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Forming this irequality and manipulating (8)ifthe numberitChoose Strategy M ifb a > hfcat2BI'l)]> l)((l9/Bwhere pf > 1 and 3 > 1.to relative The left-hand-side of decision rule (9) reflects the marginal benefit of avaccinatdon that of encounter while the containsparameters of the cost functions of the two strategies.
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According to the decisionis sufficientlyrule, larger superiorit will dominete Strategy F for savivgefficiency at vaccination guarantees life-days.the number of healthy-life-days than saved per vaccination then Strategy the number saved per encounter, right-hand-side that h'3 if This decision rule has a simple graphic interpretation which can be expositedas three cases.CASE 1: STRATEGY M DOMINATES.
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The ratio b/a can be representedisoquantthe straight-line e in terms of v aud a fLxed level of R.graphically as the (absolute value of the) slope of obtained from equation (1) by solving to Thus condition theisoquant be steep enough so that point 2V* on in Figure 3awhere the optimal point is marked R*. At this solution, Strategy H is used toperform only vaccinations.the healthy-life-daysvalue of R is at the highest attainable axis.
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This situation (9) is equivalent the requirement the vaccination is depicted that - 9eF±1vre 3a.\ Strateg-y l1 scrat.gy~~strtey domina tesh(s,,x)tt9 Object*ive Function\ ~Strategy _e ~s 2V VUi eFigure 3b, ,L-fV* Strategy Fdominates PuImV H Fhev , x)mV 2v*: v +_ b/aFigu.e 3c. Neither strategy dominates AIJmV* Fh(e,,x)MV- * 2 V K page 10b/a that radio CASE 2: STRATEGY F DOMINATES. Although b is likely to be greater right-hand-ade i- is possible a, the inequality (9).
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In this case the H isoquants are flatter than in Case 1. Therefore,the largest number of life-days-saved will be at the point of tangency betweentne highest attainable H isoquant asthe Strategy F possibility labeled H* in Figure 3b.
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Because of the assumedMlustrated this solution would implycomplementarity of the Strategy F production process, that in the ratdothe fxed centers provide both encounters determined by the slope of a ray from the origin to point H*.and vaccinations is smaller the point thanoffrontier than and the ';y the same as the sLpe of a straight CASE 3: THE DECISION IS INDETERMINATE.
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If the slope of the H isoquant,b/a, is exactly to be eangentto the Strategy F frontier and to pass through the point 2V on the horizontalaxis, the left- and right-hand-sides of (9) are equaL This boundary case (depictedin Figure 3c) is unlikely to obtain in practice, but is instructive for the light itthrows on the role of the complementarity assumptions in the analysis.line constr*cted imply First.
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note in Figure 3c that the assumptions of some complementatity inh(e,Strategy F, but none in Strat' v, 1) is linear, frontiers onthat segments ABC are always dominated either by point C on tha Strategy Nfrontier or by a point at, or to the northwest of, A on the Strategy F frontier.Thus it is suboptimal to use Strategy H to support VHWs or to use Strategy F tofocus predominantly on vaccination twointerventions.X4, combined with the assumption that a portions of the impacts of the two possibility - whatever the health inefficiency at vaccination.
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Figure 4a depicts the situation if such complementarity were eliminated as B approaches to the requirement As t intuitively clear, complementarity helps Strategy F to compensate forits relative thatwould obtain I (dapproaches infinity). thatb/a be greater than (9).
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Thus in theabsence of complementarity the strategychoice reduces supporting encounters alone usingalone usingfixed centers (at point A in Figure 4a) and delivering vaccinations mobile teams (at point C in Figure 4a) - a choice which is more likely to favormobile teams.than Pf/2, a less demanding requirement in the Strategy F production process, to the sample choice between In this case inequality (9) reduces On the other hand, if Strategy F benefits ininfinity and conditionthat b/a exceedt P, a condition which is twice asthat b/a exceed hf/ 2 .
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Thus the assumption ofin the Strategy F production process increases by as much as aimpact of vaccinations must exceedits production process as shown in Figure 4b, S approaches (9) becomes the requirement hard to satisfy as the condition complementarity factor of 2 the extent that of VE W services at saving life-days.121the mobile strategy more cost-effectivefrom perfect complementatity to which the health in order to render eIJfV 9%~~iV* 2V* Figure 4a.
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Strategy F suffers zero complementarityILVfromeIJf V* A~ m~SlopoZ 2ai Figure 4b. Strategy F favored byperfect complementarity IV. Applications and Interpretations of the Decision Rule.page 12integration in decision If the values of the four parameters country or region of a country and for a specific confidence assumptions of the analysis accepted, cost-eireoive is known with precision for any country. Thls section applies information three the parameters tentative the and encounter curve with the e axs.
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All of these estimates are drawn together the application and interpreeation of the decision rule in Table 7 at the end ofthe section.rule (9) were known withthe otherapplication of rule (9) would provide thenone of these parametersUnfortunately fromto arrive atperisocostto illustrateestimates and per vaccination studies, on Ghana, Java, and life-days-saved f5xed-center the Ivory Coast, tif, of the a, b and in order intercept strategy. of the the program theoretical 1.
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of the the program theoretical 1. Estimates number of based of b, immunization two estimates in an of Healthy Life-Days-Saved Per Vaccination. life-days-saved on Ghanaian 1Table (LDS) perpresents anddata vaccination the Ghana Health Assessment Team (1981). [131assumptions as presented by The first estimate of 75.4 LDS per vaccination at the bottom of column (7) isthatin based on the bottom ofcolumn.
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The second estimate of 53.8 LDS per vaccinatioon inobserved column (8) is based on an empirical distrioution of vaccinations the proper rationeighboring Ivory Coast. Apparently third doses of theof measles vaccines tothe average polio and DPT vaccines.
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Since the third doses add the program.LDS, reducing times more impact onHowever, since measles vaccination has at evenLDS per vaccination slightly has a large negative effect on the average LDS per vaccine.it to other vaccines and to deliver least than any of the others, the various vaccinations to maintain the thirty reducing less average its proportion distribution proportions is difficult increases their than the of of at on Javanese immunization of b based Table 2 presents estimate and analyzed by a University of Michigan study In e rural population of 50,000, the Michigan study estimated comparable developed 1979).
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(14] an would reduce mortality and morbidity to a degree which is calculated here save total estimated the same order of magnitude as the eatimates for Ghana from Table 1.in columns (8) and (9) the raw material for developing aas(Grosse et al,thatdoses per yeartothrough averted deaths and 22,500 days of partial orisa figure which is ofprogram consisting of 27,000 administered to save 25.0 healthy-life-days Thus on average 1,790 disability.
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and assumptions per vaccination, vaccination life years Javanese program data the However the Javanese in three ways from the immunization program presented immunization program considered by the Michiganin Tablestudy differs 1. The Javanese program includes a vaccination of 2100 mothers per year foragainst measles and polio.
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Byneonatal the value of b thatreferring would obtain in Java if the vaccination program resembled that in Table 1.tetanus to the Michigan report, but excludes vaccinations it is possible to estimate Table 1. Estimation of the Average Number of Life-Days SavedPer Vaccination from Ghanaian Datapage 13Life- Days- Lost (2) 23.36 11.01 1.20 Prop. at Risk (3) .039 1.00 .038 .014 .077 4.65 .078 4.47 .961 Vaccination/ Dose (1) 1. Measles 2. Tuberculosis 3. Polio/l 4. Polio/2 5. Polio/3 6. Diptheria/l 7.
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Polio/l 4. Polio/2 5. Polio/3 6. Diptheria/l 7. Diptheria/2 8. Dipthena/3 9. Pertussis/l 10.Pertussis/2 ll.Pertussis/3 12.Tetanus/1 13.Tetanus/2 14.Tetanus/3 TOTALS 44.70 Poten- tial LDS (4) Prop. Prdcng Im'ty (5) .60 .90 .90 .90 .90 .90 .90 .90 .90 .90 .90 .90 .90 .90 599.0 11.01 15.8 7.9 7.9 .086 .078 .018 23.8 23.8 11.9 2.2 2.2 .2 706.0 LDS Per Vac. (6) 359.38 10.45 .57 .29 .29 7.08 6.65 1.57 21.46 21.46 10.73 1.99 .22 .22 ofDistributions Vaccinations:Theory Obsrvd.
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(7) (8).191 .142 .111 .111 .111 .037 .037 .037 .037 .037 .037 .037 .037 .037 .128.152.180.096.084.060.032.028.060.032.028.060.032.02875.4 53.8SOURCES: Table 1 of Ghana Health Assessment Team (GHAT) (1981) and the appendix to itdistributed by R. Morrow, WHO, Geneva.life-days-lost per capita in entire population from GHAT, Table 1,of entire the vaccination. population which is at risk Measles - pop. 1-2 assumed polio - pop.
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1-2 assumed polio - pop. 2-3 assumed 38/1000 from and 39/1000 this disease thus can(GHAT Appendix);(GHAT Appendix); Dip. - pop.- pop. oldertet. - pop. 0-2 assumed 78/1000; Non-neonatal Column (2): Expected column (10).Column (3): Proportion from benefit TB - entire 1-3 assumed 77/1000; pert. than 1 yr. assumed 961/1000.Column (4): Column (2) / columr population; among multiple doses as follows:polio: 50%, 25%, 252; dip. : 47.3%, 47.5%, 5%; pert. : 40%, 40%, 20%; tet. : 47.5Z, 47.5%,5%.
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: 40%, 40%, 20%; tet. : 47.5Z, 47.5%,5%. (Morrow, 1984, personal communication!(3). Quotient is allocated Column (5): Makinen (1982) and Shepard, of measles vaccine effectiveness Coast at 48.5% and 60% respectively. here. well-managed effectiveness The other EPI system.Sanoh field under and Coffi conditions (1982a) have in Cameroun and more optimistic The second proportions are conjectured to be obtainable estimated and the figure theIvoryis usedin aCalumn (6): Column (5) x column (4).
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The diptheria, pertussis and non-neonatal tetanusvaccines are administered in a single vaccine called "DPT. "Column (7): The eight distinct applications of a vaccine of vaccinations are: one each of measles and BC G, three distribution these the on Mali as presented children by P. Knebel of all six vaccinations.in Agency calculations receive across for International to a "fully immunized" three of DPT. The theoreticalindividualof polio and distinct eight the Sahel Development Development (1983).
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vaccination events is basedPlanning Team, Bamako,allIt assumes that Column (8): This distribution of vaccination types can be deduced from the data presentedby Sanoh (1983) on aggregate and on estimated events.coverage vaccinations performed rural population of this in the Abengourou by each of region the eight vaccinationin 1981 Table 2.
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Estimation of Life-Days Saved Per Year in a Population of 50,000 in Rural JavaWhen an ImmunizatLon Program is Added to an Existing Health Center.page 14*0.00.022.5Without Immunization Pop. in Life Thous Expect.
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Rate (3) (4) (2) Death Disa- bility Rate (5) Death Rate (6) With ImmunizationLife- Y ears DaysSavedSaved ;8) (9)Disa- bility Rate (7) Thousands1.5 7.0 13.0 21.5 48 52 50 35 104.0 * 85.9 * 1301 *28.3 21.0 27.4 19.9 298 22.52.7 5.6 * 3.6 2.4 5.6 * 176 3.6 15 Age Group (1) 0-1 Years Old 1-4 Years 5-14 Years 15-44 Years 45 Years Oldand Older 7.0 15 * 5.5 * 5.5 * TOTALS 50.0 11.0 11.4 10.23 10.9 1790 SOURCE: Unless otherwise in thefollowing notes are "Aaealth Development Model Applicatdon to Rural Java," Final Report of Grant No.AID/otr-G-1651, Department of Health Planiing and Administration, School of PublicHealth, University of Michigan, October, 1979.indicated, to R.N.
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Grouse, J.L.deVries, R.L.Tilden, A.Dievler,S.R.Day, to pages, tables or appendices all references NOTES: Immunization program consists of 27,000 shots per year against pertussis, (6600 doses BC G vaccine), tetanos measles. See pages 30, 34 and pages 2 and 3 of Appendix A in Grosse et a.
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(18300 doses DPT vaccine plus 2100 doses tuberculosisand postnataltoxoid), but excludesand both neonatal diptheria, tetanos Column (2): From page 27 and page 20 of Appendix T.Column (3): Interpolated by author from Ghana Health Assessment Team (1981, Table A).Column (4): Deaths per thousand population additional health programs.
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See alternative page 47 or of any mortality interpolated.table rates of for the in Appendix F. Since these two groups over 15, an overall 1, PV I in the first from base run with a health center but noline of Table 7 onthefor both groups istables do not provide rate Column (5): Days of disability per person per year.
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Source is same as column (4) exceptinterpolation is required for those under 15.Column (6): From Table 7, alternative 1, PV 3 with interpolation Column (7): Same as (6) with interpolation Column (8): Using C4 to represent column (4), etc. the formula for this column is:as for column (4).as in (5).C2 x C3 x (C4 - C6).The fifth row uses a population of 28.5 and a life expectancy of 30.Column (9): Thousands of days of disability saved per year computed by:C2 x (C5 - C7).
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page 15life years First, consider rate at zero for infants the numbet of addicional mea.sles vaccination were added to estimated the incidence per chousand among children aged one to four. assumed the case fatality among the 80% untreated). Table 1, then it will save 5.76 lives per thousand vaccinated per year Assuming entering life-expectancy Table 2, column 3), the additional 449 life years per year in this Javanese (5.76 x 1.5 x 52).that would be saved ifthe Javanese program.
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The Michigan studythan one and only 200In the latter group the studyand 5%as assumed in(200 x .048 x .6).arejust are vaccinated their is 52 years (fromof measles vaccination would save anrural population of 50,0001,500 children the 1-4 age bracket where to be 4.8% (0.5Z among the 20X treated If measles vaccine is 60% effective addition they less that rate as However, the incidence of neona.al tetanus t,.tanus toxoid given to per thousand with a case fatality of Grosse et al, Appendix A, V.3) would increase deaths group by 18.2 per expectancy is 48 years, the life-years For the 1,500 thousand.
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in in Java was estimated at 21.3the 2100 dosesbyto one agelifethis age group whose in the zero the pregnant mothers (assumed 95% effective lost would be 1,310 (18.2 x 1.5 x 48).rate of 90%. Thus, removing its and morbidity was deemed impact on mortality in Ghana polio does not even rank among the The Michigan study did not include polio among the 31 diseases analyzed,small.possibly because toIndeed (Ghana Health Assessment Teram, 1981, Table 2).
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As a roughlife-days-lost approximation, lost perperson per year applies to Java as well.
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Then adding polio vaccination would(1.2 xsave an additional 164 life years in the population of 50,000 Javanese on 50,000 / 365.25), while requiring theassuaption the sametime.an a-iditional 18,300 vaccinations at the children getting DPT get polio vaccinations the Ghanaian figure of 1.2 days of life top 25 contributors assume that that of the net three Thus these effect adjustments Javanesethe (449 + 164 - 1310) andimmunization program would be a loss of 697 life-years in the number of vaccinations by 17,700 (1500 + 18,300 - 2100).
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Toan increase subtract 697 from 1790, multiply thearrive at an estimate of b for Java, result by in a year and add 22,500 days of averteddisability (from column 9 of Table 2) for a total of 421,700 LDS. Then dividethat would be requiredthis total by the 44,700 (27,000 + 17,700) vaccinations inresulting to achieve average impact from the program defined by the Michigan study. [15]is 9.4, a substantial the number of days reduction it. The estimate to of easier program The than the disease 2.
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Estimates Per Encounter. to estimate immunization produces a measureable of Life-Days-Saved is inherently animpact that of a VHWinchange an individual will evercorrelatessite. predicts whether In some cases sero-conversion immunization program, because effective blood chemistry which accurately contract in question.
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Inhighly with an even more visible sign, a scar at the impact of VHWs on health can only be measured by observing acontrast, thechange isabsence of information on the in light of the available experience with VHW projects. A reviewsurprising published fundedin 1982, which limited itself by the United States Agency for International Development, identified 52 suchtheprojects of which 42 used a VH W of one variety or another.
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However, inlocated reviewers could find only "only five evaluations of health impact of VI W services on health to primary health care projects associated with the vaccination their activites. Nevertheless in health status status status (American Public Health Association, 1982, p.the project documents reviewed" 81). One of these was for a project without VHWs. Two of the other four citedimpacts of VH W activities on health status and the otherevidence of positive two demonstrated no rignificant effect.
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Although "nearly all the projects plan. many.status, in health by measuring to evaluate ; others are executedevaluation components are initiated but never completed (ibid., pp.
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79, 80).late; and s1l others are never initiated" outcome changes .page 16of VHWAs a result of this lack of information on the effectiveness of than tentatively the estimates judgements of VH W effectiveness, per VHW encounter,activity, any estimate of a, the number of life-days-saved b, above.must be proposed even more two independentHowever, by using expert from Javaneseestimates of a are possible, one from Ghanaian and the other data and assumptions.
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Table 3 develops estimates of the number of life-dayssaved per VH W encounter based on primarily Ghanaian rough estimates of thediseaseeffectiveness categories. Column (6) gives an estimate of the number of "needed" encounterseffectivewiti a VHW per yt.
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that no traditionaldem.. d by villagers for the VH W. Based on thishealers, pharmacists or other providers substitute theundoubtedly .high estimate of encounters average number of LDS per encounter per year, column (7) computes the Ghanaian VH W at , assuming for treatment this need generates the home and 13 different that all of to be 14.9.treating outside of that from the VHW and that the VHW for colds, diarrhea, seek other to which demand for the services of a VHW will fall short ofThe extent to estimate until a study such as those of Heller (1982) and"need" is difficult M wabu (1983) on Kenya is available for VHWs in a country similar to that underColumn (8) of Table (3) gives a rough estimate of such demandconsideration.
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the villagers will not accept any preventive orbased on the assumption they do not demand "enough" carescreening services and childhood pneumonia,from thesetney consider because (It has beensymptoms is consideredreported reduce by halfto be a mark of manhood in some cultures.)
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These assumptions the number of LDS bythe total number of encounters by the VHW, but reduce toalso drops by half the average LDS per encounter three-quarters these admittedly pessimisticnumber even under about 7.5, sdil a substantial assumptions.treatment.
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serious to be that blood in ttie urine, a symptom of schistosomiasis, sources of care or because schistosomiasis insufficiently to warrant so that they total the Ghanaian computed analysts system Cor 48 diseases and While current health hoped to have on nine of those, diseases at a much more disaggregated of each of incidence under each of eight different nutrition programs, the VH Ws and of five other in the rural Javanese population of 50,000.thelost under that VHWs could bethe Michigan study considered each of only 31leveL Working from estimates of thefor each of six age-sex categoriesandimpact ofcombinations on mortality and morbiditycombinations of immunization, the Michigan study developed estimates of the these 31 diseases sanitation treatment life-days impact the Table 4 extracts number of LDS per VHtW encounter life-years days from column (9) gives a total total by number of LDS per encounter of 15.0.the estimated from this work the information necessary thein Java.
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Converting the estimated number ofthe number of disabilitysavings of 3,531,200 LDS. Dividing thisnumber of encounters of 235,000 gives an estimatedto estimate saved from column (8) to days and adding Table 3. Estimation of the Average Number of Life-Days SavedPer Encounter with a Village Health Worker.page 17Life-Days Lost If Sick (2) 0.6 VH W Effectiv- ness (3) 0.10* Life-Days Saved/ Est'ed Incidence Encntr Per Thou. "Need" (5) 1000.0 (6) 1600 (4) 0.04 Life-Life- Days Est'ed DaysSvd.
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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 important between is that choice 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 "average the chosen vaccination" is that that and 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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