigarettes smoked per day, the questionnaire contained questions on age when the person started smoking, age(s) when smoking cessation was attempted, and age of final cessation. With the supplemental data collected from the questionnaires, lifetime smoking status could be reconstructed in 88 percent of the patients. Temporary cessations were exceptional and short, and we decided to analyze final cessation dates only. Patients of whom smoking status was unknown, had slightly higher HDL levels (1.33 vs 1.23 mmol/L, p = 0.001), and they had lower triglyceride levels (1.68 vs 1.92 mmol/L, p = 0.009). On the other covariates that we analyze in this paper the two patient groups were not significantly different.

### Other risk factors

Male gender, smoking, body mass index and the presence of hypertension, and diabetes mellitus were considered classical risk factors. Hypertension was defined when the diagnosis had been made and when anti-hypertensive medication was prescribed, or if three consecutive blood pressure measurements were > 140 mmHg systolic or > 90 mmHg diastolic. Diabetes mellitus was defined when the diagnosis had been made and medication (insulin or oral anti-diabetics) was prescribed, or by a fasting glucose of > 6.9 mmol/L. In the statistical analysis, both hypertension and diabetes mellitus were handled as binary covariates depending on age; before age of diagnosis the risk factor was considered to be absent, and after diagnosis it was considered present for the remaining life.

All laboratory parameters were measured in fasting blood samples after at least 6 weeks of withdrawal of any lipid-lowering medication. The presented values are those from as close to the first lipid clinic visit as possible, with a maximum time-span of two years. Plasma total cholesterol, high density lipoprotein (HDL) cholesterol, and triglycerides were measured by standard enzymatic methods. Low density lipoprotein (LDL) cholesterol concentrations were calculated by means of the Friedewald formula. Apolipoprotein (a) (Lp(a)) was measured with immunonephelometric methods. Plasma homocysteine was measured by high-performance liquid chromatography. These laboratory parameters were handled as time-independent covariates in the statistical analysis.

### Definition of atherosclerotic events

In this study the primary outcomes were cardiovascular mortality and non-fatal cardiovascular events. Cardiovascular events were defined as (I) acute myocardial infarction (AMI), proven by at least two of the following: (a) classical symptoms (> 15 minutes), (b) specific EKG abnormalities, (c) elevated cardiac enzymes (> 2*x* upper limit of normal); (II) percutaneous coronary intervention (PCI) or other invasive procedures; (III) coronary artery bypass grafting (CABG); (IV) angina pectoris (AP), diagnosed as classical symptoms in combination with at least one unequivocal result of one of the following; (a) exercise test, (b) nuclear scintigram, (c) dobutamine stress ultrasound, (d) a more than 70 percent stenosis on a coronary angiogram; (V) ischemic stroke, demonstrated by CT- or MRI scan; (VI) documented transient ischemic attack (TIA); (VII) peripheral arterial bypass graft (PBG); (VIII) peripheral percutaneous transluminal angioplasty (PTA) or other percutaneous invasive intervention; (IX) intermittent claudication defined as classical symptoms in combination with at least one equivocal result of one of the following: (a) ankle/arm index < 0.9 or (b) a stenosis (> 50 percent) on an angiogram or duplex scan. If information on cardiovascular events did not strictly fulfill the above-mentioned criteria, or if any suspect history, symptoms, or diagnostic evaluations were found in the medical record, the case was presented to an independent adjudication committee [9].

### Statistical analysis

We consider the risk, subsequently denoted as hazard, of first (atherosclerotic) event as a function of age: *h*(*t*) represents the hazard at age *t*. Suppose that person *i* started smoking at age *a*
_{0} and ceased smoking at age *a*
_{1}. In this paper we will use the proportional hazards (or Cox) model and we model the hazard of an event in person *i* as follows:

• if *t* <*a*
_{0} then *h*(*t*|*i*) = *h*
_{0}(*t*);

• if *a*
_{0} ≤ t <*a*
_{1} then *h*(*t*|*i*) = *h*
_{0}(*t*) * *exp*(*β*);

• if *t* ≥ *a*
_{1} then *h*(*t*|*i*) = *h*
_{0}(*t*) * *exp*(*γ*(*t*, *a*
_{1})),

where *h*
_{0}(*t*) is the baseline hazard-function, *β* is the log-hazard ratio due to smoking in the age-period when person *i* smoked, and *γ*(*t*, *a*
_{1}) is the log-hazard ratio at age *t* due to smoking-cessation at age *a*
_{1} (*t* > *a*
_{1}). Simple choices for *γ*(*t*, *a*
_{1}) are (*i*) *γ*(*t*, *a*
_{1}) = *β*, or (*ii*) *γ*(*t*, *a*
_{1}) = 0. In many cases it is likely that the excess-risk due to smoking only gradually disappears, for instance as a linear function (*iii*) *γ*(*t*, *a*
_{1}) = *β*(1 - *δ* * (*t* - *a*
_{1})) or as an exponential function (*iv*) *γ*(*t*, *a*
_{1}) = *β* * *exp*(-*p* * (*t* - *a*
_{1})), where *δ* and *p* are (unknown) parameters determining the speed of decrease of excess-risk after smoking-cessation. *δ* is a slope parameter and *a*
_{0} + 1/*δ* defines age after which the excess risk of smoking equals zero. There are an infinite number of monotonic decreasing functions, but most can be approximated very well by the linear or exponential models.

Models (*i*) and (*ii*) are special cases of a proportional hazards or Cox model with a simple time-dependent covariate, and the unknown parameter *β* can be easily estimated using standard algorithms. Models (*iii*) and (*iv*) can be re-written such that they also conform to the proportional hazards model, and the unknown parameters *β*, *δ*, and *p* can be estimated using standard algorithms for the proportional hazards model. To that end the time-dependent covariate *x*
_{
it
}was introduced, which is equal to zero if *t* <*a*
_{0}, equals unity if *a*
_{0} ≤ *t* <*a*
_{1}, and equals *exp*(-*p* * (*t* - *a*
_{1})) in the exponential model if *t* ≥ *a*
_{1}. For the linear decreasing model *x*
_{
it
}equals (1 - *δ* * (*t* - *a*
_{1})) if *t* > *a*
_{1} (and *x*
_{
it
}≥ 0).

The hazard function can be therefore written as *h*(*t*|*i*) = *h*
_{0}(*t*) * *exp*(*β* * *x*
_{
it
}), which is a standard proportional hazards model with a time-dependent covariate *if p or* *δ* *is known*. Since *p* and *δ* are unknown a two-step estimation procedure was used in which *p* or *δ* was varied along a grid, and for each value of *p* or *δ* we estimated *β* using the standard algorithms (using the partial likelihood). The value of *p* or *δ* with the highest likelihood value was then finally selected. The advantage of this two-step approach was that existing software programs like SAS, SPSS, or STATA could be used. Disadvantageous of this procedure was that the unreliability of the estimates of *p* and *δ* were not automatically incorporated in the standard error of the estimate of *β*. To incorporate that uncertainty in the estimates of the standard errors we performed a 1000-fold bootstrap procedure; in each bootstrap sample we determined optimal values of *p* or *δ* as well as the associated partial likelihood estimated of *β*. Standard error of *β* was subsequently derived from the distribution of the estimates in the bootstrap samples [10].

In the Cox model we always included as covariates gender, LDL-cholesterol, HDL-cholesterol, triglyceride level, homocysteine, and Lp(a) and hypertension, and diabetes mellitus as age-dependent variables.