A comparison of economic modelling and clinical trials in the economic evaluation of...

ECONOMIC EVALUATION

A COMPARISON OF ECONOMIC MODELLINGAND CLINICAL TRIALS IN THE ECONOMIC

EVALUATION OF CHOLESTEROL-MODIFYINGPHARMACOTHERAPY

STEPHEN MORRIS*Department of Economics, City University, London, UK

SUMMARY

There are various ways in which data for economic evaluations may be obtained, including via clinical trials andvia economic modelling. There are numerous advantages and disadvantages associated with each method,although it is generally assumed that economic models lack the accuracy required for the calculation of meaningfulcost-effectiveness data. In order to assess the predictive accuracy of economic modelling in the context ofcholesterol-modifying pharmacotherapy it is possible to compare predicted coronary heart disease (CHD)incidence estimates obtained using CHD risk equations derived from the Framingham Heart Study (FHS) withactual CHD incidence rates achieved in a major clinical trial, the West of Scotland Coronary Prevention Study(WOSCOPS). FHS-derived CHD risk equations substantially underestimate the actual risks of nonfatalmyocardial infarction obtained by WOSCOPS. However, in predicting risks of death from CHD, FHS-derivedCHD risk equations estimate extremely accurately the incidence obtained by WOSCOPS. For example, fromWOSCOPS the risk of an individual fulfilling the trial entry criteria incurring nonfatal myocardial infarction orCHD death in 4.9 years is 0.079 for placebo group and 0.055 for the intervention group. Therefore, the relative riskfor the intervention group relative to placebo group is 0.696, implying a risk reduction of 30%. Comparable riskspredicted using FHS-derived CHD risk equations are 0.116 for the placebo group and 0.088 for the interventiongroup. Consequent relative risks and risk reductions for the intervention relative to placebo are 0.757 and 24%,respectively. Using both model and trial estimates of CHD incidence in an economic evaluation ofcholesterol-modifying pharmacotherapy, incremental costs per life year gained are £41 707 using WOSCOPS dataand £36 480 using FHS-derived CHD risk equations. © 1997 by John Wiley & Sons, Ltd.

Health Econ. 6: 589–601 (1997)

No. of Figures: 0. No. of Tables: 6. No. of References: 57.

KEY WORDS — economic modelling; clinical trials; cholesterol-modifying pharmacotherapy; coronary heartdisease

INTRODUCTION

There is conclusive evidence that the associationbetween cholesterol and coronary heart disease

(CHD) is one of cause and effect.1 Such evidencesuggests that modifying cholesterol levels willreduce the incidence of CHD events. High levelsof cholesterol in the population are therefore

*Correspondence to: Stephen Morris, Department of Economics, City University, Northampton Square, London EC1V 0HB,UK.

HEALTH ECONOMICS, VOL. 6: 589–601 (1997)

CCC 1057–9230/97/060589–13 $17.50 Received 24 January 1997© 1997 by John Wiley & Sons, Ltd. Accepted 13 May 1997

generally associated with high rates of mortalityfrom CHD. For example, guidelines produced bythe National Cholesterol Education Program inthe USA state that in individuals free of CHD,total cholesterol levels of less than 200 mg dl–1 are‘desirable’, those of 200 to 239 mg dl–1 are‘borderline-high’ and those of greater than 240mg dl–1 are ‘high’.2 Compared with these guide-lines, the UK population has high levels of totalcholesterol: of the population aged 25–64 years,around 45% have levels of 240 mg dl–1 or above,around 35% have levels of 250 mg dl–1 or aboveand around 11% have levels over 300 mg dl–1.3

Consistent with these high levels of total choles-terol, 15.5% of all deaths in the UK are caused bymyocardial infarction.4

For those individuals with elevated cholesterollevels in whom dietary intervention has failed, avariety of drugs are available as the next stage oftherapy. Traditionally, the recommended first lineof therapy has been to use one of the bile acidsequestrant drugs, such as cholestyramine. How-ever, the relatively new generation of HMG-CoAreductase inhibitors are increasingly becomingthe drugs of first choice. Evidence suggests thatthese agents are more clinically effective inreducing cholesterol and more cost-effective thanthe bile acid sequestrants.2

The evidence in favour of programmes aimed atmodifying cholesterol levels in order to reducethe burden of CHD is compelling. However,economic criteria represent important constraintsto the introduction of such programmes becauseat a certain point additional cholesterol reduc-tions become increasingly difficult and expensiveto achieve.5 Therefore, given the growing pressureon scarce health care resources there is an interestin the application of economic evaluation to theseinterventions. There are a number of ways inwhich data relevant for the economic evaluationof cholesterol-modifying pharmacotherapy maybe obtained, including via clinical trials and viaeconomic modelling.

USING CLINICAL TRIALS TO ASSESS THECOST-EFFECTIVENESS OF

CHOLESTEROL-MODIFYINGPHARMACOTHERAPY

Clinical trials may be used to obtain data requiredfor the economic evaluation of cholesterol-mod-

ifying pharmacotherapy. Unfortunately, clinicaltrials differ from regular practice in a number ofways, so that the results from clinical trials maynot be directly transferable to practice. Forexample:

(1) clinical trials are often performed only onselected patients meeting the trial entrycriteria;

(2) clinical trials are often performed in specialistsettings and use only the most recent medicalequipment;

(3) a strict treatment protocol is often followedand care is carefully monitored; and

(4) great efforts are made to ensure that bothpatients and clinicians comply with therapy.

Therefore, there may be significant differencesbetween what happens in a clinical trial and whatactually happens in reality because clinical trialstend to concentrate on estimating efficacy ratherthan effectiveness. In order that clinical trialsreflect reality more closely, a strategy which isoccasionally followed in economic evaluations isto undertake clinical trials using a naturalisticprotocol.

The aim of naturalistic clinical trials is toevaluate the effectiveness or cost-effectiveness ofan intervention under ‘real world’ conditions. Themain design features of such trials are that:

(1) patients typical of the normal caseload areenrolled;

(2) the therapy of interest is compared withcurrent care;

(3) the setting used and physicians involved arefairly representative of the population; and

(4) the trial protocol is flexible.

A number of examples of such trials exist, someof which incorporate economic endpoints. Forexample, Oster et al.6 compared two strategies forlowering elevated cholesterol in a clinical trialbased in a health maintenance organisation(HMO) in the USA. Costs, clinical outcomes(measured in terms of post-treatment total serumcholesterol levels) and patient satisfaction for theHMO’s current regimen (pharmacotherapy withniacin followed by other agents) were assessed,compared with pharmacotherapy with lovastatin.Naturalistic studies are therefore clearly feasible,providing adequate resources are available.

However, whilst naturalistic studies do relate to

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Health Econ., 6, 589–601 (1997) © 1997 by John Wiley & Sons, Ltd.

real world conditions, they still generally onlyprovide data for the settings in which they areconducted and they are often only able togenerate results for a limited number of patientprofiles. One solution to this problem would be torepeat clinical trials in other settings and to assessa greater number of patient profiles. However,since clinical trials are generally extremely expen-sive and time consuming to conduct, such anoption is often not viable.

These problems might be resolved if a compre-hensive and generaliseable framework for per-forming economic evaluations could be used. Apossible solution might be to use economicmodelling techniques.

USING ECONOMIC MODELLING TOASSESS THE COST-EFFECTIVENESS OF

CHOLESTEROL-MODIFYINGPHARMACOTHERAPY

Rittenhouse7 distinguishes between two differenttypes of economic model: a model as a ‘simplifiedversion of reality’; and, a model used as a meansof ‘making conjectures from some measurementsource outside the context of the other observa-tions’. A distinction has also been made betweentwo different uses of this second type of model.One is to extrapolate results from clinical trialsand the other is to perform decision analysis tocompare alternative treatment strategies by inte-grating data from various sources onto the com-ponents of a decision.8,9

One use of modelling is therefore to extrap-olate beyond the often limited follow-up period ofclinical trials. When economic evaluations ofcholesterol-modifying pharmacotherapy arebased on clinical trials, in order that effectivenessof therapy may be assessed over the lifetime ofthe patient (allowing effectiveness to be measuredin terms of final health outcomes such as life-yearsgained or quality-adjusted life years gained), it isusually necessary to extend results beyond thelength of the trial. To enable this, some form ofeconomic modelling process is required. Forexample, the model by Jonsson et al.,10 focusingon secondary prevention of CHD with choles-terol-modifying pharmacotherapy, used thewithin-trial effectiveness from the ScandinavianSimvastatin Survival Study to extrapolate beyondthe end of the trial. To do this they take the

established within-trial differences in mortalityrates and assume that the additional survivors oncholesterol-modifying pharmacotherapy as com-pared with placebo (approximately four individ-uals out of every 1000) experience the lifeexpectancy of the placebo group. This gives anexpected beyond-trial effectiveness based on lifeyears gained derived directly from the trial results.In this case, economic modelling was used andthis was built upon results achieved in a clinicaltrial.

A second use of modelling allows for theconstruction of computer-generated modelswhich use decision analytic techniques for theprediction of the costs and consequences ofalternative courses of action given baseline epide-miological data. An application of the use ofeconomic modelling in this sense to the manage-ment of hypercholesterolemia is provided byDrummond et al.11 Estimates of the cost-effec-tiveness of various lipid-lowering drugs werepreviously available for a number of other coun-tries,12–15 the general conclusions being that: ‘thewidely recommended intervention limits shouldbe adjusted to include only a small proportion ofthe population and that the use of drugs should bereserved for subjects with genetic hypercholester-olaemia or those who are otherwise at very highrisk of atherosclerotic disease.’11 No such evi-dence was available specifically for the UK andthe investigators therefore sought to assess thecost-effectiveness of lifetime drug therapy withHMG-CoA reductase inhibitors. They concludedfrom their analysis that ‘the cost-effectivenessratios are comparable with those for a number ofcurrent health interventions in the UK.’11 It wasargued that intervention limits for the manage-ment of hypercholesterolaemia by drug therapyshould be set wider in the UK than in othercountries. In this case, simple generalisations fromone country to another would have been mislead-ing. It is difficult to imagine how these issuescould have been explored without the use ofeconomic modelling.

To date, 37 published studies have examinedthe cost-effectiveness of cholesterol-modifyinginterventions in the prevention of CHD.10–46 Inorder to assess the cost-effectiveness of choles-terol-modifying pharmacotherapy, it is usual tocalculate the difference in CHD incidence frompharmacotherapy against some alternative andto extrapolate this difference to changes in lifeexpectancy. By this method, life years gained

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© 1997 by John Wiley & Sons, Ltd. Health Econ., 6, 589–601 (1997)

from pharmacotherapy may be calculated. Ofthe total number of economic evaluations ofcholesterol management, 17 examining primaryprevention of CHD have used modellingapproaches using data from sources such asthe Framingham Heart Study to estimate CHDrisk as a function of a variety of riskfactors.11–14,16–18,21,24,28,31–33,35,38,44,46

The Framingham Heart Study (FHS) is a long-term epidemiological cohort study investigatingthe incidence and effects of atherosclerotic cardi-ovascular disease. The study, from its inception in1948, has conducted routine examinations at two-yearly intervals of a representative sample ofadults resident in Framingham, Massachusetts,USA, who were initially free of cardiovasculardisease. One of the primary objectives of FHS isto document the first occurrences of CHD and torecord epidemiological data on CHD risk factors.A wide range of information has been collectedabout the characteristics of individuals in thestudy both before and after the development ofCHD, as well as standardized clinical evaluationof their CHD risk status.

The general method used in economic modelsbased on FHS is to forecast CHD incidence usingCHD risk equations. These FHS-derived CHDrisk equations allow measurement of the associa-tion between one risk factor, such as totalcholesterol level and the incidence of CHD whileat the same time allowing for some variation inother risk factors (for example, age and bloodpressure). Currently, two sets of FHS-derivedCHD risk equations have been published.47,48

Those constructed by Abbott and McGee47 maybe used to estimate the risk of CHD, the risk ofmyocardial infarction and the risk of death fromCHD over an eight-year period. These FHS-derived CHD risk equations were constructedusing data from a 24-year cohort study of 4970individuals. Complete follow-up was obtained andinformation from baseline and follow-up on CHDrisk factors and CHD incidence were combinedusing logistic regression analysis. To estimate therelationship between total cholesterol and coro-nary heart disease, multiple logistic risk functionsof the following form were constructed:

P(CHD)8 = 1

1 + e–s(1)

where

s = ·l

i=0âiXi (2)

These may be used to estimate the eight-yearrisk of coronary heart disease [P(CHD)8] for anindividual with given CHD risk factors. The CHDrisk factors (the Xis) and the coefficients (the âis)estimated by Abbott and McGee are presented inAppendix 1.

FHS-derived CHD risk equations constructedby Anderson et al.48 may be used to estimate therisk of CHD over a five-year period. These wereconstructed using data from 5573 individuals whowere followed for a period of 24 years. Completefollow-up was obtained. In this case, informationfrom baseline and follow-up of CHD risk factorsand CHD incidence was combined using a para-metric regression model. To model the relation-ship between cholesterol and CHD, a Weibull riskfunction was used to estimate the five-year risk ofcoronary heart disease [P(CHD)5] for an individ-ual with given CHD risk factors. This Weibull riskfunction is of the form

P(CHD)5 = 1–exp(–et) (3)

where

t = ln5–µ

σ(4)

The CHD risk factors and equations estimated byAnderson et al. to calculate µ and σ are presentedin Appendix 2.

PROBLEMS WITH ECONOMICMODELLING

The use of modelling of this kind is justified for anumber of reasons: models are relatively inex-pensive; they are not time consuming to construct;they are flexible; and results are generalizable to arange of settings, thus allowing a wide range ofenvironments and patient profiles to beassessed.

However, the use of modelling is not without itspitfalls. Sheldon9 discusses some of the generalproblems often encountered with the use ofdecision analytic models in economic evaluations.

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The use of decision analytic modelling approachesis often problematic because by bringing togetherinformation from several sources they are proneto bias for various reasons. First, bias may arisefrom the way in which reality is representedwithin the model. For example, models may notaccurately portray treatment protocols in theclinical situation and the empirical decision-making structure may be misrepresented. Second,bias may arise from the way in which models arestructured. For example, there may be a failure tolink accurately the variables in the model and themodel syntax may be invalid. Third, models mayalso be biased by the way in which sensitivityanalysis is conducted. For example, analyses maynot be carried out thoroughly, influential variablesmay be omitted and values used in analyses maynot be justified. These problems apply to alleconomic models. In addition, there are a numberof potential problems with economic modelsspecifically used to assess the cost-effectiveness ofcholesterol-modifying pharmacotherapy usingFHS-derived CHD risk equations of the kinddescribed above.

First, most epidemiological data are collectednormally to consider the degree of associationwhich exists between defined variables such asCHD risk factors and the incidence of disease.The underlying approach is generally geared toexplanation arising from the statistical associationof variables, rather than prediction. Such epide-miological data may help explain past incidenceof CHD, but may be a poor predictor of futureincidence levels. For example, as noted by Law etal.,1 cohort studies have generally underestimatedthe impact of cholesterol on CHD mortality andmorbidity owing to regression dilution bias. Thisbias arises because cholesterol levels fluctuateover time so that any single measurement may behigher or lower than the long-term average valuefor an individual. Population groups with highercholesterol levels will include a disproportionatenumber of low-risk individuals selected becauseof a single measurement which was by chancehigher than their long-term average. The long-term mean cholesterol level will thus be overesti-mated. Therefore, the relationship between CHDincidence and cholesterol will be underestimatedin high risk groups when based on a singlemeasurements rather than on long-term valuesdue to dilution in the high risk group by low riskindividuals.

Second, the problem of prediction may be

compounded if epidemiological data and clinicaloutcome data are collected for one geographicalpopulation in one specific time period, but thenused to assess CHD risk in another geographicalpopulation and during a different time period.Economic models derived from FHS have beenused to predict CHD events and mortality forEuropean populations and it is unlikely that theunderlying incidence of disease and the riskfactors themselves will be the same across thesepopulations. Keys et al.49 compared the estimatedincidence rate of major CHD by using riskequations derived from US populations withobserved incidence rates in seven Europeancountries. Even after adjustment to risk factorlevels, major CHD incidence from the Europeanstudies were only 50% of those estimated fromthe US models. Doubts surrounding the transfera-bility of Framingham Heart Study data to non-USpopulations have been partly dispelled by Schulteand Assman,50 who demonstrated that FHS-derived CHD risk equations predicted accuratelythe incidence of CHD shown in the ProspectiveCardiovascular Munster (PROCAM) study inWestern Germany.

Third, because of the nature of economicmodelling, it is unlikely that the full set of riskfactors will be specified. For example, data collec-tion and the inclusion of CHD risk factors may belimited and interactions between risk factors maynot be modelled appropriately. For example,whilst other distributional assumptions have beenutilised, FHS-derived CHD risk equations havebeen formulated using the Normal approximationto the distribution of the logarithm of the oddsratio. The logarithm of the odds of developingCHD is given by ln(Y/1–Y) = â0 + â1X1 +ânXn, where Y is the risk of CHD occurring, theXis are the risk factors and the âis are calculatedto represent the values that most likely estimatethe impact of these risk factors in the populationstudied. It may well be the case that not all the Xisare included and additional risk factors such asbody-mass index and family history of CHD areomitted. Furthermore, whilst there are excep-tions, there is assumed generally to be no inter-action amongst the risk factors (that is, the Xis actindependently) and the effect of one risk factor isheld to be uniform across different levels of theother variables. This may not accurately reflectreality. For example, a family history of heartdisease may affect an individual’s physical activitylevel and their corresponding risk of CHD. To



account for this, product terms (such as XiXjs)may be necessary to model interaction andprovide a model which adequately fits the data.

Fourth, economic evaluations based on FHSestimate the effectiveness of cholesterol-modify-ing pharmacotherapy via changes in life expec-tancy caused solely through cholesterol modifica-tion. The method normally employed is toestimate life expectancy with and without thecholesterol-modifying effects of pharmacotherapyand to take the difference in these life expectan-cies as the life years gained from therapy. Resultsare therefore based on the assumption that theability of an agent to decrease the incidence ofCHD events is mediated entirely through changesin cholesterol levels. This may be unrealistic if theability of an agent to reduce CHD events iscaused by factors additional to cholesterolmodification.

Fifth, a bias may arise from the use of totalcholesterol as a risk factor for CHD. Recentevidence suggests that it is preferable to baseanalyses on changes in low-density lipoprotein(LDL) and high-density lipoprotein (HDL) cho-lesterol levels rather than simply on changes intotal cholesterol. This preference is for tworeasons: first, decreases in LDL cholesterol levelsand increases in HDL cholesterol levels havebeen shown to be desirable for reducing CHDmorbidity and mortality (see, for example, Man-ninen et al..51). Second, guidelines such as thoseproduced by the US National Cholesterol Educa-tion Program state that the decision to treatpatients should be based on LDL cholesterol andtarget goals of treatment are consequentlydefined in terms of LDL cholesterol.2 Therefore, amodel using principally LDL cholesterol as a riskfactor for CHD will provide better estimates ofthe cost-effectiveness of cholesterol-modifyingdrug therapy.

Sixth, an economic model based on observa-tional data such as that from FHS assumes thatmortality differences associated with natural vari-ations in the cholesterol levels of a population willbe replicated when artificially induced by treat-ments. However, as stated by Sheldon,9 becausethis assumes no changes in deaths from othercauses, economic models are likely to over-estimate the benefits of cholesterol-modifyingpharmacotherapy. This is because non-CHD sideeffects of cholesterol-modifying pharmacotherapyare likely to be excluded from the analysis.

The objective of the following analysis is to

examine the extent to which the problems asso-ciated with economic modelling in the context ofcholesterol-modifying pharmacotherapy arelikely to be realized. To achieve this, the accuracyof economic modelling will be assessed using atwo-stage process. First, predicted CHD incidenceestimates obtained using FHS-derived CHD riskequations will be compared with actual CHDincidence rates achieved in a major clinical trial(the West of Scotland Coronary PreventionStudy). Second, in using economic modelling toassess the cost-effectiveness of cholesterol-mod-ifying pharmacotherapy, whilst economic modelsmay be able to predict CHD incidence obtainedin a clinical trial, this does not necessarily meanthey will be accurate in estimating cost-effective-ness because additional assumptions in the mod-elling process may detract from the predictiveaccuracy. Therefore, so that the difference in usingeconomic modelling versus clinical trials in eco-nomic evaluations might be ascertained, a cost-effectiveness analysis will be conducted compar-ing cholesterol-modifying pharmacotherapyversus placebo using CHD incidence data fromthe clinical trial and the economic model.

METHODS

The West of Scotland Coronary Prevention Study(WOSCOPS) was a randomized double-blindplacebo-controlled trial involving men aged 45–64years with raised cholesterol levels and withoutCHD living in the West of Scotland, UK. Theprinciple aim of the trial was to test the hypothesisthat modification of cholesterol levels by treat-ment with a cholesterol-modifying agent (in thiscase, pravastatin), will lead to a reduction in theincidence of CHD.52 A total of 6595 individualswere randomly allocated to receive the inter-vention (3302 individuals) or placebo (3293individuals).53

The intervention lowered total cholesterol lev-els by 20%, lowered LDL cholesterol levels by26% and raised HDL cholesterol levels by 5%.No change was achieved in the placebo group.There were 248 definite coronary events (definedas nonfatal myocardial infarction or death fromCHD) in the placebo group compared with 174 inthe intervention group,54 implying a relativereduction in risk from the intervention of approx-imately 30%. There were similar relative reduc-

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Table 1. Mean baseline CHD risk characteristicsrelevant to FHS-derived CHD risk equations ofrandomized subjects included in the WOSCOPS,according to treatment group (source: Shepherd et al.54)

CHD risk factor Placebo Intervention

Age (years) 55.1 55.3Systolic blood pressure (mmHg) 136 135Total cholesterol (mg dl–1) 272 272HDL cholesterol (mg dl–1) 44 44Diabetes (%) 1 1Minor ECG abnormality (%) 8 8Smoking status: current smoker

or ex-smoker (%) 78 78

Table 2. Age-specific risks of specific CHD events andage-specific 4.9 year survival data for 55 year old malesfrom Framingham Heart Study (source: Hartunianet al.55)

Probability Value

P(myocardial infarction/CHD) 0.309P(angina/CHD) 0.567P(coronary insufficiency/CHD) 0.124

P(survive/myocardial infarction) 0.594P(survive/angina) 0.603P(survive/coronary insufficiency) 0.713

tions in the risk of definite nonfatal myocardialinfarctions (approximately 29%) and in the risk ofdeath from CHD (approximately 29%). Therewere 73 deaths from cardiovascular causes and 62deaths from non-cardiovascular causes in theplacebo group and 50 deaths from cardiovascularcauses and 56 deaths from non-cardiovascularcauses in the intervention. There were therefore135 deaths from all causes in the placebo groupcompared with 106 in the intervention group(4.1% versus 3.2%).54

WOSCOPS is used as the comparison withwhich to assess the ability of economic modellingto predict CHD incidence for two reasons. First,the availability of detailed published data on thebaseline characteristics of the randomized sub-jects, on cholesterol-modification and on theprimary endpoints of the study, easily facilitatessuch a comparison. Secondly, WOSCOPS is theonly large major randomized controlled trial of itskind to be conducted in the UK.

The two sets of FHS-derived CHD risk equa-tions described above are used to estimate theincidence of CHD.47,48 The epidemiological datacorresponding to the variables used in these FHS-derived CHD risk equations, obtained from base-line characteristics of randomized subjectsincluded in WOSCOPS, are presented in Table1.

WOSCOPS involved an average follow-upperiod of 4.9 years and so that CHD risks arecomparable, it is necessary to convert risksobtained using FHS-derived CHD risk equationsto an equivalent time period. The equationsrequired for this adjustment are detailed inAppendix 3. Further adjustment to the basicresults generated by FHS-derived CHD riskequations is required because the primary end-points of FHS differ to those of WOSCOPS.

Primary endpoints of WOSCOPS were: nonfatalmyocardial infarction or death from CHD; non-fatal myocardial infarction; and, death from CHD.The primary endpoint of FHS is CHD, manifestedby: myocardial infarction; coronary insufficiency;angina pectoris; sudden death from CHD; andnon-sudden death from CHD. These adjustmentsto FHS-derived CHD risks are made using age-specific risks of CHD events and age-specific 4.9year survival data for 55 year old males alsocomputed from FHS.55 The probabilities used inthese adjustments are presented in Table 2.

Using FHS-derived CHD risk equations andbaseline epidemiological data from WOSCOPS,the risk of an individual fulfilling the WOSCOPStrial entry criteria developing CHD over a 4.9year time period may be estimated. This may thenbe compared with the actual incidence of CHDevents obtained by individuals in WOSCOPS sothat the predictive accuracy of the economicmodel may be assessed. A number of comparisonsare made. First, the predicted versus actual risk ofCHD is calculated for the placebo group. Second,the predicted versus actual risk of CHD iscalculated for the intervention group. Third, therelative risk of CHD for the intervention groupcompared with the placebo group is assessedusing the risks obtained by FHS-derived CHDrisk equations and by WOSCOPS. Fourth, the riskreduction is calculated for the intervention grouprelative to the placebo group, also using bothmethods.

RESULTS

The risks of CHD events calculated for bothplacebo and intervention groups using FHS-derived CHD risk equations and WOSCOPS are



Table 3. Comparison of actual risks of CHD eventsobtained by WOSCOPS and FHS-derived CHD riskequations

Placebo Intervention

P(nonfatal MI ordeath from CHD):Abbott and McGee47 0.116 0.088Anderson et al.48 0.065 0.047WOSCOPS54 0.079 0.055

P(nonfatal MI):Abbott and McGee47 0.028 0.022WOSCOPS54 0.065 0.046

P(death from CHD)Abbott and McGee47 0.019 0.013WOSCOPS54 0.017 0.012

presented in Table 3. The relative risks of develop-ing CHD and the risk reduction for the inter-vention group relative to the placebo group arepresented in Table 4. For example, from theWOSCOPS trial, the risk of an individual fulfillingthe trial entry criteria incurring nonfatal myocar-dial infarction or CHD death in 4.9 years is 0.079for placebo group and 0.055 for the interventiongroup.54 Therefore, the relative risk for theintervention group relative to placebo group is0.696, implying a risk reduction of 30%. Compa-rable risks predicted using FHS-derived CHD riskequations constructed by Abbott and McGee47

are 0.116 for the placebo group and 0.088 for theintervention group. Consequent relative risks andrisk reductions for the intervention relative toplacebo are 0.757 and 24%, respectively.

In all cases, relative risks estimated using FHS-derived CHD risk equations lie within the bound-aries of the 95% confidence intervals set byWOSCOPS. This is only a weak indication of thepredictive accuracy of the economic models,however, because whilst the relative risks pre-dicted by the models are not significantly differentfrom those achieved in the clinical trial, theunderlying relative risks may not necessarily bethe same. There are unfortunately no otherstatistical means by which the CHD risksobtained using FHS-derived CHD risk equationsand by WOSCOPS may be compared.

COST-EFFECTIVENESS ANALYSIS

Whilst economic models may be able to predictCHD incidence obtained in a clinical trial, thisdoes not necessarily mean they will be accurate inestimating cost-effectiveness because additionalassumptions in the modelling process may detractfrom the predictive accuracy. So that the impact ofusing economic modelling versus clinical trials inthe economic evaluation of cholesterol-modifyingpharmacotherapy might be ascertained, therefollows a cost-effectiveness analysis comparingcholesterol-modifying pharmacotherapy versusplacebo. Cost-effectiveness is calculated firstlyusing CHD risks predicted by FHS-derived CHDrisk equations and then using CHD risks obtainedfrom WOSCOPS.1

Cost-effectiveness is measured in terms ofincremental costs per life year gained relative toplacebo. This is calculated as the ratio of the netchange in costs from the intervention to the netchange in life expectancy or (D + M – C)/L,where D is the expected lifetime cost of drugtherapy, M is the expected lifetime cost ofmonitoring and treatment of drug-related side-effects, C denotes the expected savings in lifetimeCHD treatment costs from a reduced incidence ofCHD due to drug therapy and L is the expectedincrease in life expectancy resulting from theintervention.

All future costs and changes in life expectancyare discounted to present values at an annual rateof 6%. All costs are estimated in UK poundssterling and calculated in constant 1996 prices.

Measuring effectiveness

The effectiveness of pharmacotherapy is con-sidered by estimating the relationship betweenCHD risks and consequent effects on life expec-tancy. To be consistent with WOSCOPS, CHDevents are limited to nonfatal myocardial infarc-tion and death from CHD. CHD risks presentedin Tables 3 and 4 are assumed to persist through-out the life of the individual. These risks are usedto estimate the likelihood of dying from CHD upto age 75. By calculating life expectancy with

1The cost-effectiveness data calculated here are derived simply to highlight the relationship between estimates made using FHS-derived CHD risk equations and trial data, and do not pretend to be an extensive economic evaluation of the WOSCOPS data.Nor are they official estimates produced by WOSCOPS.

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Table 4. Comparison of actual relative risks and reductions in risk obtained by WOSCOPS andFHS-derived CHD risk equations

Relative risk Risk reduction (%)

P(nonfatal MI or death from CHD):Abbott and McGee47 0.757 24Anderson et al.48 0.719 28WOSCOPS (with 95% C.I.)54 0.696 30 (17 to 43)

P(nonfatal MI):Abbott and McGee47 0.791 21WOSCOPS (with 95% C.I.)54 0.708 29 (15 to 45)

P(death from CHD):Abbott and McGee47 0.692 31WOSCOPS (with 95% C.I.)54 0.706 29 (–10 to 52)

Table 5. Comparison of effectiveness, costs and cost-effectiveness of cholesterol-modifying pharma-cotherapy obtained using WOSCOPS data and FHS-derived CHD risk equations

Model Trial

Effectiveness (years):Intervention 12.393 12.414Placebo 12.266 12.308Life years gained 0.127 0.106

Costs (£):Intervention 5917 6323Placebo 1284 1902Incremental costs 4633 4421

Cost-effectiveness (£):Incremental costs

per life year gained 36480 41707

intervention and placebo, life years gained fromintervention may be estimated.

Estimating costs

Components of the cost analysis are: screening;drug therapy; initiation of drug therapy; monitor-ing of drug therapy; treating side-effects of drugtherapy; treating nonfatal myocardial infarction;and death from CHD.

Annual drug costs of £405 are taken frompublished UK NHS costs.56 Initial screening costsare £45. The annual costs of monitoring drugtherapy and treating side-effects are £130. Anadditional therapy initiation cost of £100 isincluded in the first year, representing the needfor extra clinical visits and tests when patients arefirst placed on a new drug. The average treatmentcosts for CHD events avoided through choles-terol-modifying pharmacotherapy are £1643 fornonfatal myocardial infarction and £401 for deathfrom CHD.

All non-drug cost data have been updated fromcomprehensive UK-based cost analyses,11,57 andaverage GP fundholding extra contractual refer-ral tariffs and average procedure costs for cardiol-ogy services for all Regional Health Authorities inEngland and all Health Boards and NHS Trusts inScotland.

Estimating cost-effectiveness

Effectiveness and cost data were combined tocalculate the incremental costs per life yeargained from intervention relative to placebo(Table 5). Discounted gains in life years are 0.106

using WOSCOPS data and 0.127 using FHS-derived CHD risk equations. Discounted incre-mental costs are £4421 using WOSCOPS data and£4633 using FHS-derived CHD risk equations.Therefore, incremental costs per life year gainedfrom the intervention are £41 707 usingWOSCOPS data and £36 480 using FHS-derivedCHD risk equations.

DISCUSSION

It is generally the case that economic modelling isable to predict fairly accurately the incidence ofCHD experienced by individuals fulfilling theWOSCOPS trial entry criteria. FHS-derivedCHD risk equations substantially underestimatethe actual risks of nonfatal myocardial infarctionobtained by WOSCOPS. However, in predicting



risks of death from CHD, FHS-derived CHD riskequations estimate extremely accurately the inci-dence obtained by WOSCOPS. These resultssuggest that the fairly accurate predictions ofnonfatal myocardial infarction and CHD deathtogether are the result of a combination pooraccuracy in predicting nonfatal myocardial infarc-tion, but extremely good accuracy in predictingCHD death.

This has obvious implications for the economicevaluation of cholesterol-modifying pharmaco-therapy in the primary prevention of CHD.Because FHS-derived CHD risk equations areable to predict accurately the risk of death fromCHD, but not the risk of nonfatal myocardialinfarction, it is therefore possible to predictaccurately CHD mortality, but not necessarilyCHD morbidity. Economic models examiningprimary prevention of CHD will therefore reflectthe results of clinical trials provided effectivenessis measured in quantitative rather than qualitativeterms (that is, in terms of quantity of life ratherthan quality of life). In other words, economicmodels can accurately estimate life expectancygiven a particular CHD risk profile, so that lifeyears gained from pharmacotherapy may becalculated. This is borne out by the cost-effective-ness analysis conducted, where estimates of effec-tiveness, costs and cost-effectiveness obtainedusing economic models closely resemble thoseobtained using clinical trials. However, for cost-utility analyses where effectiveness measures alsoinclude CHD-related quality of life, economicmodels may be imperfect since nonfatal CHDevents which impact on quality of life may not beaccurately predicted.

Of the 17 published economic evaluations ofcholesterol-modification in the primary preven-tion of CHD which have used FHS-derived CHDrisk equations, 16 measured cost-effectiveness interms of costs per life yeargained11–14,16–18,21,27,28,31–33,35,38,46 and one meas-ured cost-effectiveness in terms of costs perquality adjusted life year gained.44

In the absence of strong statistical inference, itis difficult to draw any firm conclusions regardingthe accuracy of economic modelling using FHS-derived CHD risk equations compared withWOSCOPS. It is therefore difficult to ascertainwhether CHD incidence predicted by economicmodelling reflects that achieved in the clinicaltrial and to what extent the estimates of cost-effectiveness are similar. Nevertheless, in

response to the potential problems with economicmodelling, because the incidence of CHD pre-dicted by FHS-derived CHD risk equations wouldappear to reflect reasonably well that achieved inWOSCOPS and since consequent cost-effective-ness data based on these estimates are similar,claims regarding the inaccuracy of economicmodels when estimating the cost-effectiveness ofcholesterol-modifying pharmacotherapy may beunfounded. Of course, the results of this analysismay not be generalizable if models are unable topredict accurately results obtained in other clin-ical trials. However, the use of economic model-ling based on FHS-derived CHD risk equationswould appear to be at least partly justified by thisanalysis, particularly for the prediction of CHDdeath.

APPENDIX 1

The CHD risk factors and multiple logistic riskfunction coefficients for risk of CHD, myocardialinfarction and CHD death in eight years con-structed by Abbott and McGee47 are given inTable A1.

APPENDIX 2

The CHD risk factors and equations derived fromFHS to estimate risk of CHD constructed byAnderson et al.48 are as follows.

Compute an interim value a that is based onrisk factor measurements, as follows:

a = 11.1122–0.9119´ln(systolic blood pressure)–0.2767´(cigarette smoking)–0.7181´ln

(total cholesterol/HDL cholesterol)–(0.5865´(left ventricular hypertrophy)(A1)

Then compute a second interim value m, asfollows:

m = a–1.4792´ln(age)–0.1759´diabetes (A2)

From these two interim values we can calculatevalues for µ and σ as follows:

S. MORRIS598


Table A1. CHD risk factors and multiple logistic risk function coefficients

bi (myocardiali Xi bi (CHD)a infarction)b bi (CHD death)c

0 Constant –17.4477 –17.7341 –18.77201 Age 0.3091 0.2926 0.24182 Systolic blood pressure 0.0142 0.0140 0.02003 Cigarette smoking 0.4098 0.4271 0.65814 Glucose intolerance 0.2077 0.3131 –0.20215 Left ventricular hypertrophy 0.4300 –0.2302 0.68146 Total cholesterol 0.0226 0.0232 0.01937 Age´age –0.0017 –0.1144 –0.00118 Age´total cholesterol –0.0003 –0.0003 –0.0002

a bis to calculate eight-year risk of CHD.b bis to calculate eight-year risk of myocardial infarction.c bis to calculate eight-year risk of CHD death.

µ = 4.4181 + m (A3)

σ = exp (–0.3155–0.2784m) (A4)

APPENDIX 3

To transform n-year estimates of CHD risk,P(CHD)n, into m-year estimates, P(CHD)m, firstestimate the probability that an individual will notdevelop CHD in n years, P(–CHD)n:

P(–CHD)n = 1–P(CHD)n (A5)

The probability of not developing coronary heartdisease in m, years, P(–CHD)m, is estimated byadjusting this figure to the power m/n:

P(–CHD)m = [P(–CHD)n]m/n (A6)

The m-year probability of coronary heart diseaseis one minus this figure:

P(CHD)m = 1–P(–CHD)m (A7)

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