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"Demand" Savad(9)0.02(7) 0.02 800 (8) Disease (1) 1.
Cold 2.
SkinTnfection 3.
Malanra 4.
Malnutrition,Severe 5.
Gastro-enteritis 6.
Accidenrs 7.
Schisto-somiasis 8.
Pneumonia- Child 9.
Pneumonia- Adult 10.
PrematureBirth 6 815 0.10* 0.26 0.4 29.3 11667 0.63 1016.8 207 1935 0.38 0.20* 49.2 241.9 629 0.69 271.3 7750 0.37 1792.2 1300 1750 0.15 0.10 121.9 18.7 51.1 11.
Complicationsof Pregnancy 1229 0.39 12.
BirthInjury 13.
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Other10250 0.21 229.6 470.0 40.0 1.5 70.0 7.7 7.0 2.4 7.0 9.6 4.8 1.6 752 289 11 112 12 11 4 11 90 45 15 0.09 2.58 3.40 1.68 0.91 0.92 2.09 0.42 0.51 0.70 1.05 752 0 0 56 12 6 2 11 0 0 0 0 0.170.000.001.681.820.932.100.830.000.000.000.007.53Diseases 786 0.01* 4.9 209.0 334 0.50 TOTALS 38,325 1,830.6 3,287 14.86 1,639 NOTES: Column (2): Denved by dividing the life-days-losc calculated by the GhanaHealth Assesment Project (1981) by the estimated incidence rate from column (5).Column (3): The National Health Planning Unit (1978, Table 6) of Ghana estimatedlife days thatincludingtheformula:forhealthy days of life currently would be saved by the VHWs, LDS, and the portion of these savings that would be achieved without VHW system, LDSt.
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(LDS-LDSt)/(LDL-LDSt).
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diseases omitted in the National Health Planning Unit document.fully implemented primary health care system from each disease, LDL, the Figures with asterisks the estimates are derived by Figures without asterisks author's lost the are Column (4): Column (2) x Column (3) divided by an estimate of number of encounters perepisode, which is given by the ratio of column (6) to column (5).target Column (5): From Ghana Health Assessment Project (1981).Column (6): Prevention of malaria and malnutrition on the one hand and birth problemsthe VHW andon the other requires frequent encouters and pregnant women respectively.groups of children under the Assuming there are 60 children under three and 30 pregnant women per thousandand 150 encounterspopulation, totals are distributed &cross diseases 3 and 4 on the onerespectively.
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ratios.hand and diseases 10, 11 and 12 on the other according ratioto average 1.6 encounters Other diseases are assumed observed in a sample of VH W huts in Senegal in 1979 (Over, 1980).(e.g.
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five per year) between three two groups would require 300 encounters to the incidence per episode, These the the Column (7): Column (4) x Column (6) divided by the sum of Column (6).Column (8): Assume the VH W performs no preventitive or screening services and, forlack of demand, sees only half the episodes of diseases 1, 5, 7 and 8.Column (9): Column (4) x Column (8) divided by the sum of (8).
Table 4.
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Table 4.
Estimarion of Life-Days Saved Per Year in a Population of 50,000 in Rural JavaWhen 200 Village Health Workers are Added to an Exiscing Health Cencer.page 18Without VHWs P op.
in Life Thous Expect.
Rate (4) (3) (2) Death Disa- bility.
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Rate (4) (3) (2) Death Disa- bility.
Death Rate (5) Rate (6) Age Greup (1) With VHWsDisa- bility Rate (7) Life- Y ears DaysSaved Saved(9)(8) Thousands0-1 Years Old 1.5 1-4 Years 5-14 Years 7 13 15-44 Years 21.5 45 Years Oldand Older TOTALS 7 50 48 52 50 35 15 104.0 * 67.2 * 2647 *28.3 21.0 13.4 17.2 5424 81.42.7 5.6 * 3.6 1.6 4.6 * 696 3.2 639 * 5.5 * 4.7 * 11.0 11.4 6.9 9.4 9405 *9.25.396.0SOURCE: R.N.
Grosse, J.L.deVries, R.L.Tilden, A.Dievler,S.R.Day, "A Health Developmentof Grant No.
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ATD/otr-G-1651,School of Public Health,to Rural of Health Planning Final Report and Administration, Model Appladon Department University of Michigan, October, 1979.Java," that NOTES:- Village Health Worker Program as defined by Grosse et al (ibid., pp.
5-7 ofAppendix D) consists of one VHW per 250 people (or per 50 households) handling 4.7encounters per person per year, for a total of 235,000 encounters in the populationof 50,000.
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Of the 31 disease categories analysis, Grosse et alassume effect oneither morbidity or mortality these, but inevery disease where the health center has an impact.Columns (2) through (5): Repeated from Table 2, this paper.Column (6): From Alternative 6, PV 1 the results of which are given on the eighth line fromas forthe bottom of page 4 of Appendix F of Grosse et al (1979).
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Interpolated column (4).can have a beneficial that a VHW has some impact at a rural health center in 20 of treatment included in their Columns (7) through (9): Same notes as for Table 2 this paper.
page 19incorporates the proportion assumptions on that wil seek treatment Unlike the estimate of need in column (7) of Table 3, the Michigan studyin each ageexplicitly group for each disease Appendix B).
These proportions respiratory complicatdons of childbirth and pregancy.
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While some of these rather Javanese "demand" as large as the comparable one for Ghana.range from .90 for severe diarrhea and upperand for.10 fLgures seemthebased onis twiceestimate more comparable than to that based on "need."
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Thus the Javanese estimate from the VHW (Grosse et l.have been made makes these adjustments the Ghanaian of cases intestinal infection parasites estimate down high, face that .30 the for to to of for that than were the details of An examination the productivity on mortality or morbidity the Ghanaian analysts hoped of the VH W. The Michigan analysts assumed the they were more optimisitic the Michigan study calculationsanalyststhe Ghanaian reveal regarding thefor 20 of the 31VUW vould have some effect diseases analyzed, whereas for such an impacton only nine diseases.
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Furthermore, those problems which both studiesassumed the VHW would influence, the Michigan study assumed a greater VhWeffectiveness.
Column (6) of Table 5 presents of theVHW in the Michigan study which compares most directly with each of thevalues from column (3) of Table 3.
Setting aside colds and skin infections as(and in any event of trivialnot having been considered by Ghanaian analysts consequence istypically figure.
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These greatereffectiveness thelevel of assumed demandJavanese VHW is assumed to influence and the higher a relatively optimisticcombine one.
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Nevertheless, is of the same order of magnitudeas the estimate to make the estimate of 15 LDS per encounter total LDS), the column (6) effectiveness the together with larger number of diseases corresponding Ghanaian the implied effectiveness it for Ghana.than estimates, is encouraging for greater for Java fliure that the it (9), rule decision consider on budget C* could deliver on site 3.
Estimates of Parameters of of the Cost Functions.
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Estimates of Parameters of of the Cost Functions.
Turning now Ilf dight-hand-sLde parameter was defined denominator of this ratio operating responsibility was called V*.)
The numerator is the number oZ encounters center could support on the same budget VHWs.
To determine and management activities theThisin section m above as the ratio of two numbers.
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Thethat a fixed centerin one year, if it has no(In section ml, this numberthe same fixedthe supervision of outlyingthis number with any confidence will require detailed costand VH W supervisionstudies of fixed centers with outreach for VHW support and supervision.
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is the number of vaccinations in several developing countries.parameter through that the to in to scale the cost (net of vaccine However suppose costs) of traveling as the returns Suppose that within reach of Q people is directly proportional is the degree of returns interpretation section I).
purpose of travel or to supervise of these two an estimate estimates of the costs of a mobile vaccination Ivory Coast, in 1981 (Sanoh, 1983).
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(16]toto Q to the power s, where sthe same(and bears introduced (2) offunction thethe the target group within Q by a mobile teamserve Q by a fixed center, provided that only oneis performed.
Under these assumptions, Table 6 developsfor each of several values of s based on preliminaryin Abengourou,the VHWs aho tasks of Pf the cost is to vaccinate in equation same whether to scale parameter the cost function team operating roughly is Table 5.
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The tstimated Problems of Table 2 of the Text.EffectLveness of page 20the Javanese VIHW on the Twelve DiseaseGhanaian Di"as Category (1) 1.
C old Ghanaian Effec- Ghanaian Diseas tdvuess Incidence Category Javanese (2) (3) (4) Aggregated Javanese Age Group (5) PercentageImprovementin CaseFatality Rate (6) JavaneseIncidence(7)10 2 1000 2.
URI 0-15 15+ 0-15 15+ 0-15 15+ 2.
Skin Inf.
102 470 4.
Sidn Dii.
3.
M alria 4.
MalnutritLon 5.
Gastroenteritis 262 632 382 40 8.
Malaisi 1.5 not included70 5.
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Malaisi 1.5 not included70 5.
Mild Diarrhea 0-15 15+ 0-15 15+ 6.
Severe Di&.
6.
Accidents 20Z 7.7 13.
Burns 14.
Fractures 15.
C uts 7.
Schistosomiasus 692 7 not included8.
Pneumonia, Child 37X 2.4 1.
LRI 9.
Pneumonia, Adult 152 7 1.
LRI 0-15 15+ 0-15 15+ 0-15 15+ 0-15 15+ 10.
& 12.
Prem.
Brth 10Z 21S & Birth Injury 9.6 1.6 21.
Comp.
Brth 0-1 & Pregnancy02 02 0Z 0Z 962 1002 02 0 692 40 2 542 0 442 292 632 70 Z 792 792 85Z 20001000501002050200010002508030101115155010902411.
Comp.
of Preg.
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Comp.
of Preg.
392 4.8 21.
Comp.
Brth Wom.
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Brth Wom.
15-44 212 SOURCES: Grosse et aL (1979), Ghana Realth Assessment Team (1981) and Naciol HealthPlanning Unit (1978).NOTES: Columns (2) and (3): From Table 2 in the text.Column (3): Incidence per in overall population thousand from Table 1 of Ghana HealthAssessment Team (1981).Column (4): Appendix A of Grosse et al (1979).Column (5): Aggregates of the ssx age-sex categories Grosse et al (1979).used in Appendices A and C ofColumn (6): Calculated from the last two columns of Appendix C of Grows.
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et al (1979) byis the case fataiicty rate without(CFNRX-CFRX)/CFRX, where CFNRX the formula treatment, CFRX is the case fatality Column (7): Derived from the incidence al by choosing a value in the mi4dle of the range of incidence source.rate with treatment by a VHW.rates by age-sex group in Appendix A of Grosse etraces given in that Table 6.
EsCimation of If in Abengourou, Ivory CoastUnder Constanc and Increasing Returns to Scalepage 211.
Population covered by V8Ws attachedto a sngle fixed center.
2.
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2.
Number of fixed centers "needed" the entire region of Abengourou: to srve3.
Eimated number of encounters by VHWs attachedto a. single flxed center with budget given underAsumption F2 below (ie.
pf V*): ConstantReturns to Scale (s-l.0) Increasing Returnsto Scale(su.9) (s. 8) (su.7)7,900 5,750 3,860 2,32017 24 36 6037,100 27,000 18,200 10,9004.
Estimate of the parameter pf.
10.6 7.7 5.2 3.1Data and Asumptions Used:Abengourou Mobile Team: Fixed Centers as VaW Supervisors:Ml.
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Estimated rural population of Abengourou: 138,000 42.
Total cost of mobile team for one year.
5,293,814 1,009,600 M43.
Cost of vaccine: 44.
Cost to reach rural pop.
w/o vaccinating: 4,284,210 M5.
Average Cost per Cap to reach rural pop.
: 31.0' F1.
Number of vaccinationswith no encounters, V*: F2.
Budget for V* vaccinations, C*: F3.
Assumed number of supervisiontrips per year to each VaW: F4.
Maximum cost per spvsn tripthat stays within budget, C *: F5.
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Assumed number of encounterswith VHW per capita per year 3500735,7003245,2334.7NOTES: Row 1: Asume to scale parameter with a similar interpretation a is the returns in equatLon (2) of section m of the vhom come sufficiently almost all of the target group among them or to supervise and C represents values of Q is equal The entries in this row are thus equal to:the dLmple model of transport and supervision cost C - A Qs, wherethe s introducedtoresidents close to either vaccinatethe VHW who treats them,twol/s.Then to the ratio of the two corresponding costs all costs except drugs and/or vaccines.
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text, Q is the quantity of rural the traveling health professionals the ratio of to the power to (item MDl)xCtem F4/Item M4)(1/a)Row 2: Item Mli/Row 1.Row 3: Row 1 x Item F5.Row 4: Row 3/Item F1Ite Ml: The rural population is estimated at about 69% of the total population ofAbengourou given by Sanoh as 200,000 in 1981.Items M2, M3, M4 ae from Table 3 of a draft &nal report on a cost-effectiveness and are measured in 1981 CFA francs.
studythe Boston University Strengthening Health(Approx.
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260 CPAby L. Sanoh of CIRES, Abidjan and Delivery Services Project, francs/dollar in 1981).
(Sanoh, 1983)Item M5: Item M4/item Ml.
(Notes continued on next page.)
page 22returns to scale Suppose aul, implying constant asaumptions of Table 6 yield an estimate of Uf %qual to 10.6. hand the mobile team achieves substantial would not be available attached to a fLxed center, when s - 0.7.
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At this value of s, total transport costs rise only seven percent every benefited from economies of scale as great as this, one would not expect any small independent theIf -!n the othereconomies of scale in transport thatfor smaller amounts of travel by a VH W supervisorto be as low as 3.1forindustry in an LDCto findthen the value Of Po' is estimated in Q.
If the commercial tan percent increase left in the country.in trarsport.
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trucking truckers Then According to the decision rule, if b/a function of B (or of d), Strategy M is more cost-effective However, the functicn of a vanes between one (when B approaches two (when B approaches one).
Thus if b/s is greater the value of B has no effect on the decision.
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more cost-effective is between these two bcunds is B important.is greater than the ratio of Uf to athan Strategy F.infirity) andthan p /2than Pf, or less In the former case, Strategy h lisand in the latter case Strategy F dominates.
Only iE b/ais less three sections by aotted than P1 f/2, are marked with an F 4.
Applications of the Decision Rule.
Table 7 presents four estimates ofb/a across the top and four estimates of uf down the left side.
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The cells of thetable are divided into thesewhere b/a parameter values lead to the choice of Strategy F regardless of the degree ofthe southeastcomplementarity the two dottedcontain an M to indicate lines does the strategy choice depend on the value of B.
Instead of an F or anthe criticalM, these cells contain value of 6) above which (below which) rule would prescribeStrategy F.the critical value of B (and in parentheses the reverse.
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Only in the cells between to the northwest,that the f;xed center the decision lines.
Cels to indicate function.
Cells cost of to than columns (1) and (3) respectively.
For reasons explained above, column (2) for Java ard column (4) for GhanaAlso constant orto scale, as represented by rows (A) and (B)seem more plausible only mildly increasing seem more plausible the more extreme economies of scale as representedby rows (C) and (D).
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Within these cells, Strategy F unequivocally dominatesStrategy M in Java, fixedregardless of the complementarity centers.in the Javanese .,eturns than NOTES TO TABLE 6 (continued):Item Fl: The average number of vaccinations fourteen fixed health centers as reported by Sanoh (1983, Table 6).rural two of thein Abengourou which perform such vaccinationsper year performed by the Item F2: The average Item F3: In West African VHW worker projects, total cost for producing these vaccinations.
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3 supervisions per year is a minimum(Sanoh, 1983, Table 3).See for example Over (1980, 1982).recommendation.
Item F4: Item F2/item F3.Item F5: The assumption used in Grosse et al (1979).
At one VEW per 500 inhabitants, thisIn a sample of nine Senegalese villagesfigure implies 45 encounters in the summer of 1979, Over (1980) found the average VUW was seeing 6.5visited villagers a day, with a standard devaation of 3.9.
This small sample thus supportsthe estimate from Grosse et aLper week.
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However, for Ghanaian assumptions on the health impacts of vaccinationspage 23the degree of complementarity and encounters, and v can be produced as perfect looks like Figure ld, then B is very large preferable superuviung VH Ws from a vaccinations so that approaches one (d frxed center for a > If, on the Strategy F iscoat .9. the role.
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plays an important If eisocost curve(6 approaches zero) and Strategy F iscost offoregonethen Bfor s < 1.0.in curve resembles Figure la, the opportunity terms of is substantial approaches infinity) and Strategy M is preferable joint products so that the other hand, care strategy Based on illustrative parameter seems these integration health particularities of the epidemiologLcal situation and the costs of production a specific region.
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Where the relative services and the relative costs of African data and assumptions used to generate the degree of complementarity encounters choice of primarythesensitive inand basic healththe Westresemble rows (A) and (B) of column (4),joint production of vaccinatdons andimpacts of vaccination two strategies the is an imporcant input to the strategy choice.esatmates, the to be quite in fixed centers of the to V. Concluding RemarksWith only two parameters for are function and three the objective here is extremely the coefficients and that that that the model presented this parsimony to estimate cost function, advantages of relatdvely easy understood by decision-mnakers.
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Of course, expense of several strong assumptions.
Most assumption the strategLes is is policy decision government policies and programs within and without second critical assumption encounter" and strategy assumption healthy-life-days.the national health objective important fixed and the "average important between is that is that choice and the units of analysis can be the "averageintegrationis independent of the mix or impacts of these average events.
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A thirdis to maximizein rural areas the chosen vaccination" that from eachparsimonious.
Thethe model areof relatLvely easilytheis purchased at is among theintegrationand mobile from otherseparable sector.
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Athe health these the model can be the parsimony the the are function interventions Given these assumptions and the additional assumption the effects ofdiseases and health thecan be "guess-timated" epidemiologiLalobjective the Ghana Health Assessmentthe pattern to data organized Team study, as is done here in Tables 1 and 3.
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Since each of the objectiveoithe net impact of an intervention function parameters impact on any singlean function for a region bydisease, setting up two experimental groups, one with only the vaccination program andit would be feasible to estimate than the objective index of overall health additive, from of (a and b) represents that parameters fundamental according status, rather the its of Table 7.
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Cost-Effectiv;n Choice of an Integration Strategyfor Various Parameter Estimatespage 24Estimates of the Average Healthy Life Days of: Impacr on .A vaccination (parameter b) A VHW encounter (parameter a) Java with EPI (1) 9.4 15.0 Java Orig.
Assum.
(2) 25.0 15.0 Ghana Theory (3) 75.4 14.9 GhanaDemand/Obsrvd(4)53.87.5Ratio of b/a: .6 1.7 5.1 7.2Cost Function Parameters s and pfConstant Returns to Scale:(A) For s 1, If .10.
6Increasing Returns to Scale: (B) For s -0.9, Pf.
7.
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7.
7(C) For s 0.8, hf - 5.2 (D) For s9 0.7, f - 3.1 F F F F F , 3.2(0.5)j- J2.9 (0.5) 20 3(0.05)-; F F F 71.2 (0.01) I-- HMI ~ 1.7 ( 1.4)a | Ji-- *M -NOTES: Column (1): The estimate of b is derived in the text.
The estimate of ais based on Table 4.Column (2): The estimate Columns (3) and (4): The estimates Rows (A) entries equation:of b is based on Table 2, that of a on Table 4.of b and a are from Tables 1 and 3.throough (D): The estimates in cells A4, B3, B4, C3 and D2 are of pf are from Table 6.
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The numericalthethe values of 13 which solve b a hf(2[3/(>1)]- 1 )(hl)/Bvalues The complementarity, value specified Strategy F is cost-effective (or if 6 is below the choice.cost-effective in parentheses defined the are as 8 - 1/(-1).
values In these of cells, the elasticity if 13 is above the specified choice.
value Otherwise in parentheses) Strategy M is ofthethenthe page 25the to a control relative Alternatively one with only the VH Ws, and measuring health status introduced.
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[17] could be nonexperimental techniques has the additional advantage over "guess-timation" of correcting the problems of disease interdependence relaxation of the unpalatable assumption onisa and bonEither of these estimationforand competing risk, and thus allowingcost data from the region of interest.
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impact of each intervention intervention and less satisfactorily, little that health effects are additive.group where neither the parameters by multiple regression estimated relatively at function The cost parameters could be "gvess-timated" it would be feadLble and preferable in a specificcountry by working with experienced health ministry managers and dependingon their judgement as to the costs of various combinations of activities.
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[l8]Here too these parametersstatistcally areperforming some or all of the vaccination and VHW supervision functions.
Withenough observations, a moie flexible form could be chosen in lieu ofthe constant elasticity inaverage unit cost could be attributed aswell as to changes in output mix as modeled here.
[19]changes to changes in coverage and intensity form used here.
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With increased using a sample of mobile fixed centers to estimate teams and flexibility, functional that It is the care useful present contraet to studies study with of primary health the School of Public Health othercost-effectiveness countries,both of which were led by economists from the University of Michigan.
A teambased at constructed linear-programmingmodel referenced in Tables 2 and 4 above, which depends on 3,696 differentparameters function used here(Grosse et al, 1979, Appendices A, B and C).
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Although the SPH model deals withsepar4te packages of interventions justas the present paper the SPHmodel is completely theproblem of strategy choice with joint costs.treats Strategy F and Strategy X as distinct linear and thus would require modification in place of the two parameters -to address in the objective in developing administrative as discrete entities two the constructed An independent Development objective more parsimonious 221 parameters.
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With modification this model could also be used to address function, but than a programming model which has team based at Michigan's Center for Research on Economica non-linear(Barnum et al, 1980).
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Althoughincludescost constraints,linear cost constraints the SPH model, the CRED model neveztheless the strategy choice problem.to incorporate nonlinear Given the available computer time and resources, models patterned afterthe SPH and CRED models would be useful indeveloping countries to address almost any health planning problem.
However,the suze and complexity of these models makes thess costly and unwieldy andmay reduce they are understood, believed and used bydecisionmakers.
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available, andbelieved, smaller, special purpose models such as the present one may play animportant role demand amongdecision-makers in guiding policy decisions for modelling exercises.these models are generally for health planners and generating the degree understood to which Until tools A consideration which is difficult but must be addressed strategy the future.
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Two variables are particularly opposite directions on the preferrred is the degree of uncertainty in to introduce the choice of primary health explicitly into care the model,integrationin the present about various aspects ofin this regard and act inimportanc strategy choice.
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page 26there First, suppose is uncertainty the appear optimal given region under consideradon today's them may be unjustified tofixedinhabit impactcenters parameters, thepopulation might migrate either out of the region or to new population centerswithin the region.
is athe substantial argument in in five or ten years.
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Even if estimates In this situation favor.flexibility of the mobile teams large proportion of of cost and health the population regarding creating likely if a their A second dimension of uncertainty is the regional If this budpet of operating both on healthy-life-days level of funding must be considered.
is often cut markedly from programmed levels, cotstraint.
the effect lower is the one that saves the budget varies back and forth at random from its full level level.
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Even if here and the assumption of full funding, its productivity much more sensitive the considered likely.in over a series of years whenlowestseems best based on the model presentedits absolute need for fuel may makethan would beoption when such crises arethe most healthy-life-days the mobile strategy The best strategy less preferred fixed center, to recurrent .his situationcost crises strategies .o its thus and the rural health budgetthenthis muchat In view of the is evident.
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tentaciveness of the Section IV estimates, research efforts?
Which parameter estimates would provide the greatest least cost?But which parameters should be the forthe need focus of prioritybenefit at theare effort.
However, represented here by the parameter The benefits of immunization, less well-understood, the statistdcal b, arethe best known portion of the model and of the data, so they are not at thetop of the list of research priorities.
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As discussed in Section IV, the benefitsneed ofof VHW services inresearch estimating is necessary, Ut mustproceed deliberately, without two areas, to these services health care perform.
Thus the countries planning models can better serve as practical guides to policy.In contrastfor multiple primarytosector of developingthatthe rural areas top research priority joint cost function is both in lacking and relatively the health thus and political problems are immense.
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This research research on in should be estimation of a quick payoff.
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the expectation these benefits of a set of these cost in greater functions, inherent easy and so page 27NOTES(1] While an LDC might choose Strategy F in one region of the country and Strategyto see how a combination of both strategiesregion, it is hard M in another could be implemented mixture of strategies would require management necessary.time cost-effectively to reach each village more often in same the MOH to provide expensive the region, because such aandthan would otherwise betransport t21 One argument for different weights is that atding healthy-life-days of a productively dependents.
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The political for establishing question.employed adult may save additional sensitivity of such relative weights them within the decision-making apparatus to the lifelife-days of his or heris an argumentinof the country [31 For some purposes for different consultations disaggregation diaggregation present an approach problems in an ambulatory setting.it would be desirable preventive straightforward amongand curative problems.
Such a furtherthree-foldpresented here.
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Over and Smith (1980) and Smith and Over (1981)of patientof homogeneous aggregates to disaggragate generalization the creation further the of to is a [41 To the extent of for the initial future future relevant includes cost and investment cost constraint healthy-life-days, to modify the objective the eventual cost expenses plus the value of all discounted capital have a positive opportunity the planner that cost of the project's the capital Then it would be necessary stream all However, donors frequently make funds available health projects which are not available country.
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Furthermore, many developing capital will be provided by donors, an expectation The assumption here zero so that recurrent the intertemporal discount Martens (1980) aad Over (1980) on the recurrent cost problem in LDCs.aspect of the problem can be ignored and there This assumption makes every year for other countries behave is that the only relevant also discounted for the opportunity cost constraint future capital expenditures or future healthy-life-days.
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replacementto the country,the value of aU theseexpenses.thethe present.costs ofsamethe investment in isfor the developing country is thethe same so thatis no need toSee Gray andreplacementthat has often been fulfiled.cost of capital expenditures expenditures to capture recurrent function.
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function cost the as to if developed technology best technique [5l Although not derived from profit maximizing assumptions, sustainable managerial represent by the production the space spanned by vectors e and v, then a continuous curve fitted points may be inappropriate.
turned nonlinearides.
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turned nonlinearides.
technology by a piace-wise Smith and Over (1981).these cost functionsthus should be estimatedfor thefor only a limited number of discrete points into thesethat must bejoint production and otherof a nonlinear productionseeto in this situation can, of course, capture For an example of the representation integer-programming model in health, The integer-programming functions".
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production is defined approach "frontier practice linear and If [61 The problem of joint cost allocation in the production of e and v with other health sector activities other activities of the fixed centers).
incurred is jointness(such as thecostsjointly in the production of these other activities with e and v is smallIf the amount of total its head again if there recurrent raises rules can be used as suggested then standard allocation in deFeranti 31-33).
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However if joint costs are so large chat different allocation the choice between the fixed and mobile strategy, must be expanded to include a vector of these other activities function as veU as in the cost functions.
(1983, pp.rules alterthe scope of the modelin the objecdLvethen page 28(7] a reduction influences intervention typically diminishes with In fact h(e, v, x) is likely to be nonlinear both because the health impact of anygiven intensityand because from one diseasetypically from other diseases.
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Barnum etal (1980, Chapters 2, 3) specify a programming model with a nonlinear objectivefunction though data theyare its 221 parameters responses of 16experts.
Section V and its notes discuss a nonlinear version of h(e, v, x) in thepresent modeLthe morbidity or mortality the morbidity and mortality lack of appropriate these problems, to estimate for from the survey to capture increased coverage forced or in function with form of equation production (8] The functional substitution curvature, reversed.
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complementarity) is given by percentage increase resulting vaccinations separable in prices and output.from a one percent The elasticity -in the optimal o to that of encounters (2) is that of tae constant the sign of its exponent, of product transformation 1/(3 - 1) and can be interpreted ratio of vaccinations to encounters elasticity thus and (or elasticity increase in the (b/a).
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By assumption ratio of the effectiveness the cost function ofitsofas the(v/e)ofisL9] Under this hypothesis:/ ~ * v/sf) * (1/Sm)Thus for given p, Af(j), A (2), Under constant returns , V to scale A4j) - 2 Am(5) and V - C /Af(p).s and s is an ifcreaFng function of C(10] For example, Walker and Gish (1977) found mobile services to be substantiallyless cost-effective than fixed services at the delivery of curative care.
(111 See note 9.
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(111 See note 9.
(121 The assumption of complementatity in the Strategy M production process woouldlikewise render that strategy more competitive.due Team presents Assessment to and disease-specific each disease.
(1981, Tables mortality (131 The Ghaci Health healthy-life-days-lost measured by age- rates days-lost in the populacton, the total burdea of a disease on society cannot beused directly Instead toestimate itsmarginal oflife-days-saved (ibid., pp.76, 77; Creese, 1979, pp.
24, 25).
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24, 25).
Tables 1 and 3 of this paper provide examplesof possible estimatesfrom Ghana into impact measures of this sort.interventions.
the marginal number of life-days-saved cost resources by an so across all is necessary and number that interventions.
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allocate is equalized the healthy-days-of-life-lost total2) Whetherintervention the or by healthy-life-per unit cost to prioritize approaches translating estimates disease then and of to 1, it [141 The programming model of rural orimary health care in developing countries byBarnum et al (1980) has the advantage of modeling disease interdependence.
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However, escimates of the parameters the results reported for that model.a and b cannot be easily deduced frompage 29[151 Assuming the costs of this program analyzed by Michigan, cost-effective incidence of measles assumed by the Michigan study for unvaccinated children would have to be carefully substantiated.than a program like that analyzed total LDS would make that of thelessit for Ghana.
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However, the lowJavaneserevised program would be larger smaller than the (16] All figures drawn from Sanoh (1983) are preliminary and, like the other figurespresented here, are for illustrative purposes only.
(17] With the addition of one more experimental vaccination and VHW services, an interaction objective function.
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Equation (1) of the model would then be modified to read:into group, one term could be introduced receiving boththeH - ho + a e + b v + d e v .A new version of deision rule (9) would then have to be derived accordingly.
(181 Two modifications of Creese's unit of analysis healthy-life-day and vaccinations should be changed and procedures to be treated as joint products.
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(1979) costing guidelines would be helpfuL Thethefor allowing encountersthe "fully-im munised-child' should be suggested from to [191 For example, Chiang and Friedlander (1984) use a translog function to specify ageneral multiproduct cost function.
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page 30REFERENCESAgency for International Development (1983) "Project Paper for the RuralMedical Services Project USAID ision.in Mauritania," mimeo., Noaukchott, Mauritani:Barnum, Howard, Robin Barlow, Luis Fajardo, Alberto Pradilla (1980) AResource Allocation Model for Child Survival, Cambridge, Massacusetts:Oelgeschlager, Gunn & Hain.Berggren, W.L., D.C. Evbank, G.G.
Berggren (1981) "Reduction of Mortality inProgram," New EnglandRural Haiti Journal of Medecine, VoL 304, pp.
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1324-30.a Primary-Realth-Care through Chiang, .juay Wang, Ann F. Friediander (1984) "Output HeasureuencL, NuwurkEffects, and Economics and Statistics, VoL LXVI, No.
2, pp.
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2, pp.
267-276.the Measurement of Trucking Technology," The Review ofCreese, Andrew L. (1979) "Expanded Programme on Imunization ComingGeneva: World HealthGuidelines," WHO Report OrganizatLon.EPI/GEN/79/5, de Feranti, David (1983) "Some Current Methodological Issues Analysis," mimeo., Health Population Project and Department, World Bank.in Health Sectorand NutritionEvans, J.R., .L.
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Hall and J. Warford (1981) "Health Care in the DevelopingWorld: Problems of Scarcity and Choice,"New England Journal of Medicine,VoL 305, pp.
1117-27.Ghana Health Assessment Project Team (1981) "A Quantitative Method ofin Less DevelopedImpact of Different Diseases Assessing the Health Countries," International Journal of Epidemiology, Vol 10, pp.
73-80.Sahelian Gray, C. and A. Martens(19807'The Recurrent Costs of Development Programsmimeo.,laAsn.
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forin Oua;:dougcu: Comitd LnteU-Etts Sahel; Pars: Club du Sahel Cambridge, MA: Harvard International Development.and Recommendations," In secher..e.d Countries: Analysis de Lute Istitute contre Grosse, Robert N., Jan L. deVries, Robert L. Tilden, Anne Dievler, Suzanne Rieto Rural Java," FinalDay (1979) "A Health Development Model Application Report of Grant No.
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AID/otr-G-1651 from the Bureau for Pro-ram Policyand Coordination, United States Agency for International Development,Ann Arbor Department of Health Planning and Administration, School ofPublic Health, Univeruity of Michigan.Gwatlin, Davidson R. (1983) "Does Better Health Produce Greater Wealth?
: Aand Output,"the Evidence Concerning Health, Nutrition Review of Mimeographed report.
New York: Overseas Development Council page 31Gwatkin, D.R., J.R. Wilcox, J.D.
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Wray (1980) Can Health and Nutrtion ProjectsMake a Difference, Monograph No.
13, Overseas Development Council,W"hington, D.C..HeUer, Peter (1982) "A Model of Demand for Medical and Health Services inWest Malaya," Social Science and Medecine, Volume 16.Kasongo Project Team (1981) "Influence of Measles Vaccination on SurvivalPatterns of 7-35 Month-Old Children in Kasongo, Zaire," Lancet, ApriL 4,pp.
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764-767.ielmann, Taylor, Desweemer, Uberoi, Takulia, MHaih Vohra (no date) Theinfections: Hand Indian Council ofof Nutrition the Naranswal Exzeriuent Morbidity and Mortality Effects, Medical Resarch, WHO-H9/181/23.on Interactions supported by Kiaratia, Herbert E. (1982) "The Road to Cost-Effectveness Analysis," MllbankMemorial Fund Quarterly Health and Society, VoL 60, No.
4, pp.
585-603.Mahiou, (1977) "Expanded Progras J.M.
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585-603.Mahiou, (1977) "Expanded Progras J.M.
theFeasibity, for Childrenby District Mobile Teams in Kenya," Weekly Epidemiological Record, Vol.52, No.
24, pp.
197-199.Coverage and Cost of Maintenance Immunization: Immunization Study of on Makinen, Marty (1981) "A Benefit-Cont Analysi Yaound4, Caueroun," Discussion Paper No.
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96, Center Economic Development, Uaiversity of Michigan, Ann Arbor,Hichigan.of Measles VaccinaioAs infor Research onMvabu, G. (1983) "A Household's Demand for Health Services: A Study of Ruralin economics,Health Care vith Emphasis on Kenya",Doctoral dissertation Boston University.National Health Planning Unit (1978) "A Primary Health Care Strategy forGhana," Republic of Ghana, Ministry of Health, National Health PlanningUnit, Revised April 1, 1978.Over, A. M., Jr. (1980) "Five Primary Health Care Projects in the Sahel and theto Harvardthe Sahel Recurrent Costof Recurrent Costs," Mimeographed consultant Development International report for for Isue Insitute StudyOver, A. M., Jr. (1982) "Tvo Approaches the Effect of Scale onthe Cost of a Ptimary Health Care Program in a Developing Country: TheCase of Niger," Presence Africaine, No.
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124 (4th Quarter).to Projecting Over,A.M., Jr. (1983) "On the Care and Feeding of a Gift Horse:The RecurrentCost Problem as the Result of Biased Project Design," Worling Paper No.69, African Studies Center, Boston University.Over, A.M., Jr., K.R.
Smith (1980) "The Estimation of the Ambulatory MedicalJournal ofis an Unobservable Varble," Care Technology vhere Output Econometrics, VoL 13, pp.
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225-251. page 32Parlato, Margaret Burns, Michael N. Favin and Problems An Analysis Prosress Washington, D.C.: American Public Health Associationof (1982) Primary Health Care:Proiects,52 AID-Assisted Sanoh, Layes (1983) Draft of a cost-effectiveness the expandedin the Ivory Coast and personal communicatdonanalysis of program of immunization with the author.Scrimshaw, N., Taylor and Gordon (1968) Interactions of Nutrition andInfection, Geneva: World Health Organization.Shepard, D.S., L. Sanoh and E. Coff.
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(1982a) "Estimating offrom Retrospective Household Surveys: Method andMeasles Vaccination forto Rural Zones in ths Ivory Coast," Project Preliminary Application Stengthening Health Delivery Systems, Boston University and Center forthe AnalyLs of Health Practices, Harvard School of Health, September.the Effectiveness Shepard, D.S., L. Sanoh and E Coffi (1982b) "The Cost-Effectiveness Expanded Program of Immunization: A Preliminary Report," Project Stengthening Health Delivery Systems, Boston University and Center the Analyss Septem ber.of theforforof Health Practices, Harvard School of Public Health,Smith, KR.
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and A.M. Over, Jr.
Regulations Stevenson Academic Pres, New York.on Productivity (eds.)
Productivity (1981) "The Effect of Health Manpowerandin Medical Practices," Industry,in' Regulated Measurement in Coving Walker, G. and 0.
Gish (1977) "Mobile Health Services: A Study inCost-Effectiveness," Medical Care, April, pp.
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267-276.World Health Organization (1978) "Alma Ata 1978: Primary Health Care: Reportof the International Conference on Primary Health Care, Alma Ata, USSR,6-12 September, 1978," World Health Organization, Geneva.
C. Hambidge61539C.
Hambidge61539C.
Hambidge61539M.
Kiguel61761E.
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Zamora33706PPR Working Paper SeriesTitle Author Date ContactWPSI Imports Under a Foreign Exchange Constraint Cristiat Moran March 1988 WPS2 Issues In Adjustment Lending Vinod Thomas March 1988 WPS3 CGE Models for the Analysis of TradePolicy in Developing Countries Jaime de Melo March 1988 WPS4 Inflationary Rigidities andStabilizeflon Policies WPS5 Comparisons of Real Output inManufacturing WPS6 Farm-Nonfarm Linkages in Rural Sub-Saharan Africa WPS7 Institutional Analysis of CreditCooperatives WPS8 Prospects for Equitable Growth inRural Sub-Saharan Africa Miguel A. Kiguel Nissan Liviatan April 1988 Angus Maddison Bart van Ark April 1988 Steven Haggblade Peter B. Hazell James BrownApril 1988 C. Spooner37570Avishay Braverman J. Luis Guasch April 1988 C. Spooner37570Steven Haggblade Peter B. Hazell April 1988 C. Spooner37570J.
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Israel31285WPS9 Can We Return to Rapid Growth?
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Andrea Boltho June 1988 WPS1O Optimal Export Taxes for Exportersof Perennial Crops WPS11 The Selection and Use of Pesticidesin Bank Financed Public HealthProjects WPS12 Teacher-NonTeacher Pay Differencesin Cote d'lvoire Mudassar lmran Ron Duncan June 1988 A. Kitson-Walters33712Norman Gratz Bernhard Liese June 1988 C. Knorr33611Andre Komenan Christiaan Grootaert June 1988 R. Vartanian34678 PPR Working Paper SeriesTitle Author Date ContactWPS13 Objectives and Methods of a WorldHealth Survey Trudy Harph.,m Ian Timaeus June 1988 A. Menciano33612WPS14 The Optimal Currency Composition ofExternal Debt Stijn Claes-c's June 1988 S. Bertelsme33768WPS15 Stimulating Agricultural Growth andRural Development in Sub-SaharanAfrica Vijay S. Vyas Dennis Casley June 1988 H. Vallanasco37591WPS16 Antidumping Laws and DevelopingCtA ifre Patr.ck .s.c_r!
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Juno 1988 WPS17 Economic Development and the DebtCrisis Stanley Fischer June 1988 S. T.orr}J33709C.
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