Whose costs and benefits? Why economic. evaluations should simulate both prevalent and

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1 Why economic evaluaions should simulae boh prevalen and all fuure inciden paien cohors Marin Hoyle, PhD Research Fellow Rob Anderson, PhD Senior Lecurer Peninsula Technology Assessmen Group (PenTAG), Peninsula Medical School, Universiies of Exeer and Plymouh, Exeer. orrespondence and reprins o: Dr M Hoyle PenTAG Insiue for Healh Services Research Noy Sco House Royal Devon & Exeer Hospial Barrack Road Exeer EX DW Unied Kingdom Tel: + 0 Fax: marin.hoyle@pms.ac.uk Financial suppor: The work repored in his paper was unfunded. Running head: NB: An earlier version of his manuscrip was discussed a he UK Healh Economics Sudy Group winer meeing in January 00. Word coun: (excl Absrac, references, legends) =,

2 Absrac 0 0 Background Mos healh echnology economic evaluaions simulae only he prevalen cohor, or he nex inciden cohor of paiens. They herefore do no capure all fuure paien-relaed benefis and coss. Obecive We show how o esimae and aggregae he IERs for boh currenly eligible (prevalen) and fuure (inciden) paien cohors, wihin he same model-based analysis. We show why, and in wha circumsances, he prevalen and inciden cohor IERs are likely o differ. Mehods Algebraic expressions were developed o capure all componens of he IER in hypoheical cohors of all prevalen paiens and fuure inciden paiens. Numerical examples are used o illusrae he approach. Resuls The IER for he firs (i.e. nex) inciden cohor is equivalen o he IER for all fuure inciden cohors only when he discoun raes for coss and benefis are he same; oherwise, when he discoun rae for benefis is lower han for coss, he IER for all fuure inciden cohors is lower han he IER for he firs inciden cohor. Separae simulaion of prevalen and inciden paiens reaed for a hypoheical progressive chronic disease shows widely differen IERs according o which paien cohors were included when he discoun raes were equal. onclusions In many circumsances, boh he prevalen cohor and all fuure inciden cohors should be modelled. The need for his approach will depend on he likely difference in he IERs for prevalen and inciden paiens, he relaive size of he wo ypes of cohor, and wheher coss and benefis are discouned a equal raes.

3 Key words: cos-effeciveness analysis, IER, decision modelling, chronic disease, echnology assessmen. Inroducion I is increasingly recognised ha o inform decision-making a a regional or naional level, incremenal cos-effeciveness raios (IERs) need o be based on rigorously informed decision model-based analyses which compare he incremenal coss and effecs of all relevan comparaors, and ypically for he remainder of paiens 0 lifeimes. Also, o be consisen wih he fundamenal enes of cos-benefi analysis, such models should enable he valuaion of coss and benefis in each year of he proec (p.), or for he whole of a healh echnology s life. The prevalence and incidence of a disease are fundamenal conceps in epidemiology. The prevalence is he number of cases in a populaion a a specified poin in ime, and he incidence is he number of new cases arising in a given period in a populaion. We apply he equivalen conceps of he prevalen cohor and fuure 0 inciden cohors o model-based cos-effeciveness analysis. We define he prevalen cohor as hose paiens eligible for he new echnology a he ime he echnology is firs inroduced. Any given paien will be eligible from he ime when he echnology is firs clinically appropriae (e.g. us diagnosed wih muliple sclerosis and eligible for drug reamen, or when firs eligible for a hip replacemen) unil he ime when he new echnology is no longer appropriae (e.g. paien dies, or he disease has reached such a severe sae ha he drug is no longer effecive, or he paien is oo old o receive a hip replacemen). Nex, we define he inciden cohor saring years in he fuure (i.e. years afer he dae of a echnology s inroducion) as comprising hose paiens who firs become eligible for he new echnology (e.g. diagnosed) years in he fuure.

4 0 os-effeciveness sudies generally model eiher only he firs inciden cohor of paiens or only he prevalen cohor. We argue firs ha model-based economic evaluaions of new reamens should model he coss and benefis of all paiens in he prevalen cohor and in all fuure inciden cohors over he life of he echnology. We furher recommend ha overall cos-effeciveness should be based on all hese cohors combined, i.e. ha he IER be calculaed from a weighed sum of all hese coss and benefis. The curren ISPOR guidance on good pracice in decision analyic modelling focuses mainly on he srucure of he model, he validaion of he model esimaes/inpus, and he choice beween alernaive simulaion models (e.g. Mone arlo vs. cohor). However, aside from some general encouragemen o sraify 0 models by paien sub-groups, here is no specific advice on wha saring populaions should go ino a decision model. Nor does mehods guidance from naional healh echnology assessmen agencies sae wha curren and fuure populaions of paiens should be included in model-based analyses, e.g. UK, Ausralia, New Zealand, anada, Germany. In his paper, we describe he mahemaics for esimaing he IER ha includes he coss and benefis for boh he prevalen and all fuure inciden cohors. For simpliciy, we consider a new echnology versus a single comparaor echnology, bu he comparaor echnology could represen no reamen. Equivalen equaions for more han wo comparaors in a ne moneary benefi framework are given in he Online Appendix. The echnologies can be eiher a drug, a medical device, or a screening program. We sugges parameers relaed o he srucure of he paien cohors ha could be included in he probabilisic sensiiviy analysis.

5 0 IER for inciden cohors Firs fuure inciden cohor onsider a cos-effeciveness model where fuure coss and benefis are modelled a discree imes (e.g. a Markov model). Suppose he incremenal coss, per paien saring reamen, beween he new and comparaor echnology (where he comparaor echnology could be no echnology, i.e. bes supporive care), in cycles 0,,,., H are K 0, K, K,., K H and incremenal benefis B 0, B, B,., B H (Table ). The ime horizon is H cycles. For clariy, given ha he K and B are expressed per paien saring reamen, hese quaniies end o zero wih cycle, as paiens die. Then he IER as currenly calculaed for healh echnology assessmens for he firs fuure inciden cohor, given discoun rae for coss of r* and benefis r* B over a cycle; IER (firs fuure inciden cohor) = H H 0 0 v v * * B K B where we define r v * *, r v * B * B. 0 All fuure inciden cohors Now assume, more realisically, ha a new cohor of paiens will become eligible for reamen wih he new or comparaor echnologies a he sar of each of T years in he fuure. The new and comparaor echnologies are assumed o become obsolee afer T years, possibly replaced by anoher echnology. In his paper, we presen all analyses wih closed-form algebra o aid undersanding of he mehods. However, i is of course possible o simulae each fuure inciden cohor. In general, assume ha

6 0 he number of eligible paiens a he sar of each cohor, relaive o he number of eligible paiens a he sar of he firs year, is given by n, a year, so ha n 0 =. The n are commonly used in budge impac analyses. The n could increase wih year, for example o model increasing numbers of Type diabees paiens in he fuure as obesiy becomes more common. Assume furher ha he probabiliy ha an eligible paien is given he new echnology in he h year in he fuure is p. The p could be described as he rae of adopion, rae of upake or marke peneraion of he new echnology, and are also commonly used in budge impac analyses. The graph of he volume of sales of a drug, i.e. he produc n p, agains year is generally -shaped. 0 The annual volume of a drug sold ypically increases in he firs decade afer drug launch, reflecing he diffusion of he new drug afer launch. The annual volume of a drug sold in he second decade afer launch reflecs pos- paen experience and declines as paiens swich o newer drugs. 0; Then, he relaive number of paiens in he inciden cohor saring years in he fuure affeced by he new echnology is n p. By analogy wih he special case of wo fuure inciden cohors (see Online Appendix); T 0 IER (all inciden cohors) = T 0 n p v n p v B IER (firs inciden cohor) (Equaion ) 0 where v r and v B r B, and r and r B are he iner-generaion annual discoun raes for coss and benefis beween he curren ime and he ime of he fuure inciden cohors. By conras, r* and r* B are he (per cycle) inra-generaion discoun raes. We furher assume ha undiscouned incremenal coss and benefis are he same for all inciden cohors.

7 From Equaion, he IERs for all fuure inciden cohors combined and for he firs fuure inciden cohor are equal if he cos and benefi discoun raes, r and r B, are equal. Alernaively, if r > r B, he IER for all inciden cohors is lower (see Online Appendix). For example, in he Neherlands, where coss are discouned a % and benefis a.% per year, under cerain assumpions, he IER for all fuure inciden cohors combined may be abou ¾ of he IER assuming a single inciden cohor (i.e. as calculaed in he radiional way) (see Online Appendix). When n p is equal for all, Equaion simplifies o; 0 vb v IER (all inciden cohors) = T v v B T IER (firs inciden cohor) (Equaion ) Now, if we assume ha n p follows a -shaped quadraic curve, as is ofen he case wih drug sales volumes, 0 hen Equaion is applicable again (see online Appendix). If independen esimaes of n p are available hen hey should be used in Equaion, oherwise Equaion is appropriae. Equaion is convenien since we need only have an esimae for he single parameer T, no he n p for all. 0 IER for prevalen cohor In addiion o he paiens who will become eligible for he new echnology in he fuure, here may be paiens who are already eligible a he ime he echnology is inroduced. Such prevalen paiens would swich from he curren o he new echnology. Denoing he incremenal coss and benefis of he prevalen cohor a

8 cycle = 0.H, expressed per paien a he sar of he prevalen cohor, by, and Q, he IER for he prevalen cohor is; H 0 H 0 v v * * B Q (Equaion ) IER for inciden and prevalen cohors combined 0 We define N as he number of paiens in he prevalen cohor ha are eligible for reamen, relaive o he number of paiens in he firs fuure inciden cohor, and p as he probabiliy ha a paien in he eligible prevalen cohor is given he new echnology, assumed consan over cycle. Then in he general case of any number of reamens, he opimal sraegy is o choose he reamen wih he maximum expeced ne benefi (see Online Appendix). Reurning o he paricular case of wo reamens alernaives, we calculae he IER as a raio of means, in he erminology of Sinne & Paliel (). In paricular, he IER equals oal incremenal coss divided by oal incremenal benefis during he whole ime he echnology is used: IER (prevalen and all fuure inciden cohors) = 0 pn pn H 0 H 0 v v * * B Q T 0 T 0 n p v n p v B H 0 H 0 v v * * B K B (Equaion )

9 0 0 In his equaion we make he simplifying assumpion ha he proporion of paiens in a given inciden cohor ha are given he new echnology, p, does no change over cycle. Noe ha if he cos and benefi discoun raes are equal, hen Equaion implies ha he IER for he prevalen and inciden cohors combined will lie beween he IER for he prevalen cohor alone and he IER for he firs fuure inciden cohor alone. We now inroduce parameers o allow us o esimae N and p. Denoe he average age of paiens a he sar of any inciden cohor as A (assumed consan over ime). Suppose a paien is eligible for reamen wih he new echnology over an average period of M years, from age A o age A+M. To avoid confusion, noe ha parameer M relaes o he age range of any given paien. I should no be confused wih parameer T, which relaes o he age (lifeime) of he echnology. oss direcly associaed wih he echnology occur during some, bu no all he period of eligibiliy. For example, for paiens in he inciden cohor, he cos of a hip replacemen occurs a he very sar of he period of eligibiliy, whereas, he cos of a drug for a chronic condiion migh occur over he whole period of eligibiliy, M. When M is small, e.g. reamens for acue infecion, he coss and benefis of he inciden and prevalen cohors are similar, because he paiens iniial parameers, such as he average age and average severiy of condiion are similar beween he inciden and prevalen cohors (see below). onversely, when M is large, for example, for long-erm herapies for chronic condiions, he coss and benefis of he inciden and prevalen cohors can be subsanially differen for a variey of reasons. Hence he IER for he prevalen cohor is similar o he IER for he inciden cohor for acue condiions, bu can be very differen for chronic condiions. On average, we would expec ha paiens in he prevalen cohor will be approximaely half way hrough heir reamen wih he comparaor echnology. orrespondingly, we expec ha paiens a he sar of an inciden cohor (i.e. a he

10 0 sar of heir reamen) o be reaed for approximaely wice he lengh of ime as paiens in he prevalen cohor. If he number of paiens in he prevalen cohor ha are eligible for reamen, relaive o he number of paiens in he firs fuure inciden cohor, N, is known from he lieraure, hen his value should be used. For example, he annual incidence of end-sage renal disease in he UK in 00 was, paiens, and he prevalence was,, which gives N =, /, =.. Alernaively, we now describe how o esimae N. Denoe he probabiliy ha a paien who is reaed wih he comparaor echnology survives from age A, a he sar of an inciden cohor, o age A + as s ( A, A ). Such daa are ofen available from cos-effeciveness models. Then; N M n s( A, A ) n s( A, A ) n s( A, A )... n s( A, A M ) (Equaion ) 0 Hence when M is large, for condiions ha require a long period of reamen, N is large, and when M is small, for condiions ha require shor-erm reamen, for example acue infecion, N is small. We esimae p as he weighed average of he p, wih he weighs equal o he number of paiens in he prevalen cohor years in he fuure; M M pn is( A, A i) 0 i 0 p M M (Equaion ) n s( A, A i) 0 i 0 i 0

11 where subscrip -i refers o he inciden cohor ha sared i years in he pas. Now suppose he cos and benefi discoun raes are equal, i.e. v = v B = v. Then Equaion becomes; IER (prevalen and all fuure inciden cohors) = T 0 T 0 pn n p v pn n p v H H * v 0 0 H H * v Q 0 0 v v * * K B From which i is clear ha he prevalen cohor is negligible when T 0 pn n p v is 0 small. This is rue when T is very large, or M is very small. We now consider hree cases; : Parameers for boh he inciden and prevalen cohors are known : Parameers for inciden cohor only are known : Parameers for prevalen cohor only are known 0 ase : Parameers for inciden and prevalen cohors known Suppose we know he model parameers for boh he inciden and prevalen cohors from lieraure reviews of primary research. Then we can calculae, Q, K, and B. We hen calculae he IER for he inciden and prevalen cohors combined from Equaion, using an esimae of he p and hence p (as explained in he

12 0 Discussion). To calculae he, Q, K, and B direcly, we would need daa from wo ypes of clinical rial. One rial (or rial subgroup) wih paiens from an inciden cohor, i.e. newly diagnosed, and anoher rial wih paiens from he prevalen cohor. This would be especially useful if paiens respond differenly o a new echnology according o previous reamens received, for example, for coricoseroids for ashma. If he prevalen cohor is large relaive o he inciden cohor, he range of values of inpu parameers, such as paien age and disease severiy, for paiens in he prevalen cohor may be wide. In his case, i may be preferable o allow for such heerogeneiy of inpu parameers in he cos-effeciveness model which is used o generae he and Q for he prevalen cohor. For example, he model could be run for each of a range of paien ages, and he and Q esimaed as a weighed average of he incremenal coss and benefis for each model run, wih weighings proporional o he probabiliy densiy funcion of each age (e.g. as in Dewilde & Anderson 00). 0 ase : Parameers for inciden cohor only known Suppose we know he parameer values for he inciden cohor only, e.g. if he clinical rial(s) were based on inciden cohors of paiens only. We now ouline a mehod for esimaing he incremenal coss and benefis for he prevalen cohor,, Q. As above, we hen calculae he IER for he inciden and prevalen cohors combined from Equaion. In he Online Appendix, we describe an alernaive mehod for esimaing and Q, where we esimae he parameer values ha specify he characerisics of paiens a he sar of he prevalen cohor. Alhough his second mehod is simpler o implemen han he firs mehod, i is slighly less accurae because we assume no variabiliy in he inpu parameers of he prevalen cohor.

13 Reurning o he firs mehod, suppose he coss in he inciden cohor, expressed per paien a he sar of he inciden cohor, are K and K' a cycle = 0 H for he new and comparaor echnologies respecively (Fig. ). As above, we assume ha hese coss are he same across all inciden cohors. We canno simply assume ha he fuure coss wih he new echnology for he inciden cohor ha sared in year (i.e. in he pas, so ha is negaive), K,, cycles since he sar of he inciden cohor, are given by K, because his would assume (incorrecly) ha paiens had been reaed wih he new echnology in he pas. Insead, in he Online Appendix, we show how o esimae he K, by an algorihm, which can be coded as 0 a macro. The prevalen cohor coss and benefis for he new echnology a cycle = 0 H are calculaed as K, n N and Q Q, n N and for he ( M ) ( M ) comparaor echnology as K ( M ) n N and Q Q ( M ) n N (Fig. ). 0 ase : Parameers for prevalen cohor only known In he Online Appendix, we describe a mehod o esimae he incremenal coss and benefis for he inciden cohor, K, B, given ha we know he parameer values, e.g. average age, for he prevalen cohor only. As above, once we esimae K, B, we calculae he IER for he inciden and prevalen cohors combined from Equaion. Example of applicaion

14 Here, we apply he mehods described above o an example cos-effeciveness model of a new mainenance drug versus an exising comparaor drug o rea a chronic progressive condiion. Deails of he model srucure and resuls are given in he Online Appendix, however we provide a brief descripion here. We assume ha he new drug will be used in he healh sysem for he nex T = 0 years, and ha he probabiliy ha a paien eligible for reamen akes he new drug a ime, p, follows a -shaped quadraic curve. The relaive number of paiens in he inciden cohor, 0 0 n, is assumed equal over ime. The new drug reduces he rae of disease progression. Non-drug coss increase and uiliies decrease wih increasing disease severiy. The average age a diagnosis, i.e. a he sar of an inciden cohor, A = 0 years, and we assume a cerain disribuion across disease severiy saes for paiens in he inciden cohor. Paiens were modelled from age 0 o deah or age 00. This gives M = 0 years over which paiens are eligible o be reaed wih he new drug. We esimae ha he prevalen cohor is N = imes he size of a single inciden cohor (Equaion ), and he average age of paiens in he prevalen cohor is approx. years, compared o A = 0 years in he inciden cohor. As expeced, paiens are a a more advanced sage of illness in he prevalen cohor compared o he inciden cohor. The IER for he firs inciden cohor was calculaed as,000 per qualiy-adused life year (QALY). Given ha he cos and benefi discoun raes were assumed equal, he IER for all fuure inciden cohors combined was also,000 / QALY. The oal discouned coss and benefis for he prevalen cohor were calculaed using he algorihm described in he Online Appendix (Fig. ). The IER for he prevalen cohor alone was subsanially higher, a,000 / QALY, and for boh he prevalen and all inciden cohors combined,,000 / QALY.

15 0 Discussion In his paper we have argued ha he cos-effeciveness of a reamen should be assessed in relaion o all paiens whose coss and benefis will be affeced; boh hose currenly eligible and hose who will become eligible for he new reamen in he fuure. On average, paiens in he prevalen cohor will be older and will ypically be a a more advanced sage of disease han paiens in he inciden cohor. Furhermore, he more life-years over which he echnology is applicable for paiens (e.g. mainenance herapies for chronic condiions), he greaer hese differences. In summary, he suggesions in his paper are paricularly imporan o implemen in cos-effeciveness analysis in any of he following circumsances: for long-erm herapies for chronic condiions (paricularly for chronic progressive condiions), e.g. Alzheimer s disease, muliple sclerosis, cysic fibrosis, diabees, eczema, rheumaoid arhriis. when he discoun raes for coss and benefis differ. 0 In hese cases, he IER as calculaed in his paper for all affeced paiens may differ subsanially from he IER as radiionally calculaed (for he nex inciden cohor). In paricular, we have described a simplified bu realisic example coseffeciveness analysis of a chronic progressive condiion, assuming equal cos and benefi discoun raes. In his example, he IER as calculaed by our mehod is. imes he IER as radiionally calculaed by assuming us a single inciden cohor, and 0. imes he oher radiional mehod of assuming a single prevalen cohor. We have shown ha when he discoun raes for coss and benefis differ, i is paricularly imporan o esimae he coss and effeciveness of all fuure inciden cohors. While many healh economiss, and mos counry s official guidance for

16 0 0 he cos-benefi analysis of healh echnologies, recommend equal discoun raes for coss and benefis he maer is by no means seled. Some sugges r should be greaer han r B. -0 In paricular, Brouwer e al (00) recommend r =.% and r B =.%, and Gravelle & Smih (00) sugges ha r should be -% greaer han r B. There remain some counries where differen discoun raes are recommended for healh care economic evaluaions (e.g. Neherlands: r = %, r B =.%; and Belgium: r = %, r B =.%; source, ISPOR websie ). An obvious quesion is: when he prevalen cohor is no negligible, when is he IER for he prevalen cohor greaer han he IER for he firs fuure inciden cohor, and vice versa? We sugges an answer o his quesion for hree ypes of condiions-wih-reamens. Firs, we have shown ha for he example coseffeciveness model of a coninuous reamen for a progressive chronic disease, he prevalen cohor IER is subsanially greaer han he inciden cohor IER, because a each cycle, he raio of incremenal coss o incremenal benefis is greaer for he prevalen cohor (Fig. online Appendix). This may be a ypical resul for a progressive chronic condiion, suppored by economic evaluaions in cardiology. Neverheless, his quesion warrans furher analysis, paricularly since a conrary resul has been found in a cos-effeciveness sudy of a choleserol-lowering sain. In his sudy, he incremenal cos per life year gained was lower for older paiens han for younger paiens. The difference in he IERs was due o higher incremenal coss in he younger age group, bu similar incremenal life years gained. Whils hese wo paien groups did no correspond o inciden and prevalen cohors, his resul does sugges ha he prevalen cohor IER may, in some cases, be lower han he inciden IER, given ha paiens in he prevalen cohor are, on average, older han hose in he inciden cohor. Second, we consider a coninuous reamen for a non-progressive chronic condiion, such as ashma. Suppose here are wo healh saes A and B, and paiens are in he worse sae A (e.g. poorly conrolled ashma) under he

17 comparaor drug and he beer sae B under he new drug. Suppose furher ha life expecancy is independen of he drug and ha coss are a funcion us of he drug (higher for he new drug) and wheher he paien is in sae A (higher) or sae B (lower). Furher, suppose ha paien uiliy is a funcion of us he sae, and is higher in sae B han in sae A. In his case, he raios of incremenal coss and benefis K and B Q are consan over cycle and are he same for he inciden 0 and prevalen cohors. Hence he prevalen cohor IER equals he inciden cohor IER. Third, consider he scenario where he maoriy of coss are incurred up fron for chronic condiions. This is paricularly appropriae for medical devices, such as cardiac pacemakers for hear condiions and cochlear implans for deafness. Again, suppose here are wo healh saes A and B, and suppose ha paiens are in he worse sae A under he comparaor echnology and in he beer sae B under he new echnology. Again, suppose ha life expecancy is independen of he echnology. Suppose he cos of he echnology, e.g. cos of cochlear implan iself plus cos of implanaion surgery, is incurred in he firs cycle, and is greaer for he new han he old echnology. Healh sae coss can be higher or lower in sae A han in sae B. Paien uiliy is again solely a deermined by healh sae. In his case, for he inciden and prevalen cohors, he raios of incremenal coss and 0 benefis K and B Q are high in he firs cycle, and far smaller in all fuure cycles. The raios for he wo cohors are equal by cycle. However, given ha paiens are older in he prevalen han in he inciden cohor, and will herefore use he echnology for fewer years, in he prevalen cohor, here will be fewer cycles wih low incremenal cos/benefi raios. Hence, he prevalen cohor IER will be greaer han he inciden cohor IER.

18 Anoher quesion is wheher he IER calculaed according o our approach will be greaer or smaller han he IER as radiionally calculaed. In general, i is no possible o say: some echnologies will appear more cos-effecive, and ohers less cos-effecive. onsider firs he case when he prevalen cohor is negligible compared o he inciden cohor, for example wih reamens for acue condiions. Then, if he cos and benefi discoun raes are equal, he IER will no change. Alernaively, if he discoun rae for coss is greaer han he rae for benefis, he IER will be less han radiionally calculaed. Now, assume ha he prevalen cohor is no negligible. In previous model-based cos-effeciveness analyses, eiher; 0 : all paien-relaed parameers (e.g. average age, average disabiliy level) refer o he prevalen cohor, or : all paien-relaed parameers refer o he inciden cohor, or : some parameers refer o he prevalen cohor and he res o he inciden cohor. 0 Again, assuming equal discoun raes, in he expeced scenario ha he prevalen cohor IER is greaer han he inciden cohor IER, he combined IER as calculaed here would be lower han he IER calculaed in case, greaer han in case, and uncerain in case. onversely, in he less likely even ha he prevalen cohor IER is lower han he inciden cohor IER, hen hese conclusions are reversed. However, in a review of model-based cos-effeciveness analyses, we found very few sudies ha explicily sae wheher model parameers were derived from inciden or prevalen cohors. Therefore, our analysis suggess ha he IER as calculaed in previous cos-effeciveness analyses may be subsanially differen from he IER as calculaed according o he mehods of his paper. As a side issue, noe ha we have assumed ha he coss and benefis in all fuure inciden cohors are equal. This assumpion would be violaed if, for example, one componen of he

19 0 0 coss is prediced o increase in he fuure a a differen rae o he oher componens of he coss. Then we mus adus Equaions, and appropriaely. One disadvanage of our suggesed mehods is ha hey require esimaion of addiional model parameers. The following algorihm may allow he analys o decide when i is necessary o implemen our suggesed mehods. Firs, if he cos and benefi discoun raes differ, our suggesed mehod should be followed. Specifically, we mus esimae he relaive sizes of he affeced paien populaions (n p ) for each year in he fuure up o year = T (Equaion ). If such daa is no available, we sugges above ha n p can be assumed a quadraic funcion of year. We hen require only an esimae of he lifeime of he new echnology, T (Equaion ). Variabiliy in n p and/or T should be incorporaed in he probabilisic sensiiviy analysis. The values of n p, T, and he variabiliy in hese quaniies could be esimaed by analysing rends in he volumes of sales of similar echnologies in he pas. Nex, wha if he cos and benefi discoun raes are equal? When he size of he prevalen cohor is negligible compared o he size of he inciden cohor, hen he IER for he prevalen cohor and all fuure inciden cohors combined can be approximaed by he IER for he firs fuure inciden cohor alone. However, when he prevalen cohor is no small, he analys should firs compare he IERs for he prevalen and inciden cohors. Given ha he IER for boh ypes of cohor combined lies beween he IER for he prevalen cohor and he IER for he firs fuure inciden cohor when he cos and benefi discoun raes are equal (see analysis), if he wo IERs are similar, hen he IER for he prevalen cohor and all fuure inciden cohors combined can be approximaed by he IER for eiher he prevalen cohor or he IER for he firs fuure inciden cohor. If he IERs for he prevalen cohor and firs fuure inciden cohor are no similar, hen our mehod for calculaing a combined IER should be used.

20 0 0 The proposed mehod requires esimaes of n and p separaely for each year in he fuure up o year = T in order o esimae p (Equaion ). However, wihou relevan daa, i is reasonable o assume ha he n are equal for all. The p are hen esimaed as described in he esimaion of n p above. Nex, we mus esimae he size of he prevalen cohor relaive o he size of he firs fuure inciden cohor, N, and paien-relaed parameers, such as he average age and average disabiliy saus for boh he inciden and prevalen cohor. Uncerainy in N should also be refleced in he probabilisic sensiiviy analysis. Given ha he IER can be grealy alered by use of our proposed mehods, he exra effor in esimaing hese parameers and in adusing he cos-effeciveness analysis is usified. Noneheless, we are mindful of he exra analyical effor and daa requiremens ha are implied by our mehods. We have herefore also provided some pracical ools for esimaing he coss and benefis for inciden or prevalen paien cohors when full daa on he oher ype of cohor is unavailable. Ideally, however, cos-effeciveness analyses in hese siuaions should be grounded in rigorous empirical sudies which yield separae effeciveness esimaes and oher daa from boh inciden, newly eligible, paiens and hose prevalen paiens who are swiching o he new reamen. Given ha he clinical and cos-effeciveness of a healh echnology can differ by paien subgroup, naional guidance recommends assessing cos-effeciveness separaely by paien subgroup (England, Ausralia, New Zealand, anada, Germany ). The characerisics of paiens in he subgroup should be idenified on he basis of an a priori expecaion of differenial clinical or cos effeciveness due o known, biologically plausible mechanisms, social characerisics or oher clearly usified facors. Disease severiy is an example of such an a priori facor. For example, consider a chronic progressive disease, wih cos-effeciveness assessed for one mild disease subgroup and a severe disease subgroup. As already explained, paiens are on average more severely ill in he prevalen cohor han in 0

21 0 he incidence cohor. Therefore we migh expec he proporion of paiens in he severe disease subgroup ha are in he prevalen cohor o be higher han he proporion of paiens in he mild disease subgroup ha are in he prevalen cohor. In he exreme case, he severe subgroup migh represen only paiens in he prevalen cohor, and he mild subgroup only paiens in he inciden cohor. In his case, he IER for he severe subgroup would equal he prevalen cohor IER (Equaion ), and he IER for he mild subgroup would equal he IER for all fuure inciden cohors combined (Equaion ). In his special case, he echnology migh be deemed cos-effecive for paiens in he inciden cohors, bu cos-ineffecive for paiens in he prevalen cohor, or visa versa. Of course, cos-effeciveness is ofen assessed wihou spliing paiens ino subgroups according o disease severiy. For example, in he NIE appraisal of naalizumab for muliple sclerosis, paiens in all Expanded Disabiliy Saus Scale levels from 0 (mild) o 0 (deah) were combined o calculae a single esimae of cos-effeciveness (NIE 00). IER should be esimaed as in Equaion. In his case, he 0 We have already oulined wo possible areas for fuure research: he general condiions under which he prevalen cohor IER is greaer han he inciden cohor IER, and vice versa; and he esimaion of he sizes of fuure inciden cohors, and he produc life-ime of a given echnology, and heir variabiliy by analysis of rends in he volumes of sales of similar echnologies in he pas. Now we sugges he following addiional areas of research. Firs, we have shown ha cos-effeciveness is influenced by our mehods when applied o an example simplified model. Our mehods could be applied o oher exising cos-effeciveness models o explore heir influence on cos-effeciveness. Second, cos-effeciveness for our example model was raher dependen on he specific mehod used o esimae he coss and benefis for he prevalen cohor. I would be ineresing o invesigae his for real coseffeciveness models. Third, we have suggesed how clinical effeciveness in our model may be parameerized from rial daa. We encourage invesigaion of he

22 0 availabiliy of such clinical daa for real world models. Fourh, in he previous paragraph, we describe how he proporion of paiens in a paien subgroup ha are in he prevalen cohor may depend on he subgroup. We recommend invesigaing he exen o which paien subgroups differ in his respec in real decision problems. Finally, we have assumed ha undiscouned incremenal coss and benefis are he same for all inciden cohors. Whils we sugges ha his is a reasonable assumpion wihou evidence o he conrary, we encourage invesigaion ino how facors such as he fuure prices of he healh echnology, fuure changes in he median age a diagnosis, fuure changes in life expecancy and relaive reamen effeciveness may influence his assumpion. A presen, mos economic evaluaions of healh echnologies simulae only he firs inciden cohor. In his paper, we have argued ha model-based economic evaluaions should simulae he coss and benefis for all people who will be affeced by a given healh policy decision. In paricular, we have (a) demonsraed how o calculae he incremenal cos-effeciveness of new healh echnologies when including he coss and benefis associaed wih eiher he curren prevalen cohor or he fuure inciden cohors of paiens, or boh ypes of cohor ogeher, and (b), using hese equaions, we have described he circumsances under which he combined cohors IER is likely o differ from he IER for he nex inciden cohor of paiens. 0 An Excel spreadshee implemening he example cos-effeciveness model is available from he auhors on reques.

23 Acknowledgemens We are graeful for useful commens on our manuscrip made a he UK Healh Economics Sudy Group winer meeing in January 00. We also hank Ken Sein and hree reviewers of his manuscrip for heir helpful suggesions. Reference Lis 0 () Sculpher M, Fenwick E, laxon K. Assessing qualiy in decision analyic cos-effeciveness models - A suggesed framework and example of applicaion. Pharmacoeconomics 000; ():-. () Layard R, Glaiser S. Inroducion. In: Layard R, Glaiser S, ediors. os- benefi analysis. nd ediion ed. ambridge, UK.: ambridge Universiy Press;. -. () Beaglehole R, Bonia R, Kellsröm T. Basic epidemiology.. Geneva, World Healh Organisaion. 0 () Weinsein M, O'Brien B, Hornberger J, Jackson J, Johannesson M, Mcabe e al. Principles of good pracice for decision analyic modeling in healhcare evaluaion: Repor of he ISPOR ask force on good research pracicesmodeling sudies. Value in Healh 00; ():-. () Naional Insiue for Healh and linical Excellence. Guide o he Mehods of Technology Appraisal. 00. London, NIE. () PBA. Guidelines for preparing submissions o he PBA. Par II: Guidelines for preparing he main body of a maor submission. Secion D: Economic

24 evaluaion for he main indicaion. 00. Ausralia, Ausralian Governmen. Deparmen of Healh and Ageing. URL: hp:// () PHARMA. Prescripion for Pharmacoeconomic Analysis (PFPA). Mehods for cos-uiliy analysis. 00. New Zealand, Pharmaceuical Managemen Agency. URL: hp:// 0 () ADTH. Guidelines for he economic evaluaion of healh echnologies. 00. Oawa, anada., anadian Agency for Drugs and Technologies in Healh. URL: hp:// () IQWIG. Mehods for Assessmen of he Relaion of Benefis o oss in he German Sauory Healh are Sysem. 00. Germany, Insiue for Qualiy and Efficiency in Healh are. URL: hp:// _Mehods_of_he_Relaion_of_Benefis_o_oss_Version 0.pdf (0) Danzon P, Kim J. The life cycle of pharmaceuicals: a cross-naional perspecive. 00. Whiehall, UK., Office of Healh Economics. URL: hp://hc.wharon.upenn.edu/danzon/hml/books_and_monographs.hm 0 () Salomon JA, Weinsein M, Goldie SJ. Taking accoun of fuure echnology in cos effeciveness analysis. Briish Medical Journal 00; ():-. () ISPOR. ounry-specific guidelines. 00. Inernaional Sociey for Pharmacoeconomics and Oucomes Research. URL:

25 () Briggs A, Sculpher M, laxon K. Decision modelling for healh economic evaluaion. Oxford, UK.: Oxford Universiy Press; 00. () Sinne AA, Paliel AD. Esimaing E raios under second-order uncerainy: The mean raio versus he raio of means. Medical Decision Making ; ():-. () Ansell D, Fees T. UK Renal Regisry Repor Brisol, UK, UK Renal Regisry. 0 () Shepherd J, Rogers G, Anderson R, Main, Thompson-oon J, Harwell D e al. Sysemaic review and economic analysis of he comparaive effeciveness of differen inhaled coricoseroids and heir usage wih longacing bea() agoniss for he reamen of chronic ashma in aduls and children aged years and over. Healh Technology Assessmen 00; ():XI-+. () Dewilde S, Anderson R. The cos-effeciveness of screening programs using single and muliple birh cohor simulaions: A comparison using a model of cervical cancer. Medical Decision Making 00; ():-. () Gravelle H, Smih D. Discouning for healh effecs in cos-benefi and cos- effeciveness analysis. Healh Economics 00; 0():-. 0 () Brouwer WBF, Niessen LW, Posma MJ, Ruen FFH. Need for differenial discouning of coss and healh effecs in cos effeciveness analyses. Briish Medical Journal 00; ():-. (0) Gravelle H, Brouwer W, Niessen L, Posma M, Ruen F. Discouning in economic evaluaions: Sepping forward owards opimal decision rules. Healh Economics 00; ():0-.

26 () van Hou BA, Goes ES, Griseels EWM, van Ufford MAQ. Economic evaluaion in he field of cardiology: Theory and pracice. Progress in ardiovascular Diseases ; ():-. () Tonkin AM, Eckermann S, Whie H, Friedlander D, Glasziou P, Magnus P e al. os-effeciveness of choleserol-lowering herapy wih pravasain in paiens wih previous acue coronary syndromes aged o years compared wih younger paiens: Resuls from he LIPID sudy. American Hear Journal 00; ():0-. 0 () NIE. Muliple sclerosis - naalizumab: Appraisal consulaion documen. 00. Naional Insiue for Healh and linical Excellence, London, UK. URL: hp://guidance.nice.org.uk/page.aspx?o= () Hoyle M. Fuure drug prices and cos-effeciveness analyses. Pharmacoeconomics 00; ():-0.

27 Table. Key parameers. Parameer Definiion K, B incremenal inciden cohor cos and benefi beween he new and comparaor echnology a cycle = 0,,,., H, expressed per paien a he sar of he inciden cohor, Q incremenal prevalen cohor cos and benefi a cycle = 0,,,., H, expressed per paien a he sar of he prevalen cohor K, K' inciden cohor cos per paien for he new and comparaor echnology a cycle = 0,,,., H, Q prevalen cohor cos and benefi per paien for he new echnology a cycle = 0,,,., H ', Q' prevalen cohor cos and benefi per paien for he comparaor echnology a cycle = 0,,,., H K,, Q, fuure coss and benefis per paien wih he new echnology for he inciden cohor ha sared in year (in he pas, so ha is negaive), cycles since he sar of he inciden cohor H ime horizon of each inciden cohor in cycles r, r B iner-generaion annual cos and benefi discoun raes v, v B r, r B r*, r* B inra-generaion cos and benefi discoun raes over a cycle

28 v*, v* B r *, r * B T expeced lifeime of new echnology in years n number of paiens eligible for he new echnology a he sar of he inciden cohor saring in year = -H,, -, -, 0,,,.,T, relaive o he number of eligible paiens a he sar of he firs year p probabiliy an eligible paien is given he new echnology = 0.T years in he fuure p probabiliy ha a paien in he eligible prevalen cohor is given he new echnology N number of paiens in he prevalen cohor ha are eligible for reamen, relaive o he number of paiens in he firs fuure inciden cohor A average age of paiens a he sar of he inciden cohor s(a, A+) probabiliy a paien who is reaed wih he comparaor echnology survives from age A o A + M number of years over which paiens are eligible o be reaed wih he new echnology

29 0 Figure. Prevalen and inciden cohor coss for (a) he comparaor and (b) he new echnology. Inciden cohors are shown as separae rows. For simpliciy, one cycle equals one year in his example. Here, he echnology is applicable on average o a given paien for M = years ( black cells in each row), and he prevalen cohor comprises M - = inciden cohors. The fuure prevalen cohor comparaor and new echnology oal coss a cycle, N ' and N equal he sum of he coss in he respecive highlighed boxes. In (b), all coss before he assessmen ime (ime zero) refer o he comparaor echnology, because he new echnology was no used hen. oss direcly associaed wih he echnology occur in some, bu no all he black cells. For simpliciy, we display coss only four years ino he fuure, whereas he expeced echnology lifeime, T, will probably be much longer. 0 Figure. Undiscouned coss ( ) over ime in he example cos-effeciveness model. (a) displays he per paien comparaor drug coss showing separaely all inciden cohors ha sared in he pas. The coss in he fuure, i.e. o he righ of he verical line, comprise he coss of he prevalen cohor. For clariy, a single example inciden cohor is displayed in bold. oss iniially rise as disease becomes more severe, hus incurring higher healh sae-relaed coss. oss evenually fall o zero as paiens die. (b) displays he same daa for imes in he pas, bu coss for he new drug in he fuure, i.e. for he new drug coss in he prevalen cohor. (c) displays comparaor drug coss. In (c), he downward sloping line represens oal coss in he prevalen cohor (summing over coss in all inciden cohors ha sared in he pas), and he upward sloping line represens oal coss in all fuure inciden cohors. To demonsrae scale, he inciden cohors ha make up hese quaniies, some of which are shown in (a), are us visible a he boom of he graph. We assume ha here are he same number of paiens in all inciden cohors.

30 Time (years) (0 = presen, <0 = pas, >0 = fuure) Figure. (a) omparaor omparaor Prevalen cohor coss N 0 ' N ' N ' N '. K 0 'n - K 'n - K 'n - K 'n - K 'n - K 'n - K 'n -. K 0 'n - K 'n - K 'n - K 'n - K 'n - K 'n -. K 0 'n - K 'n - K 'n - K 'n - K 'n -. K 0 'n 0 K 'n 0 K 'n 0 K 'n 0. K 0 'n K 'n K 'n. K 0 'n K 'n. K 0 'n Time (cycles) (0 = presen, <0 = pas, >0 = fuure) 0

31 Time (years) (0 = presen, <0 = pas, >0 = fuure) (b) omparaor New echnology Prevalen cohor coss N 0 N N N. K 0 'n - K 'n - K 'n - K -, n - K -, n - K -, n - K -, n -.. K 0 'n - K 'n - K -, n - K -, n - K -, n - K -, n -. K 0 'n - K -, n - K -, n - K -, n - K -, n -. K 0 n 0 K n 0 K n 0 K n 0. K 0 n K n K n. K 0 n K n. K 0 n Time (cycles) (0 = presen, <0 = pas, >0 = fuure)

32 Undiscouned cos Figure. (a) 0,000 omparaor drug omparaor drug 0,000 0,000 0,000 0, Year ( 0 = presen )

33 Undiscouned cos Undiscouned cos (b) 0,000 omparaor drug New drug 0,000 0,000 0,000 0, Year ( 0 = presen ) (c),000,000 omparaor drug omparaor drug,00,000,00,000 00,000 00, Year ( 0 = presen )