methods for economic eval of health programmes

8/3/2019 Methods for Economic Eval of Health Programmes

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Methods for theEconom ic Evaluation-of Health CareProgrammes

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Michael F. DrummondP ro fe ss or o f Health S er vic es Ma n ag em e n tHealth Services Manag eme n t Centre ,l.:n iv er sir yo f B ir m in gham ,. UK

Greg L.Stoddart.e ..Associa te Pro je isc"rDepanmen i o f Cl in i c a l Ep id em io log y and Biostat is t ic s ,

A ss oc iate M em b er , D e pa nm e n : o f Econom i c s ,McMa s te r U n iv er si ty , Ham i lto n , C a na daGeo rg e W . Torra nc e

P ro fe ss or o fJ lan ag em er u S cien ce , F ac ulty o f Business ,A ss oc ia te M em b er ; D e pa rtm e ru o f C lin ic al E pide m io lo gyand B io suu is tic s, .Md la sle r U n iv er sity , H am i lto n ; C a na da

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OXFORD ~WYORX TORONTO

OXFORD UNIVERSITY PRESS


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4. Cost analysis

4.1. SOME BASICSThe analysis of the comparative costs of alternative treatments or healthcare programmes is common to all forms of economic evaluation andtherefore most of the methodological issues discussed in this chapter arelikely to be of relevance to alIanalyses. Two particularly thorny issues. thetreatment of overhead costs (techniques for allocating shared overheadcosts to individual projects) and allowance for differential timing of costs(the techniques of discounting and annuitization of capital expenditure),will be discussed in some detail. However. the chapter begins by covering~ ' 0 . some of the basic questions that an evaluator might have when embarking

, on a costing study in the health field.

4.1.1. Which costs should be considered?The main categories of costs of health care programmes or treatmentswere identified in Fig. 3.1 of Chapter 3; these are the organizing andoperating costs within the health sector, costs borne by patients and theirfamilies, and costs borne externally to the health sector, patients. andtheir families. The particular range of costs included in a given study islikely to be decided upon as a result of considering the fol lowing fourpoints.1. What is the viewpoint for the analy s i s?It is essential to specify the viewpoint since an itemmay be a cost from onepoint of view, but not a cost from another. (For example, patients' travelcosts are a cost from the patients' point of view and from the point ofviewof society, but not a cost from the Ministry of Health's point of view.Workmen's compensation payments are a cost to the payinggovernment,a gain to the patient (recipient), and neither a cost nor a gain to society.(These money transfers, which do not reflect resource consumption, arecalled transfer payments by economists. Costs are involved in theiradministration, but these are not measured by the amounts themselves.)

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Cost analysisPossible points of view include: society. Ministry of Health. other

provincial ministries. total provincial government. patient, employer.federal government, the agency providing the. programme, etc, If theevaluation is being commissioned by a given body, this may give a clue tothe relevant point(s) of view. However. when in doubt always adopt thesocietal point of view. which is the broadest one and is always relevant.2. Is the compar i s on restricted to the tw o or mo r e p ro g ramm e s

immediately under study?If the comparison is restricted to the programmes or treatmentsimmediately under study. costs common to both need not be consideredas they will not affect the choice between the given programmes.(Elimination of such costs can save the evaluator a considerable amount- of work.) However. if ids thought that at some later stage a broadercomparison may be contemplated, including other alternatives not yetspecified, it might be prudent to consider all th e costs o f the pro gramm es,

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3. Are some costs merely likely to con f i rm a result that It.'O!IId be obtainedby cons iderat ion of a narrower range of c om ?

Sometimes the consideration of patients' COStsmerely confirms a resultthat might be obtained from, say, consideration of only operating costswithin the health sector. Therefore, if consideration of patients' costsrequires extra effort and the choice of programme would not be changed,it may not be worthwhile to complicate the analysis unnecessarily.However. some justification for such an exclusion of a cost categoryshould be given.4. What is the relative order of magnitude o f co s e s?It is not worth investing a great deal of time and etton considering coststhat, because they are small. are unlikely to make any difference to thestudy result. However. some justification should be givenfor the elimina-tion of such costs, perhaps based on previous empirical work. It is stillworthwhile identifying such cost categories in any event. although theestimation of them might not be pursued inany great detail.Above all, the main point to remember when em barking on a costing

study is that, to an economist, cost refers to the sacrifice (of benefits) _made w hen a given resou ...rceis consumed in a programme or treatment,Therefore, it is important not to confine one's attention to expenditures,but to consider also other resources. the consumption of which is notadequately reflected in market prices. e.g.. volunteer t ime. patients'leisure time. donated clinic space, etc.

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Co st a na ly sis4.1.2. How should costs be estimated?Once the relevant range of costs has been identified the individual itemsmust be measured and valued. In general, the programme ingredientsapproach suggested in Chapter 3 should suffice and market prices will bereadily available for many of the cost items. Although the theoreticalproper price for a resource is its opportunity cost (i.e.the value of theforgone benefits because the resource is not available for its best alterna-tive use). the pragmatic approach to costing is to take existing marketprices unless there is some particular reason to do otherwise (e.g, theprice of some resources may be subsidized by a third party such as acharitable institution).Although the costing ofmost resource items is relatively unambiguous,the following five issues commonly arise in costing studies.1. How are values imputed for nonmarket items?The major nonrnarket resource inputs to health Care programmes arevolunteer time and patient/family leisure rime. One approach to thevaluation of these would be to use market wage rates (e.g..for volunteertimeone might use unskilled wage rates). The market value of leisure timeis harder to assess. One can argue for a value of lost leisure lime ofanything from zero, through average earnings. to average overtimeearnings (time and a half or double time). The argument for the overtimerate is that this is the price that an employer must pay. at the margin. tobuy some of the worker's leisure time. The most common practice is to

.. ~ value lost leisure time at zero in the base case analysis. and to investigatethe impact of the other assumptions through sensitivity analysis.A slightly different approach is to identify and measure uni ts of. say,volunteer input and to document these alongside the other costs whenreporting results. This would enable the decision-maker to note thoseprogrammes relying heavily on volunteers. It would then be up to theprogramme director to demonstrate that such an input could be obtainedwithout an opportunity cost to other prograrrunes arising from thediversion of volunteers to the new programme.The valuation of nonmarket items is discussed further inChapter 7 oncost-benefit analysis.

2. How should capital outlays (on equipment, buildingsand land) behanaUed? .Capital costs are the costs to purchase the major capital assets requiredby the programme: generally equipment. buildings and land. Capital costsdiffer from operating costs in a number of ways. First. they representinvestments at a single point in time, often at the beginning of the

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Cost analysisprogramme, rather than annual sums like operating costs.F requendy, thecapital costs are not listed in the accounts or budgets of the organizationbecause they have been funded inadvance, perhaps by a one-time grant.while th e budgets and accounts represent operating expenses only.Sometimes, the annual budgets and accounts contain an item cal leddepreciation which relates to capital costs, as explained below.Capital costs represent an investment in an asset which is used over

time. Most assets, such as equipment and buildings. wea r out. ordepreciate, with time. On the other hand, land is a non-depreciable assetbecause it maintains its value. There are two components of capital cost..One is the opportunity cost of the funds tied up in the capital asset. This isclearly seen in the case of land. Although an investment in non-depreciable land will rerum the original capital sum when sold. there isstill a 'cost', This cost is the lost opportunity to invest the sum in someother venture yielding positive benefits. This is called the opportunitycost and is valued by applying an interest rate (equal to the discount rateused in the study) zo the amount of capital invested,The second component of a capital cost represents the depreciation

over time of the asset itself. Various accounting procedures (straight line,declining balance, double declining balance. etc.) are available for use inthe accounts of the organiiation. Often. accounting practices relate moreto the company tax laws governing the depreciation of assets than to thereal change in the value of the assetThere are several methods of measuring and valuingcapital costs in aneconomic evaluation. The best method is to annuitize lbe initial capital

outlay over the useful life of the asset; that is , to calculate the 'equivalentannual cost'. This method and its advantages are discussed inmore detailby Richardson and Gafni (1983). The method automatically incorpo-rates both the depreciation aspect and the opportunity cost aspect of thecapital cost. It is our preferred approach and is described in Section 4.2below. An alternative but less exact method is todetermine the deprecia-tion cost each year using an accounting method and to determine theopportunity cost on the undepreciated balance for each year (See Levin1975, Boyle. Torrance, Horwood, and Sinclair 1982). Where marketrates exist for the rental of buildings or lease of equipment, these may beused to estimate capital costs. This method also incorporates both thedepreciation and the opportunity components of the cost (A series ofexercises illustrating the different methods of measuring and valuingcapital costs is given in Annex 4.1.)If capital outlays relate to resources that are used by more than one

programme they may require allocation in a similar fashion to 'overhead'costs. See the discussion of this point below.

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Cos t a na ly sis3. What is the s ig nific an ce o f the av e rag e co st/m arg in al co st d is tin a io n?Econom ists tend to em phasize this poin t. and the example of the sixthstool guaiac in Chapter 2 illustrated the pitfalls in making decisions basedon average cost. In fact, marginal cos t and average CO Stare but tw o con-cepts relating costs to quantity (Horngren 1982). A longer list wou ldcomprise:Toral cost (TC) - cost of producing a particu lar quantity of

output.Fixed cost (FC) - costs w hich do not vary with th e quantity ofoutput in the short run (about one year). e .g .ren t. equipm ent lease paym en ts, so me wagesand salaries. That is, costs w hich vary with t ime,rather than quantity.V ariable co st (VC) - costs w hich vary with th e level of outpu t. e .g .su pplies, foo d. fee fo r service.

Co s t fun ctio n (T C) -f( Q), to tal cost as a func tion of quantity.Ave ra ge cost (AC) - TCI Q, the average cost per unit o f ou tpu t.M arginal cost (MC) - erC of x + 1 units) - (TC of x units).

- d(TCYd Q evaluated at x- the extra cost of producing on e extra unit o f

output.T he m ajor significance of the averge-cosr/m arg inal-cosr d istinction to

the evaluator is as follows. FIrSt, when mak ing a com parison of rw o orm ore program mes, it is w orth asking independent ly a t e ac h. 'W h at w o uldbe the costs (and consequences) of having a little m ore or a little less?'(e.g.,suppose Neuhauser and Lewick i (1975) had been comparing th esix-stoo l protoco l for detecting co lon ic cancer w ith another d iagnostictest. Perhaps the question of six- versus five-tests m ay never have beenaskedq Second , when examin ing , the effects (on cost) o f small changes inoutput. it i s l ik el y that these will differ from a vera ge costs. F or e xamp le ,th e extra cost of keeping a patien t in hospital fo r another day at the end ofh is treatm en t m ig ht be less than the average daily cost for his w h ole sta y.(In fact, this i ssue usually ar ises in th e o pp osite sense-the savings from areduction of one day's stay are usually low er than th e a ve ra g e daily cost.)

4. How should shared (or overhead) costs be hardkd?The term o ve rhe ad c os ts is an accounting term for those resources thatserve m any different departm ents and program mes. e.g. general hospitaladministration, central laundry, medical records, cleaning, pone r s ,

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Cost analysispower, etc. If individual programmes are to be costed, these shared costsmay need to be attributed to programmes.The main point to note at the outset is that there is no unambiguously

right way to apportion such costs. The approach that is favoured byeconomists is to employ marginal analysis. That is , to seewhich(if any) ofsuch costs would change if a given programme were added to, orsubtracted from, the overall activity. Whilst this is fine up to a point, themost common situation is that the choice is nOIsuch an addition orsubtraction. but one between two programmes. each of which wouldconsume the given central services (perhaps because they arecornpeti-tors for the same space in the hospital). For example. suppose the ques-tion concerned space in the hospital that could be used either foranticoagulant therapy for pulmonary embolism. or for renal dialysis. Ifthe economic evaluation concerned a choice between these twOprogrammes, then there would be no methodological problem. the costsassociated with use of the space would be common to both.and could beexcluded from the analysis. However, typically the comparison might bebetween the anticoagulant therapy and another programme in the samefield. This could be a programme of more definitive diagnosis ofpulmonary embolism. which would avert some hospitalization. In such aninstance it would be relevant to obtain an estimate of the valueof the freedresources (e.g. hospital floor space) that could be diverted to other uses.Essentially, the issue at stake here is that of accurately estimating all thecosts attributable to a given programme or treatment when this isdelivered alongside other programmes. as in the BCO.!teospital. InChapter 3 the reader was warned against the unthinsing use of hospital(or other institutional) per diems or average costs. Before the methodsavailable for apportioning institutional costs are described in more detail.the dangers of using per diems require more elucidation.Many institutions calculate a per diem or average cost of their

operations. This is essentially their total operating. costs for the yeardivided by their total patient utilization forthe year. A common exampleis a hospital's average cost per patient-day. It is tempting. simply tomultiply this figure by the number of patients and their average length ofstay to determine the hospital cost of a programme. What is wrong withthis procedure? First, it is only valid for truly ' ave rage ' patients-that is,patients who use an average amount of radiological services. laboratoryservices, operations, nursing attention, drugs, and soon. If patients illtheprogramme being costed are not average, the result will be in error.Second, many per diem calculations include arbitrary adjustments. For

example, certain types of patients (outpatients, day patients. newbornpatients, etc) may be excluded from the denominator of the calculation in

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Cost a naly sisrecognition that they are not typical. Then an estimate of the costs of thesepatients (often a very crude estimate) is subtracted from the numeratorbefore calculating the per diem. The result is that the per diem itself isimprecise, even for the truly average patientFinally. typical per diem cost figures are incomplete, as they totally

ignore capital costs. In summary. per diem costs are only applicable toaverage patients and even then are imprecise and incomplete.A number of methods can be used to determine a more accurate cost of

a programme in a hospital or other setting where shared (or overhead]costs are involved. The methods are illustrated below in terms of ahospital setting. The basic idea is' to determine the quantities of serviceconsumed by the patient (days of stay in ward A. B. or C. number oflaboratory tests of each type, number of radiological procedures. numberof operations. etc.), to determine a full cost (including the proper share ofoverhead. capital. ete.) for a unit of each type of service. and to multiplythese together and sum up the results. The allocation methods describedbelow are different ways to determine the cost per unit for each type ofservice. In these methods the overhead costs (e.g.. housekeeping) areallocated to other departments (e.g.. radiology) on the basis of somemeasure. called an allocation basis. judged to be related to usage of theoverhead item (e.g., square feet of floor space in the radiology depart-ment might be used to allocate housekeeping costs to radiology).In deciding which of the following approaches to use. the comments

made in Section 4.1.1 above, should be borne in mind. That is.the moreimportant the cost item is for the analysis. the greater the dart thatshould be made to estimate it accurately. There may conceivably beevaluations for which simple per diem costs will suffice. sin ce th e result isunlikely to change irrespective of the figure assumed for the cost ofhospital care. However, we suspect that such situations are in theminority, given the relative order of magnitude of hospital costscompared to other elements of health care expenditures.Alternatively, the intermediate approach suggested by Hull. Hirsh,

Sackett, and Stoddan (1982) may suffice. Here the pe r die m cost ispurged of any items relating to medical care COSts.eavingjust the 'hotel'component of hospital expenditure. It is then assumed that all patients are'average' in respect of their hotel costs and that this expenditure cantherefore be apportioned on the basis of patient days. Thus. the hotel costcan be calcu1atedfor the patients in the programme of interest andcombined with the medical care costs attributable to those patients to givethe total costs of the programme. (The medical care costs would beestimated separately, using data specifically relating to the patients in theprogramme.)

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Cost a n aly sisIf a more detailed consideration of costs is required, various methods

for allocating shared (or overhead) costs are available, namdy:(a) Direct allocation (ignores interaction of overhead departments).Each overhead cost (e.g, central adminisuation, housekeeping) is

allocated directly to final cost centres (e.g..programmes like day. surgery; departments like wards or radiology). Programme X'sallocated share of central administration is equal to centraladministration cost times Programme X's proportion of theallocation basis (say. paid hours). Note. Programme X's' propor-tion is Programme X's paid hours divided by total paid hours ofallfinal cost centres. not total paid hours for the whole organization.The latter method would underestimate the COsts in all final costcentres.(b) Step down allocation (partial adjustments for interaction of over-head departments). The overhead departments a re a ll oc ate d in astepwise fashion to a U of the remaining overhead departments andto the final cost centres.

(c) Step down with iterations (full adjustment for interaction ofoverhead departments), The overhead departments are allocatedin a stepwise fashion to all of the other overhead departments andto the final cost centres. The procedure is repealed a number oftimes (about three) to eliminate residual unallocated amounts.(d) Simulumeous allocation (full adjustment for interaction of over-head departments). This method uses the same data as (b) or (c)but it solves a set of simultaneous linear equations to give theallocations. It gives the same answer as method (c) but ia vo l v es le sswork. (The method is shown diagrammatically in Fig. .U.)

An example showing the different approaches to the allocation ofoverhead costs is presented in Section 4.3. Further details are available inHomgren (1982). Clements (1974). Kaplan (1973), and Boyle. e t a l(1982),The effort that one would put into overhead cost allocation would

depend on the likely importance of overhead costs (in quantitative terms)for the whole analysis. Amuch simpler. but cruder, approach is to(a) identify those hospital. costs unambiguously attributable to the

treatment or programme in question.(e.g .. physicians' fees, l abora-tory tests, drugs). (These are known as the directly allocatableeosts.) Allocate these directly and immediatdy to the programme,then;

(b) deduct, from total hospital. operating expenses, the cost of depart-

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Cost analys is

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PaIiInI(1) Direct casts assigned directly to cost centres. 12 } capital costsassigned to cost centres. (3) SuPPOrt cost centres simultaneouslyalloCated to each other. (4) Support cost centres allocated to other costcentres. 1 5 ) Costs assigned to each patient based on services used.F ig . 4 .1 . Schematic illustration of COSt a llo ca tio ns (from Boyle et aL

1982)ments already allocated above and departments known not toservice the programme being costed, then;(c) _allocate the remainder of hospital operating e x p e n s e s on th e basisof number of patient days, e.g.:

Net hospital HospitalHosnital cost Direcdy expenditure paticm..


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Cost analysis(d) finally, undertake a sensitivity analysis.Whilst there is nothing to suppose that this method is anything but

crude, if the choice between programmes is fairly insensitive to the valuederived it may suffice.5. How should indirect costs be euimated?As was mentioned in Chapter 3, this is a particularly contentious issue.The discussion of this point will be postponed until Chapter 5 sincechanges in productive output more often enter into the economic evalua-tion as a consequence of health care programmes. that is, the therapyoften averts future production losses in that it enables the sick person toreturn to work or work until later in life. Production losses occur lessoften on the cost side of the equation since the patient is already off workbecause of his or her condition. Exceptions here would include popula-tion screening or other preventive programmes and anyone consideringa . . , evaluation of these should consult the relevant section in Chapter 5.4.2. ALLOWANCE FOR DIFFERENTIAL TIMINGOF COSTS (DISCOUNTING AND THEANNUITIZA nON OF CAPITAL EXPENDITURES)As w as mentioned inChapter 3, some allowance needs tobemade for thedifferential timing of costs and consequences. That is. even in a worldwith zero inflation and no bank interest, it would be an advantage toreceive a benefit earlier or to incur a cost later-it gives you more options.Economists call this the notion of lim e p re fe r en c e .Typically, economic evaluation texts discuss the situation where thecosts of the alternative programmes A and Bcan be identified by the year

in which they occur:Year Cost of Programme A

( SOOOs )51015

Cos t o f P rog ram m e B( S fXXJs )15104

123In this exampJe,B might be a preventive programme which requires moreoutlay in Year 1 with th e promise of low er cost in Year 3. The crudeaddition of the two cost streams shows B to be of lower cost. but theoutlays under A occur more in the later years.A comparison of A and B (adjusted for the differential timing ofresource outlays) would be made by discounting future costs to present

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Cost analys isvalues. The calculation is performed as follows. If P - present value;F.. - future cost at year n; and r - annual interest (discount) rate (e.g..0.05 or 5 per cent), then

)P- I . ; ( / + rf"

r , F, Fj---+~+--(l+r) {1+rt (l+rfIn o ur e xample this gives:Present value of cost of A - 26.79Present value of cost of B-2 6.81This assumes that th e costs all occur at th e e nd of each year. An

alternative assumption wh ich is commonly used is to assume that thecosts all occur at the beginning of each year . Then. Year 1 costs neednot be discounted, Year 2 costs should be discounted by one year , etc.Calculated in this way, th e previous example is;.P L F,.(l+rf"

..0

_ 1: ..I... ~ _ ._ _ _ _ _ _'0 '(I+r)--'(l+d

Present value of A - 28.13Present value otB - 28.15The factor (I+t: is known as the discount factor and can be

obtained for a given n and r from Table 1 inAnnex 4.2. For example. thediscount factor for three periods (years) ata discounlrate of 5 per cent is0.8638.While this approach is th e most convenient for a number of pro-gramme comparisons, a m ore common situationis t h a t wher e iOOSt of thecosts are easily expressed on an annual recurring basis and it is onlycapital costs wh ich differ from yea r to year-( typical ly these wiD be at thebeginning of the p rog ramme. . or Year O}-Here it might be more convenient to express all th e costs on an annua l

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Cost analysisbasis, obtain ing an equ ivalen t annual cost (E) fo r the capital outlay by anam ortizatio n or an nuitiza tion proced ure . This w orks as follows:'

H the capital outlay is K, w e need to find the annu al su m E which over aperiod of n years (the life o f th e facility). at an interest rate of 1 ' ,will beequivalent to K.

This is expressed by th e fo llo w in g fo rm u la:E E EK- (--) +(-)1+..+(--)~1 + 1 ' 1 + 1 ' 1 + 1 '

K _ E_l_-_(.;._l_+_r..;...)_It

K - E [Annuity factor. n periods. interest 1',As before. the annuity factor is easi ly obtainable from Table 2 in

Annex 4.2. For exam ple, in !he cost analysis of providing long termoxygen therapy L ow soa, D rum mond, and B ishop (1981) found the totalcapita l (se t up) costs (K) to be 2153.

T herefo re. a pplyin g th e fo rm ula g iven ab ove:E E E E E2153- -- + -- + -- + -- + --- (1+1') {1+rr (l+r? (l+rt (1+1');

2153 - E [Annui ty factor. 5 years, interest rate 7 per cent!2153 - E (4.1002J (from Table 2 inAnnex 42)E - .525 (as sho w n inTable illofLowson et aI.. (1981).

Note that Lowson et a 1 (1981 ) a ssum ed that th e annu ity was inarrears,that is, due at the end of the year. It m ight be argued that a mo re re alisticassumption would be that it were payable inadvance. This is equivalent to-the formula:

E E E E2153 - E+-+--+--+-(1+1') (l+ry (l+r)ll+rtThe va lue fo r E can stili be obtained from Table 2 by ta kin g o ne less

period and adding 1.000. This gives a lower v alu e fo r E - 491. This islogical since the repayments are being made ear l ier (a t th e beginning ofeach year) rather than in ar rears .

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Cost analysisnus approach can be generalized to handle the situation where th e

equipment or buildings have a resale value at the end of the programme.HS- the resale value;n - the useful life of the equipment;r - discount (interest rate);A(n, r) - the annuity factor (n years at interest rate r);K - purchase price/initial outlay;E - equivalent annua l cost;then

SK- (l+rtE - ----'-----A(n,r)

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The method described above is unambiguous for new equipment. Forold equipment, there are two choices:Choice 1 - Use the replacement cost of the equipment (or the original

cost indexed to current dollars) and a full life.Choice 2 - Use the current market value of the old machine and its

remaining useful life.Choice 1 is usually better as the results are more generalizable-lesssituational. Note that using the undepreciated balance from the accountsof the organization is never a method of choice.It can be seen that the equivalent annua l cost of buildings or equipment

to a given programme depends on th e values of n, r, and S.all of wbichmust be assumed at the time of the evaluation. Practical points thatevaluators might care to note are:1. Use[u l l i f e and resale va lue (nand 5)It is important tomake a distinction b etw ee n the pbysicallife of a piece ofequipment and its useful clinical life. The latter is highly dependent ontechnological change. Obviously one can undertake a sensitivity analysisus ing different values for n,but ingeneral it is best to be conservative andassume shon lives (say, around five years) for clinical equipment.2. Clwice o f the discowu rare (t)There are two c ompe tin g th e orie s regarding th e proper measure for th ediscount rate for public projects (the social discount rate):(a) r - the real rate of return (to society) forgone in the private sector.

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Cost analysisThis can be estimated empirically, although not withoutcontroversy.

(b) r - the social rate of time preference.T he social rate of tim e preference is a m ea su re o f so ciety 's w illin gn ess.

collectively, to forgo consumption (gratification) today in order to havegreater consumption (gratification) tomorrow. Frequently it is assumedthat the interest rate on a risk free investment (e. g, l ong -t erm governmentbonds) represents the individual investor's willingness to forgo thepresent for the future, and that this rate is the individual's rate of timepreference. Then if society's collective rate of time pre fe rence is simplythe aggregate of the individual rates (a controversial assumption), therequired rate is simply given by the real (adjusted for inilation) rate ofreturn on long-term government bonds,However, in practice it is usually admissible to select a central 'bestestimate' of r, and then vary this systematically iiia sensitivity analysis todetermine the impact on the study conclusions. The criteria to use inselecting a central r and a range for sensitivity analysis are that these

" .. should:(a) be consistent with economic theory (2 per cent to 10 per cent);(b) include (bracket) any government recommended rates (5 per cent,7 per cent, 10 per cent);(c ) include (bracket) rates that have been used in other published

studies to which you might wish to compare results (3 per cent to10 per cent);(d) be consistent with 'current practice' (for example, 5 per cent hasbeen used recently in papers published in the New EnglandJournal of Medicine).

3. How to handle inflationIf it is assumed that all the items of cost in the programme will inflate at thesame Tate and that this wil l be the same rate as inflation ingeneral, thereare tw o equivalent choices:(a) Inflate all future costs by this predicted inflation tale and then use alarger discount tate that allows for the effect of general inflation

(the inflation adjusted discount rate*), or Calculation 0f inflation adjusttd discount nne: if th e r e a l discount r o u e is 5 per cent

and general inflation is 8 per cent, then the inflation adjusted T - (1.05)( 1.08) - 1.134or 13.4 p er c en t.

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Cost a na ly sis(b) Do not inflate any future costs (i.e..we constant dollars) and use asmaller discount rate that does not allow for inflation (the r ea l

-discount rate).Method (b ) is th e simpler and preferred approach.Iit is assumed that different items of cost in the programme will inflateat different rates, there are also two equivalent choices:(a) Inflate all future eosjs by their particular predicted inflation ratesand then u se a larger discount rate that allows for the effect ofgeneral inflation (the inflation adjwted discount ratej. or

(b) Do not inflate any future costs (i.e.. use constant dollars) and use asmaller discount rate that does not allow for inflation (the realdiscount rate), but adjust th e discount rate for each item to accountfor the differential inflation tate between this item and the 'general'rate of inflation, e.g., if general inflation is 8 per cen t, this item isexpected to inflate 10 per cent, and the rea! r is equa l to -! per cent,then r adjusted for this item is

O L08 "1"r - 1. 4 x -- - 1.0_ i.e, _.1 per cent.LlOMethod (b ) is again the preferred approach. In general. however. moststudies perform the whole analysis in constant price terms and use asingle discount rate.4.3. ALLOCATION OF OVERHEAD COSTS:EXAMPLEThe following example demonstrates th e various methods of handlingoverhead costs discussed in Section 4.1.2 (4). p. 43. Suppose we wish todetermine th e cost of neonatal intensive care (NIqfor a specificgroup ofpatients. For each patient we have data on the length of stay in theneonatal intensive care unit (NICU) and data on the Dumber and type oflaboratory tests performed. For simplicity, let us assume that these werethe only services received by the patients-that is, the patients had nooperations, no radiological or nuclear medicine investigations. no socialwork, etc. Furthermore, let us assume that there are o nly th re e overheaddepamnents that serve the laboratory and -the NIeu : administration;housekeeping and laundry. (in principie it wouid be possible to considerother overhead departments, like plant operations and maintenance,bioengineering, andmaterials management.)- See footnole au p, 52.


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54

Cost analysisThe first task is to determine a unit of output for those departments thatdirectly serve patients. We will be determining a cost per unit of output,

and multiplying this cost by the usage of each patient to determine thecost per patient. Thus. the unit of output must be as homogeneous aspossible with respect to cost, and yet be available in the data for eachpatient. We have selected a patient-doy as the unit of output of the NICU.and a DB S unit for the laboratory. A DBS (Dominion Bureau ofStatistics) unit is a standard laboratory work unit used inCanada; eachlab test is assigned a predetermined number of DBS units according tothe amount of work needed to perform the test,Anallocation basis must be determined for each overhead department.For example, square feet of floor space has been selected for house-keeping. This means that housekeeping costs will be allocated to depan-ments receiving housekeeping services in proportion to the squarefootage of floor space in the department, Similarly.paid hours has beenselected as the allocation basis for administraC.on costs, and pounds oflaundry for the laundry costs.The data for this simplified example are given in Table 4.1. Thecalculations. as performed by the different methods. are given inTables 4.2 to 4.7.


18/36

C; e!:: --= -0< C i .

-"C.:y c~:(I). . . . ~C C i .!!._'"c::: -C i ...,-=- Q_C Q- e

Qo,o,o,0, Qo Qo 0DO N-0000000,0OOO-Q ~'


19/36

Cost analysis

Table 4.2. Method I-ignore overheadLab cost/DBS unit ... 54 000 000/8 000 000 - S0.50IDBSunitNICU cost/pt-day - $500 000/5000 - $lOO/pt-day

Table 4.3. Method 2 -d iT eC I a llo ca tio n o f overhead(Note; Allocation denominator - sum of 'final' department.)

Lab cost - direct cost + lab's share o f a dm in + lab's share ofhousekeeping + lab's share oflaundry2,,()oon .,n,\,,-r._ " - - - 000+ -- - --- (? 000 000)+ ;>v VVV (1500 OOO}+4 000 2 000 000 - 600 000

25 000 (1 300000)1300000- 4 000 000 + 250000 + 75 000+ 25 000 - 4350000

Lab costIDBS unit - 4 350 000/8 000 000 - $O.54/OBSunitN1CU cost - direct cost + share of admin + share of housekeeping +share of laundry

....500000 + 50000 (2000 000) + 8000 (1500 OOO}+2 000 000 600 00075 000 (1300 000)1300000- 500 000 + 50 000 +20 000 + 75 000+S645000

NICU cost/pt-day =645 000/5000 -S129/pt~y")~"iII~

56


20/36

E E= =. . . . . . . .= -0 :;: ..; . . . .= ' " ' . . . . . .= . . . . . . . . . . . . .'" ' . . . . . . . . . . . . -0. . ;;; . . . . . . . . . 2! . . . . . . . . . . .0 = . . . .'" '"~!~ ' " ' ' 1 ' ' ' = 1 ' : :" ' > C O ~i~. . . . . . . " "~ . . . ~ ! i.

~

. . .. . . '" . . .~ . . . . . . . . . . . .- . . , : 1 '".J '" > C OZ +" " o c 1 > C O ,-:;N ~!~ ~!~' . . . 1-

~ '" ' " ' " " ~-. . . . , '" ~. . . . . . . . . .. . , , . . . . . .1 5 e- '" . . . . . . . . ~ : : : : : :: 5 . . . . . . . .. . . . . . . o c ~+ < i i ,'" ilr..l% -': '0o ! I ":: ; N~N ~ \~ "_;NN~"'!'"C . -

0- '" ".. or . ; : : ;g'" e e :: - . , . . . . .. . . . . . . . . .~ . . . . . . . , . . , = -1: ; : : ; " ' " N.g . . . . . . .. . . ,5 = =c. . ,I. ! : ! "'I~ ""I > C O ol-=-. . . '!::I~ ~~~~- = g . . . ~I- or . '". . '" . . , e-E 'i 5 2 . . . . :. . .u :; ; : : ; . . , .E . .t: -i - I"t: !.~ u ....~ = I~e ~~ coCc;) .- = ~I ..;' Q - . g g " "'" . . . .~ E :; . . .- . . .~ . . . . . N . . .?: .._.~ 0- E- "'I~0 : : : :::~ . .R~ . . . ~I i9~i! . . . ~I ~~'E e- = . . .I 0 -


21/36

:"';'.

l! E'-' -.. ; ; : ; =- V>.'" ~ = - . . . . . . . '" . . . .'" . . . ~ 0- . . . '" . . . .- . . . . . . '" . . . . , . . . .. . . . . :;; o o . . . . . . . . . . . .~ ; ; : ; '" = - . . . V>. . . N =s

'". . .. . .

" .~ " ' j " ' ' ' ' I ' " = r ; : . . . j . , . . . . I ' " = 1 &... '" ';Po:;l _ - M\c O\;CIIn""N ~ 1I'lI r-N""- -_ . . . . . . . . . . . . . . . . . . . . . .'" g . . . . . , . . . , . .. . '" . . . '" . . .? % . . . . . . . . . . . .; ; : ; . . . . . . . .J . . . . ' "I f ~ I ' " I ' " 1 - " " I ' " I ' " 1 =N~ ~~ ~ QNOC 0 ' 1 . " " =. . . . . ,p ~ -,I:

5 ! : '" '" . . . '". "~ e- ;c . . . '" ';Po ';Po~-~ - . . . . . . . . . . . . .'" .,. . . . . . . . . . . . . . .5 . . . '" '" '"" ~ '":sj "! . . . . . .- : !i_-, I'~ V > I " , _ I ' " 1 ' : : :::i1~gl~"'lg~ r.. i t ' o I ' : = ; I = " " ~ =--:- t " 'o C " 'l ~ . . . . . . . '"I~ " Bk' ::; . . . . !:: . . , . . . . .~ '" '"~ ~ . . . . ;: " " . . . . . . . . .f ~ - . . . . . . . . . . : r - o c . . .~ . . % . . . :; " " . . , . . . , .; ~ ; : : ; . . .'" . . , o o;~.r ~ = =I" ] " ' I ~ ~ r ~ = i g " ' 1 " ' ' ' ' 1 ' ' ' = 1 =~ o u - t o - - : ! f : : : : N~~::: ~'f t I II I

o u- = . . . . ';Po . . , . = . . . . ~I . . .. . . . . . ~ . . , .c. e - o c '" . . , . . . .~ . . . , . . ~ . . . . . . .o u ; : : ; . . .. , . . .. . ~. ,


22/36

e e E= > 0 "i. . . . . . .::. = > . . . . . . . . . . . . . . = - NOQ . . . . . . . . . . . . OQ0- . . . . . . . . . . .'" . . . ~0- 0- 0-. . . . . . . . .. . . . . . '"

. . .. j . . . "' jOQ = 1 3 ...."''''J=N-.oO\~ - N"C I I I ' l !1n f"'o-N W i . . . . . . . . ,. .OQ . . . OQ . . . ; : ; ::. . . . Ii. . . . . . . =. . . . . . . . .. . . . . . = '". . . . . . . . . .OQ '0 '" + a l"!1~"' I~"" lg " ' 1 " ' " ' : : c o::. . . . . . . . . . . :::::''''I~

~I. . . . . . . . . . . . . . . . . . . . . Q . . . ' ". . - . . . . . . . . . = ~. . . . . . . . . . ~ -0 '0 OQ ~ : : : ~~. . . . . . . . . . . . . . .. . . . . . . . . ~. . . . . . . . . ~ ~+ (i)"'1100 _ I'" 1= ;31~~!~I"';;;I~ ....' : .. . . '" '" I....;..,

'0 . . . OQ ~ . . . . . . . . . . . '". . . . . . . . . . . . . ~. . . . . . =. . . . . . . . ' "- 0- ~. . . . . '"= = Q. . . 1 . .. . . . 1 " ' = 1 = ~I~~~~N: ~~~ -, . . .t= " " '01 . . . = > =. . . . . .. . . N"'I~ ...!~ :. . . . ~ I . . . . . . . N '" Q0- . . ,. . . OQI

..,[~ = I . . . . . .~I '0 . . . . - = . . . . . . - =~ . . . . . . NI . . ,

;;I~=I~= e~e = . .~ . . i~~ . .. . . . . < : : r ; . ." 1 i .~ S S . . 5 ~ -; - = s : :. . . . B . .u . 2 !~ . . . . . . . . .It t! . . ! i ! ~ ~ ~. t! < ; ; : < =% . . . . Ii: Ii:


23/36

Table 4.6. Me tlwd 5-s imu lttz TU !OUS a llo ca tio n ( r e c i p T O C Q / mdwd)(N ote: A llocation denom inator - sum of all departments) .

1I$~

: n:~!-~= . . .; , . ..~"tt.~:~;r1'i : , - f'r~t. '.,~.i: !t"". '~.:;~

' = " _ "f:,-i.fr ;

t~II

2 30Admin C,-2000000+-C, +-Cz30 8003 4 80HK C-1500000+-C, +-Cz+--C330 800 15002 8Laundry C3 -1300000 +-C +-.-


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61

Cos t ana ly sisTable 4.7. M e th od 6-p atie n t-da y a llo catio n o f o ve rh eadThis is the sim ple m ethod described in the foo tno te of page 27 ofChapter 3 and on page 46 o f C h ap te r 4. It may be useful in som e c ase s.L aboratory costs w ou ld be ch arged w itho ut o verhead : S0.5 0ID B5 unit.NICU costs w ou ld be the direct costs of S500 000 plus a share of allre lev an t o th er departments (2.0m + l .5m + 13m - 4.8m) inproportion to patien t-days (5 000/500000 w here the denom inator isto tal annual hospital patien t-days). T hus.N ICU cost - 5500 000 + 54 800 000 (5 000/500000) - 5548 000.NICU cost/pt-day - $548 000/5 000 - SIIO /pt-day. :."

4.4. CRITICAL APPRAISAL OF A PUBLISHEDARTICLERe f e r enc e : Lawson , K. V., Drummond .M, f., and Bishop, J.M.(1981). Costing new services: L ong-term dom iciliary oxygentherapy ..Lanc e t i, 1146-9 ..

This paper is assessed below using th e 10qu estio ns set o ut in Annex 3.l.Itis suggested tha t you locate the article and attem pt th e exerc ise beforereading th e assessment.

1. W as a w ell defined question posed in answ erable fo rm ?x YES NO CA.J."IT TELL

The s tudy addresses the question, What is the most efficient way toadm in is te r lo ng -te rm o xy ge n the rapy ? The analysis proceeds by com -paring the costs o f alternative methods of providing oxygen therapy.How ever, the ef fects of the therapy are n ot included fo r co nsidera tio n.The ra tionale for the om ission is that t he e ffe c ts g ene ra te d by e ac h o ptio nare similar, and thus a C o s t analysis is th e most appropriate sru dy desig n.The extent to w hich this is true d epen ds., o f c ou rse, o il th e accuracy of th eassum ption of sim ilar effec ts.

The alternatives com pared are cylinder oxygen ( large and sma l lcontainers), liquid oxygen and oxygen concentrators (a m ach ine thatextracts oxygen from air).


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Cost analysisThe viewpoint for the analysis is not specified explicitly.However, th e

costs chosen for inclusion suggest that the authors adopt the combinedviewpoint of both the United Kingdom National Health Service (NHS)and patients.

"

:'i j,, . :1 +~'1 . ' -! : - It i;H tf ~ " ' : .!~.i !1I : ;I. nI t :~ .~1 4:' Ir :I : :: WI'iI I! P. .,~

rt- I ;; [:.I;;t~it;t:t1 < 1 1! i;~I"!~. .I

2. Was a comprehensive description of the competiDg alternativesgiven?

NO CANT TEllYESThe three alternatives are fairly well described under thesection Methodsof Oxygen Administration, The paper explicidy excludes the do-nothingoption, as the question of whether treatment is wor thwh i le per se is notbeing addressed (and presumably the effects associated with no treatmentpreclude it from being a plausible alternative). The paper alludes to, butdoes not describe in detail, the alternative of renting concentrators. Sinceth is option is fa irly new and u ntried , the om ission is acceptable.More ....over, the authors do identify the conditions under which this option mightbecome attractive in the future.

3. Was there evidence that the programmes' effectiveness had beenestablished?YES NO x CANT TELL

The authors cite two studies, references 7 a nd 8 in the paper, which haveconfirmed that long-term domiciliary oxygen therapy reduces mortalityand im proves the quality of life . T h e r ela tiv e e ffe ctiv en es s of ea ch alte r-native was assessed in the second study specifically. The quality ofevidence, however, cannot be determined without first consulting thesupporting references. Nevertheless, in terms of the classification offorms of analysis outlined inChapter 2, th e study probably qualifies as acost-minimization analysis.

4. Were all the importaDt and relevant costs and consequences roreach alternative identified?NO x CANTTELLES

The costs considered in the study are those falling on the NHS andpatients, as a result of the incremental resource use o f oxygen therapy(i.e., only those treatment costs which are different across treatment

62


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63

Cost analy sisoptions). But the cost estimates, as currently presented. do not allow.separate identification of the costs to either the NHS or patients. (Forexample, there is no way to determine how much patients would have topay for necessary items such as electricity for runn ing concentrators).The costs which are common to all options (e.g.. physician visits.hospiraii:m tion. etc.) a.re excluded. This approach to r o s r i . . n g is appro-priate. as long as the actual amounts of the 'common' services consumedare indeed identical for all alternatives. Although costing only thedifferences in resource use brought about by the al temanves mayfacilitate the costing exercise. readers should be aware that if thisapproach is employed, nothing can be concluded about the total cost (LC-,total resource commitment) of any alternative.The authors choose therapeutic effects as the outcome measure. Butwhat if one option, although producing therapeutic effects equa l in

magnitude to the other options, is inherently more attractive because itallows, say, greater mobility for the patient? The authors contend that alloptions L-n.PI-Ol~ the quali ty of life, but the re lat ive contr ibution of each toincreasing patients' utility is not known.

S. Were costs and consequences measured accurately in appropriatephysical units? -

YES NO _L CANTTELLIt is difficult to determine whether costs have been measured accuratelybecause only total costs are provided for items such as running costs.rather than the individual quantities and prices of component costs.An intel


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_x_ YES NO CAN7TELL

Cos t ana ly s is6. Were costs and consequences valued credibly?

x YES(for costs) x NO CANT TELL(for consequences)--Market prices were used to estimate costs. based on a typical pattern ofcare (15 hours oxygen therapy). There is no reason to believe that in thisstudy market prices do not adequately reflect the true cost of resourcesused. Given the co ncen tratio n o n costs. however. there is linle discussionof the valuation of consequences. The authors state that the therapyreduces mortality and improves the general quality of life, and that thealternative modes of delivery a ll s ee m e d to b e e qu ally e ffe ctiv e. But it isimpossible to' determine the outcome measures used to derive thisconclusion. Amore sophisticated cos t-ut i l i ty antllysis design would haveemployed a more systematic approach to th e measurement of quality oflife.

" _ ~ . -

7. Were costs and consequences adjusted for differential timing?x YES NO CANT TELL

Adjustments are made to allow for the fact that. under the concentratoroption. more resource outlays will occur earlier as capital expendituresare required for the machines and workshop facilities.This is done byconvening the lnitiallumpsum purchase price into an equivalent annualcost using a seven per cent discount rate. Although no theoreticalrationale for the choice is provided, 7 per cent was the public sectordiscount rate advised by the 1 ,jK Treasury at the time of the study. (Ibisreinforces the notion that the viewpoint is primarily that of the NHS.)

8. Was an incremental analysis of costs and consequences ofalternatives perfonned?

A grapb is used to illustrate the differential costs between alternatives.(Recal l that the difference in e ffe cts is a ssum ed to be zero.) This type ofgraphical presentation is especially useful when costs vary as theservice(s)is(are) expanded. The difference in distance between any twolines can be interpreted as the incremental cos t of one option over theother.Readers should not confuse the concepts of in cre m e ntal c os t and

64


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Cos t a naly s isma rg in al c o st. The in c re m e n tal c o st is the additional cost that one serviceor programme imposes over another; however. marginal co s t is thechange in total cost resulting from a one-unit expansion or contraction ofthe service programme. Thus in c re m e n tal c o st is concerned with costdifferences between services or programmes, while m a rg in al c os : isconcerned with c o st d iff er en c es within services or programmes. Figure 1shows that as the number of patients increases. the average costs for theconcentrator options fall. (Average costs for the other options remainconstant). Figure 2. however. shows that as the number of patientsincreases. the in c re m e n ra l c o sts between the concentrator options andthe other options actually increase [i.e., the distances between the linesget bigger). This is a situation in which. as the number of patients expands,falling average costs make the concentrator option increasingly morecost-effective.

9. Was a sensitivity analysis performed?YES NO x CA.."ITTELL

The sensitivity of the results to (1) variations in the number of patientsserviced. (2) variations in the discount rate. (3) alternative assumptionsabout the existence of workshop facilities and ("') the length of useful lifeof the capital cost items was tested. No justification is provided for therange of patients considered (0-100) and the authors do not mentionwhich number is likely to be realistic for practical purposes. The range ofdiscount rates chosen for the sensitivity analysis is not provided. and theresults are summarized with the sole comment. The choice of discountrate bas little effect on the results'. (perhaps this brevity isa result of spacerestrictions imposed by the journal.) The rationale for the assumptionsabout the existence of workshop facilities is well described on p. 1147,column 2. Figure 2 indicates that the results are more sensitive to th echoice of assumption When the number ofpatients serviced is low.As thenumber of patients increases, the cost difference between the twomethods becomes less pronounced.There is no indication as to th e range of assumptions used concerning

the length of life of capital equipment The authors claim, albeit withoutevidence. that, ' ... the assumption of longer lives does not change theresults very much'.Apart from the capital cost items discussed above, the various cost

components were not subjected to any sensitivity testing. The authorsshould have explored the extent to which different assumptions aboutthese would change the study results.

65


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: 1n : ,' s !tr,-:!,. .! 1 ;r :. >~:.T-!'f~t'_~1 .~I.'L(~~~,~!'~' "~. .t o~;: ;,f -t ,~

Cost analysis10. Did the presentation and discussion or study results include a Uissues of concern to users?

x YES NO CANT TELLThe study compares, in a graphical format, the total costs of providingoxygen for all methods and concludes that. for all but the smallestnumbers of patients, concentrators are the most economically efficientmethods of service delivery. 'The graphical presentation has certain advantages for an evaluation

such as this. where the costs of the alternatives are a function of the scaleof operation. Figure 1, for example, is a good illustration of how programmes or services which are characterized by high set-up costs mayinitially appear to be relatively more costly than other options. but whencosts arc spread over an increasingly greater number of patients, theaverage cost per patient falls.A significant implication of this finding is that the average cost perpatient for the concentrator option will depend on the acrual number of

patients receiving care. If a concentrator programme is running withfewer than 13 patients, th e other alternatives will prove to be moreefficient. The authors recognize this point and caution, 'What is cost-effective inone location may not necessarily be cost-effective in another'.The authors cite two barriers to possible implementation of theconcentrator methods. First, the concentrators require a large capitaloutlay which might exceed budgetary allowances. This problem can be at

least partially overcome, it is suggested, by introducing more flexibilityinto the budgetary allocation process. Second, the provision of con-centrators would fall O n a different budgetary authority from the onecurrently funding small cylinder provision, thereby creating a disincen-tive for adopting the less costly concentrator method. Administrativechange is recommended to overcome this obstacle .

REFERENCESBoyle, M. H., Torrance, G. W.. Horwood, S. P., Sinclair. 1. C. (1982). Ac o st a lU 1 .iy sis o f pro vidin g n eo ntlltll in te ns iv e c are to 5~ 1499gram

binh we igh t infanrs. Research Report #51, Programme for Ouantita-av e Studies h i Economics and Populat ion , lY1cl"lastef University,Hamilton, Canada.

Clements, RM. (1974). The Canadian h o sp ir ai a cc o u n ti ng manualsupplemens, Livingston Printing. Toronto.

66

,;


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Cost analysisHorngren, C. T. (1982). C o st acc ou ntin g: a m an ag er ial empluzs i s (5thedn), Prentice Hall. Englewood Cliffs, N.J.

Hull. R, Hirsh. J., Sackett, D.L., and Stoddart, G.L (1982). Cost-effectiveness of primary and secondary prevention offatal pulmonaryembolism in high-risk surgical patients. Can . Med. Assoc. 1. 127.990-5.

Kaplan, R. S. (197 3). Variable and self-service costs in reciprocal alloca-tion models. The Accounting Rev i ew XLVIII, 738-48.

Levin, H. M (1975). Cost-effectiveness analysis in evaluation research.InM Gurtentag and E. L Struening (eds) Handbook of~"re search , Vol. 2 pp. 89-122. Sage, London.Lawson , K .. V., Drummond, M. F.. and Bishop. J. M. (1981). Costing newservices: Long-term domiciliary oxygen therapy. Lance t l, 1146-9.

Neuhauser. D. and Lewicki, A M. (1975). \Vhat do w e gain from the sixthstool guaiac? N. Eng! 1. Med. 293(5). 226-8.

Richardson, A W. and Gafni. A. (1983). Treatment of capital costs inevaluating health care programmes. Cos t and Manageme l l l :"Iov-Dec:26-30.

ANNEX4.1. METHODS OF MEASURING A:-i'DVALUING CAPITAL COSTSWe are indebted to Morris Barer of the University of British Columbia

for producing these examples, which should clarify th e treatment ofcapital costs.As a first note, we need to distinguish two classesof'capital'-Iand andequipment. TIlls is an -important consideration, because in costing

exercises w e assume land does not depreciate, while of course capitalequipm ent does. You can think of there b ein g a co ntin uum a lo ng whichmaterials and supplies 'depreciate' or are used up instantaneously and soare costed fully in the year of use; capital equipment depreciates moreslowly, and may be handled ina variety of ways; land does not depreciaIeat all.As a second note, recall that 'capital equipment costs have three

components-depreciation, opportunity cost, and actual operating costs.We wi l l igilore the last of these here. -First consider equipment, and let us use an example of a machinecosting $200 000 that, at the end of 5 years, has re-sale value ofS20 000.

Assume straight-line depreciationand adiscount rate of 4 per cent.Thereare, then, four approaches to costing:(i ) one can assume all costs accrue at time0,This amounts to treating

the equipment as one would less durable materials and supplies:

"

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Cost analysisTune 0 1 2 3 4 5Depreciation 200000 0 0 0 0 (20000)Undepreciated balance atbeginning of period 0 0 0 0 0Opportunity cost 0 0 0 0 0Dep'n. + opp cost 200000 0 0 0 0 (20000)Present value (PV) 200000 0 0 -0 0 (16439)Net present value (NPV) of equipment cost - S183 561

/ 1-~: ,it; . ( >

Alternatively, but equivalently; one can treat the machine as'instantaneously depreciating. except for the $20 000 resale value,which then is maintained t !L~ugh the 5 years;

Twe 0 2 3 4 5Depreciation 180000 -Undepreciated balanceat beginning of period 20000 20 000 20 000 20 000 20000Opponunity cost 800 800 800 800 800Oep ' n . + opp cost 180000 800 800 800 800 800py 180000 7 6 9 7 4 0 711 684 658NPV of equipment COSt - $183 562

.,.- (ii) One can compute depreciation and opportunity costs separately.They a re r e la te d in that the oppornmity cost of equipment refersto the use of th e resources embodied inthe equipment, intheir nextbest use-this is 'approximated' by calculating the-return on thefunds implicit in t h e undeprec ia ted value o f th e equipment at eachpoint in t ime ..H enc e, th e h ighe r t h e tat: of dep...eciation, the lowerthe opportunity cost, a D else eq ua l Again. one bas th e choice ofbuilding the $20 000 resale in at the end. or just depreciating lessof the machine. It wo rks out the same:

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Cost analysisTime 1 2 3 4 5Depreciation 36 000 36000 36 000 36000 36000Undepreciated balanceat beginning of period 200 000 164 000 128 000 92 000 56 000Opportunity cost 8000 6560 5120_ 3680 2240Dep'o. + opp costpV 44 000 42560 41 120 39680 3824042308 39349 36556 33919 31430NPVof equipment cost - 5183 562

Time 1 2 3 4 5Depreciation 40 000 40 000 40 000 40 000 20 000Undepreciated balanceat beginn ing of period 200 000 160000 120 000 80 D O O 40 000Opportunity cost 8 000 6 400 4 800 3 200 1600Dep ' n . + opp costPV

48000 46400 44 800 ~3 200 2160046 154 42899 39827 36928 17754NPV of equipment cost - S183 562

(ill)' One can compute an equivalent annual cost. This maybe useful ina situation where other operating costs are the same each year,making necessary the comparison ofonly a single year ofcost datafor each alternative in the economic evaluation:NPV -E AFs.~ ' ! ' . (WhereAFj.~..istheannuityfactor-fo r 5 years at an inte res t ra te of4 per- cent. See Table 2 inAnnex 4.2)183562 - E 4.4518 - E - $41233Inother words. an equal stream of costs amounting to 541 233 ineach of th e five yea rs of the program bas a present valueequivalent to any of the unequa l cost streams in (i ) or (ti) above.Note. therefore. that th e equivalent annual cost embodies bothdepreciation and opponunity cost.

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. ,

L

!..

Cost Analysis(iv) O ne tan use equivalent or actual ren ta l co sts. if availab le o r

estim able . N ote that because the ren ter wil l need to r ecover notonly deprecia tion of the rental equ ipm en t but also a ra te o f re tu rnat least as good as that from th e next best use of th e re so urc e. o necan take rental cost to embody bo th d ep re cia tio n a nd o pp ortu nitycost

Second, th e trea tm en t o f land is qu ite d if fe ren t because of th e J a c k ofdepreciat ion. A land purchase of $200 000 at t ime 0 would g en era te th efoUowing cost time stream:Time 2 3 4 5DepreciationUndepreciated balanceat b t - - _ g i ! - . .?!i!'.g of periodOpportunity costDep'n + opp costPVNPV - 535613

200000 200 000 200 000 200000 2000008 000 8 000 8 000 8 000 8 0008 000 8 000 8 000 8 000 8 0007692 7396 7 111 6838 6575

Conver ted to an equ ivalen t annual cOSLNPV-E' AFs , . .. , .535 613 - E 4.4518

It com es as no particular su rprise that E - $8000!

70


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methods for economic eval of health programmes

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