A search strategy was developed, piloted and run in MEDLINE and EMBASE electronic databases on 12^th May 2003, supplemented by screening reference lists of relevant articles and reviews. Electronic searching within the databases included 'coronary heart disease or synonyms' and 'model or synonyms' as key words. Both key words and MeSH headings were used (Appendix 1) [see Additional file 1]. The search strategy was validated using ten key papers already known to the authors; all ten papers were captured by the search strategy. The search initially identified 4,531 articles and checking the references identified a further 17. All the records were imported to 'Reference Manager'. By checking the titles and abstracts for the terms 'model', 'coronary heart disease' or 'population', the number of articles was reduced to 275. Two reviewers (BU, SC) independently checked the titles and abstracts of all papers initially identified, and then independently screened the articles for inclusion and appraisal. Agreement between the two reviewers was good (Kappa = 0.76).

Any CHD modelling study was included if it reported on a key outcome (deaths prevented, life years gained, prevention cost, treatment cost, mortality, prevalence, incidence or disability) in a defined population (community, region or country). Models were excluded if they simply described animals, cell lines, clinical series, cohorts or estimates of individual risk. Decision analytic models were also not included in this review since they mostly focused on clinical decision making in individuals, rather than population benefits.

Figure 1 illustrates the flowchart for the search and review process. Excluded articles are listed in Appendix 4 [see Additional file 1]. In total, 75 articles were included for critical appraisal and 200 articles were excluded.

A pre-piloted form was used for data extraction (Appendix 2) [see Additional file 1]. Articles were categorised according to the specific models that they described. Each paper was then critically appraised by two reviewers using explicit quality criteria. There are no universally accepted lists of appropriate quality criteria for model papers. However reviews by Weinstein 11 , and Edwards 12 , and recent guidelines from the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) 3 have suggested useful quality criteria. Using these sources 3 11 12 , we created, piloted and refined a grading system, based on sensitivity, validity and transparency of the model (Appendix 3) [see Additional file 1].

Papers were evaluated on the basis of whether a sensitivity analysis was carried out, the validity was checked, data quality was reported, illustrative examples were provided, assumptions stated, if model was potentially available to the reader (transparency), and if potential limitations such as assumptions, confounding, lag times and competing causes were specified or discussed. The model evaluation was based on authors' reporting on that specific item in the related articles. A model was considered as comprehensive if it included multiple coronary heart disease categories, and a range of treatments and major risk factors.

Our search was limited to English language articles or abstracts. Publication bias can be an issue since our search was mostly based on electronic search of biomedical databases. The grey literature was not formally searched; however, we contacted key people who were working in this field.

The majority of the models (36, 86%) explicitly stated their key assumptions. However, illustrations or examples of estimations were provided in only 14 (33%). Working versions of the models were potentially available in just 4 (10%).

Barely one fifth of the models reported on limitations of their methodology such as competing causes (8, 19%), lag times (7, 17%) or confounding (8, 19%).

Papers excluded are listed alphabetically in Appendix 4 [see Additional file 1] with reasons for exclusion. The commonest reasons for exclusion were that the paper was not a modelling study, that it did not report on CHD outcomes, or that it was only a review.

The details on model methodology used in modelling papers included in this review can be seen in the Appendices [see Additional file 1].

The methodology used in models varied widely. The Coronary Heart Disease Policy (CHDP) Model is a state-transition, cell based model developed in the1980s 13 . It was initially used to examine trends in CHD mortality 14 15 and expected gains in life expectancy from risk factor modifications 16 . This model was also used to evaluate the cost-effectiveness of specific medical interventions for primary and secondary prevention of CHD 7 17 18 19 and health promotion activities 20 .

The model was based on the 1980 US population and mortality statistics. It consists of three sub-models:

- A demographical/epidemiological model, which represents the disease-free population aged 35–84 years, stratified by sex, age group and cardiovascular risk factors. This model includes risk factors as categorical variables, therefore over 5,000 cells are required in total. It then uses a logistic risk function based on the Framingham equation to estimate the annual incidence rates of CHD events for each cohort.

- A bridge model, which covers subjects for the first 30 days after they develop coronary disease. Using CHD incidence data from Minnesota, the model initially determines whether the first event is angina, myocardial infarction or cardiac arrest 13 .

- A disease history model, which includes the survivors after the first 30 days, places them in 12 CHD states by age and sex, and then follows them through treatment pathways.

This model allows the user to simulate the effects of an intervention (either risk factor modification, or therapy) by changing case fatality rates and observing the effect on mortality, morbidity and costs for up to 30 years.

The CHD Policy Analysis Model, comprised two distinct parts. The primary prevention component of the model developed by the London School of Hygiene and Tropical Medicine aims to simulate the impact of different primary prevention strategies on benefits and costs 21 . The treatment component of the model developed in the Universities of Southampton and Birmingham 21 22 evaluates the impact of different treatments given to two different groups of CHD patients, stable angina or acute myocardial infarction 21 .

PREVENT was a cell based model developed by Gunning-Schepers in the Netherlands during the 1980s 23 . It has been used to estimate the health benefits of changes in population risk factor prevalence by comparing i) continuation of existing trends with ii) alteration of the proportions of the population with given risk factor levels. The model allowed one risk factor to be associated with more than one disease and one disease to be associated with more than one risk factor. Demographic evolution was also taken into account in simulations 23 .

The Cardiovascular Life Expectancy Model was initially developed by Grover et al in 1992 in Canada to examine the cost-effectiveness of different treatment options for CHD 5 . From 1998 onwards the model was also described as a Markov model. The model includes primary and secondary prevention parts. The primary CHD part calculates the annual probability of dying (from CHD or other causes) and the annual risk of CHD events (with or without intervention) for a person without symptomatic CHD at entry to the model. The annual risk of developing specific CHD endpoints is based on data from the Framingham Heart Study.

After developing CHD, a person then moves to the secondary CHD model. This part calculates the risk of dying during the 12 months following a non-fatal myocardial infarction. The risk estimations are based on the Framingham logistic equations for primary events after adjustment for the presence of CHD 5 .

The difference between the predicted annual cumulative mortality with and without the intervention over the remaining total life expectancy then represents the total years of life saved after that intervention.

The IMPACT CHD mortality model is a cell-based model originally developed by Capewell and colleagues in 1996 6 . Using a MS EXCEL spreadsheet, this model combines data from many sources on patient numbers, treatment uptake, treatment effectiveness, risk factor trends and consequent mortality effects. The deaths prevented or postponed (DPPs) over a specified time period are then estimated. The model can therefore be used to estimate the proportion of a mortality decline (or increase) over a certain time span that might be attributed to specific treatments or risk factor changes. It can also examine the consequences of increasing treatments provided, or reducing risk factor levels. Other outputs include life years gained and cost-effectiveness of specific interventions (Appendix 3) [see Additional file 1].

The Global Burden of Disease (GBD) model was developed at WHO by Lopez and Murray. It is an example of a model, which uses population attributable risk percentage (PAR %) estimations. The model can calculate the attributable burden of disease for a specific risk factor, population and time, defined as the difference between currently observed burden and the burden that would be observed if past levels of exposure had been equal to the lowest relative risk 24 25 ).

The GBD Model has five components: causes of death, descriptive epidemiology of disabling sequelae, burden attributed to selected risk factors, projections of burden for the future and sensitivity analyses. Cause of death data are obtained from vital registrations or other sources. Data on 107 disorders and selected disabling sequel were investigated regarding average age of onset, duration, incidence and prevalence. Burden of disease and injury attributable to ten major risk factors were then calculated. The model uses attributable fractions, taken from reviews and meta-analyses, applied to the population of a region to calculate the burden of disease attributable to these risk factors 25 . Where data were not available, assumed values were used. Burden of disease is measured using disability adjusted life years (DALYs), calculated as the sum of years lost and years lived with disability 26 .

The Coronary Heart Disease Policy Model includes major risk factors such as smoking, total cholesterol, DBP and relative weight, which are necessary to estimate CHD risk using Framingham Equations. The model considers most CHD categories. Individual CHD treatments such as statins, aspirin, and beta-blockers have also been considered in different publications 7 17 18 .

The PREVENT Model is a primary prevention model and therefore only considers risk factors: smoking, cholesterol, hypertension, obesity, physical activity and alcohol use 27 28 29 30 .

The Cardiovascular Life Expectancy Model estimates the annual risk of developing specific CHD endpoints. Initially based on data published from the Framingham Heart Study from 1998 onwards the model used data from the Lipid Research Clinic follow up cohort. It therefore includes risk factors of age, sex, diastolic blood pressure, total cholesterol, HDL cholesterol level, left ventricular hypertrophy, glucose intolerance and smoking status 31 32 33 . The only treatment considered was statins. 31 32 33

The CHD Policy Analysis Model has separate primary prevention and CHD treatment parts. The primary prevention component includes risk factors such as age, sex, systolic blood pressure, total cholesterol, and smoking 21 . The disease events included are stable angina, unstable angina, myocardial infarction, sudden cardiac death, stroke death, other cardiovascular death, cancer death and death from other known and unknown cause 21 . The CHD Policy Analysis Model originally aimed to include many treatment categories but the only publication thus far focuses on angina 31 32 33 .

The IMPACT Model considers a comprehensive range of risk factors, CHD categories and treatments. For primary prevention the model includes smoking, cholesterol, blood pressure 6 34 35 36 , deprivation, obesity, diabetes, physical activity and also primary prevention with anti-hypertensive medications and statin therapies 37 .

The disease categories and treatments include: AMI: (Cardiopulmonary resuscitation, thrombolysis, aspirin, angioplasty, beta blockers and ACE inhibitors); Secondary prevention following MI, and, separately, following CABG or angioplasty: (aspirin, beta blockers, ACE inhibitors, statins, warfarin and rehabilitation); Chronic angina: (CABG surgery, angioplasty, aspirin, statins); Unstable angina: (aspirin, heparin, platelet IIB/IIIA inhibitors and clopidogrel); Heart failure: (ACE inhibitors, beta blockers, spironolactone, aspirin, statins) and all standard treatments for Hypertension.

The Global Burden of Disease Model includes ten major risk factors for global disease burden: malnutrition, poor water quality, unsafe sex, alcohol, occupation, tobacco use, hypertension, physical inactivity, illicit use of drugs, and air pollution 25 . CHD is included in the model, and is modelled as being caused by tobacco use, hypertension and physical inactivity, and reduced by all levels of alcohol consumption.

Most of the models were restricted to young and middle-aged groups, generally 15 to 64 years (Tables 1–7 in Appendix 3) [see Additional file 1]. However, the CHD Policy Model, IMPACT and the CHD Policy Analysis Model considered groups aged up to 84 years. None of the models specifically considered non-Caucasian populations.

The most common outcomes reported were numbers of deaths prevented, life-years gained, CHD incidence and cost or cost-effectiveness (Table 1 and Appendix3) [see Additional file 1]. Among the six models included in this paper, CHD Policy Model, PREVENT, IMPACT, Global Burden of Disease and CHD Policy Analysis have capability to predict future trends in disease and other related outcomes except the Cardiovascular Life Expectancy Model. This model has been used to assess cost-effectiveness of interventions rather than predicting or explaining the trends.

Relatively few papers included in this review reported on quality issues. In a few models, sensitivity analyses were reported, examining the effect of varying key factor such as treatment costs or measurement imprecision. However, the majority were one-way analyses (varying one factor at a time), rather than the more rigorous multi-way sensitivity analyses (varying several factors simultaneously) (Table 1 and Appendix 3) [see Additional file 1].

Assessment of validity was reported in very few models. In the CHD Health Policy Model, this was done by comparing the CHD deaths estimated by the model with the actual CHD deaths observed in 1990 14 . In the IMPACT Model, validity was likewise checked by comparing the estimated fall in CHD deaths with the observed fall in specific age and sex categories 6 37 . In PREVENT, model validity was checked by comparing model estimates with another estimation method 38 . In the Cardiovascular Life Expectancy Model, predictive validity was checked by comparing the model estimates with events observed in primary and secondary prevention trials 39 40 . The original 1992 Cardiovascular Life Expectancy model was similarly validated against the data set from the Lipid Research Clinic cohort 32 .

The CHD Health Policy model was similarly calibrated using life years estimated from the model compared with life expectancy from 1980 national statistics 16 . Only two of the models had been replicated in different populations (PREVENT 28 41 and IMPACT 6 10 34 35 36 37 42 43 ).

Many of the papers included in this systematic review failed to provide sufficient detail to allow thorough evaluation of the model used. This obviously constrained our systematic review. When assessing the quality of a model, one should ideally consider the system being modelled, the model structure, the elements included and excluded, the probable effects of existing trends in mortality and risk factors and the model assumptions-both explicit and implicit 3 4 . The description of the model should be sufficiently detailed so that the model can be replicated mathematically. Therefore modeling papers should include some basic information on models listed in Table 2. If the validity of a model cannot be checked, it simply represents a "black box" rather than a useful tool. More extensive validation studies thus represent a priority for future research. Although most of the models have potential to predict future trends depending on how the model is populated, the methodological challenges are considerable, and there is substantial need for further research and development.

Finally, although this review focussed on CHD models, many of the issues are generic. Some findings may therefore be cautiously generalisable when modelling other diseases or interventions.