metadata: authors: 0: author: Over,A. Mead
docna: 0: docna: Cost - effective integration of immunization
            and basic health services in developing countries : the
            problem of joint costs
docty: Policy Research Working Paper
subtopic: Health Care Services Industry,Disease Control & Prevention,Public Health Promotion,Reproductive Health,Early Child and Children's Health,Health Service Management and Delivery,Immunizations,Transport Services,Law and Justice Institutions
teratopic: Health, Nutrition and Population
abstracts: cdata!: With limited budgets for rural primary
            health care, developing countries are under pressure to
            integrate the basic medical services that government health
            centres provide, with the vaccination programs that mobile
            immunization teams handle. Application of cost effectiveness
            analysis is complicated by two inherent difficulties. First,
            because the two types of health care programs improve the
            health of different target groups, some common measure of
            the effectiveness of the two programs must be agreed upon.
            Here the "healthy life years" saved by the two
            alternatives is implemented as a useful measure of
            effectiveness. The second difficulty is that of modelling
            the joint costs of simultaneously producing more than one
            health care service. Using the method described here,
            economists can address this problem in a way that does
            justice to both the superior efficiency of the mobile teams
            and the superior comprehensiveness of the fixed centres.
repnme: repnme: Cost - effective integration of
            immunization and basic health services in developing
            countries : the problem of joint costs
display_title: Cost - effective integration of
            immunization and basic health services in developing
            countries : the problem of joint costs
listing_relative_url: /research/1988/07/700689/cost-effective-integration-immunization-basic-health-services-developing-countries-problem-joint-costs
topicv3: Transport m1326661 135,Health Services Delivery m1327294 1305,Immunizations m1327505 1459,Mortality m1504365 3661,Health m1504661 3480
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Health, Nutrition and Population
origu: Policy Plan & Prog Review Dept
no_of_pages: 37
author_keys: 0: author_key: 92737
model_extractions: <!-- Start of picture text --> Polcy aPtning, and R rech |<br>Population, Health, and Nutrition<br><!-- End of picture text -->

With limited budgets for rural primary health care, developing countries are under pressure to intcgrate the basic medical services that govemment health centers provide with the vaccination programs that mobile immunization tearns handle. For health planners, the question is whether to organize the integrated services around the fixed health centers or around the mobile health teams. Implicit in this decision is a choice between more comprehensive health care from the fixed center versus more selective care from the mobile teams.

Application of cost-effectiveness analysis is complicated by two inherent difficulties. First, because the two types of health care programs improve the health of different target groups, some common measure of the effectiveness of the two programs must be agreed upon. Here the healthy-life-years saved by the two altemative programs is proposed and implemented as a useful common measure of effectiveness.

The second difficulty is that of modeling the joint costs of simultaneously producing more than one health care service. In some situations the degree of "jointness" of the cost structure and the associated production technology have an important impact on thc relative cost-effectiveness of the two altemative approaches.

Using the Liethod described here, economists can address this problem in a way that does justice to both the superior efficiency of the mobile teams and the superior comprehensiveness of the fixed centers. Special purpose models such as this one can guide policy decisions since they are less complex than more general models and can be easily understood by decisionmakers.

This paper is a product of the Population, Health, and Nutrition Division, Population and Human Resources DepartmenL Copies are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Noni Jose, room S6-105, extension 33688.

The PPR Working Paper Series disseminates the fuidings of work under way in the Bank's Policy, Planningn and Research Complex. An objective of the series is to get these findings out quickly, even if presentations are less than fuilly polished. 'Me findings, interpretations, and conclusions in these papers do not necessarily represent offilcial policy of the Bank.

Copyright i) 1988 by the Intemational Bank for Reconstruction and Development/Tc World Bank
<!-- Start of picture text --> Cost-Effective Integration of Immunization and Basic Health Services in<br>Developing Countries:<br>The Problem of Joint Costs<br>by<br>Mead Over<br>Table of Contents<br>Page<br>I. Introduction ................................................. 1<br>II. The Planner's Decision Problem ......................... 2 ..................<br>m. A Rule for Choosing the Cost-Effective Integration Strategy.. 4<br>IV. Application and Interpretations of the Decision Rule . . 12<br>1. Estlmates of Healthy Life-Days-Saved Per Vaccination ... 12<br>2. Estimates of Life-Days-Saved Per Encounter ................... 15<br>3. Estimates of Parameters of the Cost Functions ............... 19<br>4. Applications of the Decision Rule .................................... 22<br>V. Concluding Remarks ................................................ 23<br>Notes .27<br>Refereices .30<br><!-- End of picture text -->
**page'**

# L Introduction

The delivery of life-saving primary health care (PHC) to the rural poor of less developed countries (LDCs) has been a goal of almost all of these countries' governments since the Alma Ata Conference of 1978, if not before (World Health ergam.zation, 1978). To achieve this goal, each LDC must choose how much of its limited recurrent budget to allocate to rural primary **heaLth** care, what mix of health care services n deliver with this limited budget and how to organize and manage their deliver,. As the scarcity of LDC recurrent budgetary resources grows more acute, minL-ries of health (MORs) are being urged to focus on consolidating and enhancing the efaciency of current programs rather than on implementing new ones. However, the search for efficiency "will raise difficult questions about trade-offs (such as] the choice between disease-specific, vertically organised health services and the multi-purpose, horizontal (basic health services] approach" (Evans, Ral and Warford, 1981, p. 1124).

The choice between vertical immunizatio-n programs using mobile vaccination teams and horizontal basic health services programs using polyvalent village health workers (VHWs) is particularly painful because the two types of programs attack different high priority diseases. An alternative to this choice is to integrate both VaWs and vaccination into a program that is more cost-effective than either would be alone. Indeed this kind of integration has been Achieved in some of the most successful primary health care experiments (Gwatkin, Wilcox and Wray, 1980; Berggren, Ewbank and Berggren, 1981). For the integrated program to be cost-effective, the two critically scarce and expensive inputs, transport and management skill, must be conserved by the chosen integration strategy. There are at least two different integration strategies which fulfill this criterion and again a choice must be made.

On the one hand, immunization activities can ba added to the functions of the horizontally organized government health centers which also function as the support system and referral target for the VH Ws who deliver basic health services. The MOH that follovs this strategy chooses to allocate its limited transportation budget to the support and supervision of fixed centers and to trips by fixed center personnel to supervise VH Ws, rather than to vertically organized mobile vaccination teams. Villagers could obtain vaccinations on pre-speciEied days at the center, but most vaccination would be done by the frxed-center-based VH W supervisor when he or she visits the VH Ws in their villages several tides a year. rn the rest of this paper this integration strategy is referred to as "Strategy F." On the other hand, VHW support and supervision could be added to the tasks of the vertically organized mobile vaccination team. With this option, "Strategy M," the fixed centers would have no respousibility for either vaccination or VRW supervision, but might remain involved with basic health services as the trainirg sites and referral targets for the VHWs.[l] The planner who attempts to choose between these two integration strategies for a given country or region of a country wiMl not lack for advocaces of the two alternatives. Primary health care experts are likely to prefer Strategy F, the approach that allocates the transport to the support of the VHWs, while immunization experts will probably prefer Strategy H, because it
page 2 allocates transport to the mobile vaccination teams. However, when the pianner turns to the economist for guidance in choosing a cost-effective integrated program, he may be told that "there is no general solution" to the problem of allocating joint costs among several outputs of a program and that the results of applying cost-effectiveness analysis to such a program, "although ... not capricious, ... are arbitrary and subject to change when other, perhaps equally plausible, (allocation] rules are adopted" (arman, 1982, p. 595).

The goals of this paper are to contribute to the methodology of cost-effectiveness analysis in the presence of joint outputs and to address the substantive problem of primary health care integration in developing countries. The paper characterizes the planner's choice problem in a way that avoids the need to allocate joint costs, while capturing both the superior efficiency of mobile teams at producing vaccinations alone and the greater degree of complementarity between VHW support and vaccinations in fixed centers. The model is set out in general terms in Section HI and then with sufficient structure that a decision rule can be derived in Section II Section IV derives preliminary estimates of the parameters of the decision rule from available information on the epidemiology and costs of rural primary health care in developing countries and uses these estimates to illustrate the application and interpretation of the proposed decision rule. Section V contrasts the model developed in this paper to two other large programming models, remarks on the impact of u ertainty on the proposed decision rule and suggests directions for fruitful res.

# IL The Planner's Decision Problem

A con-etuent index of a health strategy's success in reducing both morbidity and mortality is the number of "healthy-life-days" that the s.rategy saves (Ghana Health Assessment Team, 1981). By counting a day of reduced health as only a fraction of a day of ful health, this index is able to summarize in cne number the effects of a policy on both mortality and morbidity. As applied here, the healthy-life-days index weights a child's life-day the same as that of a working adult, but it would be straightforward for a country which applies this decision process to develop its own weights for life-days saved in each rural demographic group. (21 In the context of the present decision problem, there are two health sector activities that could potentially contribute to the healthy-life-days of rural ciizens: VHW services and immunization services. Each of these aggregates is itself a mix of different elementary activities.

VH W services can, in turn, be further disaggregated among preventive consultatons, curative drug dispensing and referrals to the local clinic or dispensary. Typically the VHW, the villager-patients and the health ministry will have different opinions regarding the "best" mix of these three categories of services. The mix actually achieved in the field will depend upon a variety of factors including the quantity and quality of VHW supervision, the pecuniary and non-pecuniar; rewards attached to each kind of service, the distance of the VHiW from other care providers, the price and quality of those alternatives, and so on. Let the term "encounter" refer to any health-related contact between a villager and a VH W. Then the three different categories of encounters can be represented by el, e2 and e3. (31
**page** 3

Immunizatdon services can also be disaggregated among vaccinations for different diseases and then among the first and subsequent vaccinations for diseases that require more than one. The "expanded program of immunization" (EPI) recommended by the World Health Organizaticn is designed to protect against sLx diseases through the administratio", of four vaccines, two of which are to be administered three times each Thus there aret eight distinct vaccination services delivered by an EPL 'aking such a progzam as the norm, let vl, v, . v represent the 2ight distinct vaccination services that are relevant tk a "cLve LDC.

With healthy-life-days represented by h, the health planner's objective function is given by: H - h(e, v, x), where e and v represent respectively the vectors of subscripted encounter variables and vaccination variables. The function H is assumed convex **and** increasing in all of the elements of e, v and **x.** The **variables** in x represent cther health sector activities and the environmental, behavioral and socio-economic determinants of health, which are all asumed to be independent of the chosen primary health care integration strategy. In the rest of this paper these variables are held constant at .

In attempting to maximize h subject to a given annual operating budget, the health planner faces one of two different recurrent c-*t constraints depending on whether the fixed or mobile strategy is followed.(41 Let A be a vector of the prices of inputs such as the wages of the various manpower categories, the prices of gasoline for transport, kerosene for refrigerators, essential drugs and vaccines, or office supplies. Then denote the "fixed" and "mobile" primary health care integraron strategies by the subscripts f and m, respectively. The recurrent cost functio.. for the two strategies can be written: C f **.cf(,v,** V , Cm acm(e,v,2) where the cf and cm functions are increasing in (the elements of) e, v and a. concave in e and v, and homogeneous of degree one in p .51 If these functions are known, then the planner must solve two constrained optimization problems and then compare the two optimal solutions. If the maxiw.um annual recurrent budget for the health planning region is represented by C and the vector of expected input prices by j, then the two problems are: For Strategy F: max h(e, v, it) subject to: cf(e,v,) O< C* For Strategy t: max h(e, v, if) subject to: cm(e,V,i) < C .
page 4 By solving each of the two problema for the optimal vectors of encounters and vaccinationr and then substituting those optimal vectors into h(e, v, R) it is possible t i compute the number of healthy life days that would be saved by each strategy. Call these amounts Hf and H*. Then the health planner's decision rule is just to choose the strategy that saves the larger number of healthy life days for the given budget. In other words:

# Decision Rule:

If Hm > Hf, choose Strategy M. (C ase 1) If Hm < Hf, choose Strategy F. (Case 2) If Hm a Hf, choose either strategy. (Case 3) Thus the problem of choosing the most cost-effective intsgration strategy for rural primary health care is easily solved once the functions h, cf and c are known. Since the ectivities e and v are all judged in terms J1 life-days-saved, it is neither necessary nor desirable to allocate joint costs among these activities. Therefore the arbitrariness of such allocations highlighted by Klarman (1982, p. 595) and others does not attach ta the analysis.[6] The fact that present-day knowledge is inadequate to specify these functions with much confidence creates the prevailing uncertainty about which is the correct integration strategy. On the basis of some assumptions regarding the nature of these functions, the next section illustrates how a precise decision rule can be developel for a given region and discusses the behavior of that rule under various circumstances.

# II A Rule for Choosing the Cost-Effective Integration Strategy

To simplify the characterization of the objective function h and the cost functions cf and cm, assume that the cost-effective mix of VHW services el, e2 and ei is constant and therefore independent of such variables as the scale of &he program, the ratio of vaccination services to VHW services and whether Strategy F or Strategy M is chosen. In this case the three VHW services should be produced in fixed proportions and can be represented by the simple sum of the three types of encounters. Let e represent this scalar sum of the elements of e. Adopting a similar assumption for the eight different vaccination services allows vaccination activity to be represented by the simple sum of all vaccinations oerformed, v. Then a first-order approximation to the objecive function, h(e, v, !), can be wricten: H ho + a e + b v , (1) where a represents the number of healthy-life-days saved by an average VH W encounter and b represents the number of healthy-life-days saved by an average vaccination. The intercept ho is the nupiler of healthy-life-days lived in the absence of any VH W or vaccinatLon activity and thus represents the baseline health status of the population.[7] To do justice to the two competing integration -trategies, their cost functions must capture their respective strengths. A functional form capable of representing the strengths of both strategies is: c(e, v, - A(p) ((/u)1e)<sup>3</sup> + v'3](/3) W (2)
page 5 where A(2 ) is a linear homogeneous increasing function of input prices, the parameters ui and s are strictly positive and B3 is greater than or equal to one. The parameters 1i and s determine respectively the intercept of the isocast curve on the e axis and the degree of returns to scale of the production technology. The parameter a measures the degree of complementarity in the production of the two outputs of an integrated rural primary health care program. It us related to 6, the elasticity of product transformation, by _6 -_ 1/(B1 Figure 1 depicts the shape o , :e isocost or production possibility frontier associated with equation (2) for foar different values of B. W`ien B equals one, there is no complementarity between e and v and the isocost curve is linear as in Figure la. For larger values of B t&,e isocost curve bows outward, demonstrating increasing complementarity in the production of encounters and vaccinations. As a approaches infinity, the two ouCptUL. become joint products which should be produced in fixed proportions if both im prove health status.[81 The next paragraphs bring to bear a few "stylized facts" in order to specify the relative magnitudes of the parameters of equation (2) for each of the two competing strategies.

Evidence from tie Ivory Coast supports the observation that vertically organized mobile vaccination teams can be as much as twice as cost-effective as fixed centers at the delivery of vaccination services alone (Shepard, Sanoh and Coffi, 1982b). The observed difference in cost-effectiveness is probably due to the greater accountability and compliance that are properties of vertically organized management structures, the tight task definitions of the vaccination teams, their mobility and flexibility which allow them to go where the people are on a given day, the speed of their itinerary and the physical limit on the number of employees per vehicle which acts as an effective check on the political pressure to increase employment on the teams.

To capture this stylized fact, set e equal to zero in equation (2) and solve for v: The assumption that Strategy M is twice as cost-effective as Strategy F at the production of vaccinations alone can then be represented by supposing that, for the same recurrent budget C*, the actainable value of v from equation (3) is twice as large for Strategy M values of A(2) and s as it is for Strategy *F values.d9l Call * the number of vaccinations produceable from budget C by Strategy F, V . Then the nu%ber of vaccinations produceable from the same budget by Strategy M will be 2V . Advocates of fixed centers argue that once such a center is operating at a given annual recurrent budget and one of its staff is making periodic vaccination visits to the surrounding villages, the number of vaccinations that would have to be foregone for the traveling staff member to also supervise and support a VHW in each village would be quite small. In other words, the fixed center could add VH W supervision to its tasks at little "opportunity cost" in terms of .oregone vaccinations. The technology of producing both VH W services and vaccinacions from a fixed center can thus be characterized by substantial complementarity.
6 <!-- Start of picture text --> e e e e<br>(a) (b) (c) (d)<br>Figure 1. The Effect - Varying R3 on the Production<br>Possibility Yrontier<br>e<br>Strategy F<br>P-mV, | | i. / ICombinod Feasible Region<br>m . 0 | | > /for Budget C<br>| , S | E K ~Strategy 11<br>V* 2v*<br><!-- End of picture text -->

Figure 2. Superposition of the Feasible Combinations of e and v for Budget C* and the Two Strategies
page 7 Although there is no accumulated experience on the use of mobile vaccination teams to supervise VHWs, there is reason to be less sanguine about the effects of adding VHW supervision to their tasks. The very features of the mobile teams which make them so efficient for their given tasks, the tight task definitions, their mobility, the speed of their schedules and the physical limit on the number of employees per vehicle, imply that the adoition of VH W supervision and support to team duties will substantially slow the progress of the team. In other words, for a given recurrent budget the opportunity cost of adding VHW support and supervision to the duties of the mobile team is likely to be high in terms of foregone vaccinations.

To capture this hypothesized difference in complementatity, suppose that the production technology for Strategy F demonstrates a modest degree of complementarity between encounters and vaccinations such as that shown in tigures lb and lc, while that for Strategy M demonstrates zero complementarity as illustrated in Figure la. Then a is two or greater for the Strategy F cost function while it equals one for the Strategy M function.

Finally consider the relative magnitudes of the parameter i for the two strategies. For Strategy F and budget C*, the parameter Pf is defined **as** the ratio of **the** number of encounters produceable with no vaccinations to the nuaber of vaccinations produceable with no encounters. Thus if V* is the intercept of the Strategy F isocost curve with the v **axis,** then pfV* is its intercept with the e axis.

While Strategy M is twice as cost-effective as Strategy F **at** producing vaccinations alone, it **is** unlikely to be more cost-effective than Strategy F at producing encounters alone[101 To capture this last stylized fact, define<sup>1</sup> im for the given budget C*, as the ratio of the number of encounters produceable by Strategy M with no vaccinations to the number of vaccinations produceable by Strategy F with no encounters (ie. to V ) Thb , will be less than , but greater than one. The intercept of the Suategy e isocost curve with f.he e axis is thus m v * as shown in Figure 2.

These assumptions allow the superpo&tion of the production possibility frontiers for the two strategies operating under the same cost constraint. The equations for the two constraints are: where V **is** an increasing function of C .ll Figur# 2 depicts the combined feasible region for the two strategies. For budget C it is possible to attain any combination of e and v that is on the northeast boundary of the union of these two possiblity sets. The problem is to choose **the** best of these combinations and thereby to choose the best strategy.

Following the solution technique described in Section IL the irst step is to maximize equation (1) with respect to e and v subject to equation (4), the Strategy F cost constraint and then to substitute the resulding values of e and v into equation (1) to obtain the maximum number of healthy-life-days that can be **saved** under budget C* with Strategy F. The result is:
page 8 (6) Hf w where B/Cu1) a (d4-l) and B > 1.

Because the possibility frontier for the mobile strategy is li'ear, the Strategy M maximizatioo problem reduces to a choice bseween one of the two intercepts of that frontier with the e and v axes. That is, e,xcapt in the special case where b/a - Pm2, the mobile team should devote itself entirely to either vaccinations or encounters and should not mix the two tasks. Formally the maximization problem is: Hm f max ( aimV* , 2 b V (7) Since mobile teams could probably save many more healthy-life-days doing only vaccinations than doing only VH W supervision and support, the maxim: - valu of Hm **is:** Hm 2 b V* (8) According to the decision rule of Section U, Strategy M is preferable if the number of life-days saved according to equation (8) exceeds the number saved according to equation (6). Forming this irequality and manipulating it yields the condition: Choose Strategy M if b hf a > _cat2BI'l)]>_ l)((l9/B where pf > 1 and 3 > 1.

The left-hand-side of decision rule (9) reflects the marginal benefit of a vaccinatdon relative to that of encounter while the right-hand-side contains parameters of the cost functions of the two strategies. According to the decision rule, if the number of healthy-life-days saved per vaccination is sufficiently larger than the number saved per encounter, then Strategy h'3 superior efficiency at vaccination guarantees that it will dominete Strategy F for savivg life-days.

This decision rule has a simple graphic interpretation which can be exposited as three cases.

CASE 1: STRATEGY M DOMINATES. The ratio b/a can be represented graphically as the (absolute value of the) slope of the straight-line isoquant obtained from equation (1) by solving - e in terms of v aud a fLxed level of R. Thus condition (9) is equivalent to the requirement that the healthy-life-days isoquant be steep enough so that the highest attainable value of R is at the point 2V* on the vaccination **axis.** This situation is depicted in Figure 3a where the optimal point is marked R*. At this solution, Strategy H is used to perform only vaccinations.
9 <!-- Start of picture text --> e<br>F± vre 1 3a.\ tt9<br>scrat.gy~~strtey<br>Strateg-y l1 Object*ive Function<br>domina tesh(s,,x)<br>\ ~Strategy U<br>_e ~s 2V V i<br>e<br>Figure 3b, ,L-fV* H F<br>Strategy F<br>dominates PuImV hev , x)m<br>: v +_ b/a<br>V 2v*<br>Figu.e 3c. A<br>Neither IJmV* F<br>strategy h(e,,x)<br>dominates M<br>V- * 2 V K<br><!-- End of picture text -->
page 10 CASE 2: STRATEGY F DOMINATES. Although b is likely to be greater than a, i- is possible that the radio b/a is smaller than the right-hand-ade of inequality (9). 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 between tne highest attainable H isoquant and the Strategy F possibility frontier as Mlustrated ';y the point labeled H* in Figure 3b. Because of the assumed complementarity of the Strategy F production process, this solution would imply that the fxed centers provide both encounters and vaccinations in the ratdo determined by the slope of a ray from the origin to point H*.

CASE 3: THE DECISION IS INDETERMINATE. If the slope of the H isoquant, b/a, is exactly the same as the sLpe of a straight line constr*cted to be eangent to the Strategy F frontier and to pass through the point 2V on the horizontal axis, the left- and right-hand-sides of (9) are equaL This boundary case (depicted in Figure 3c) is unlikely to obtain in practice, but is instructive for the light it throws on the role of the complementarity assumptions in the analysis.

First. note in Figure 3c that the assumptions of some complementatity in Strategy F, but none in Strat' X4, combined with the assumption that h(e, v, 1) is linear, imply that a portions of the two possibility frontiers on segments ABC are always dominated either by point C on tha Strategy N frontier 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 to focus predominantly on vaccination - whatever the health impacts of the two interventions.

As t intuitively clear, complementarity helps Strategy F to compensate for its relative inefficiency at vaccination. Figure 4a depicts the situation that would obtain if such complementarity were eliminated as B approaches I (d approaches infinity). In this case inequality (9) reduces to the requirement that b/a be greater than Pf/2, a less demanding requirement than (9). Thus in the absence of complementarity in the Strategy F production process, the strategy choice reduces to the sample choice between supporting encounters alone using fixed centers (at point A in Figure 4a) and delivering vaccinations alone using mobile teams (at point C in Figure 4a) - a choice which is more likely to favor mobile teams.

On the other hand, if Strategy F benefits from perfect complementatity in its production process as shown in Figure 4b, S approaches infinity and condition (9) becomes the requirement that b/a exceedt P, a condition which is twice as hard to satisfy as the condition that b/a exceed hf/<sup>2</sup> . Thus the assumption of complementarity in the Strategy F production process increases by as much as a factor of 2 the extent to which the health impact of vaccinations must exceed that of VE W services in order to render the mobile strategy more cost-effective at saving life-days.121
**IL**

<!-- Start of picture text --> e<br>9%~~ i<br>IJfV<br>V* 2V* V<br><!-- End of picture text --> Figure 4a. Strategy F suffers from zero complementarity <!-- Start of picture text --> e<br>IJf V* A~ m~<br>i SlopoZ 2a<br>Figure 4b. Strategy F favored by<br>perfect complementarity<br><!-- End of picture text -->
page 12

# IV. Applications and Interpretations of the Decision Rule.

If the values of the four parameters in decision rule (9) were known<sup>with</sup> confidence for a specific country or region of a country and the other assumptions of the analysis accepted, application of rule (9) would provide the cost-eireoive integration strategy. Unfortunately none of these parameters is known with precision for any country.<sup>Thls section</sup> applies information from three studies, on Ghana, Java, and the Ivory Coast, in order to<sup>arrive</sup> at tentative estimates of the parameters a, b and tif, life-days-saved per encounter and per vaccination and the intercept of the f5xed-center isocost curve with the e axs. All of these estimates are drawn<sup>together</sup> to illustrate the application and interpreeation of the decision rule in Table 7 at the<sup>end of</sup> the section.

1. Estimates of Healthy Life-Days-Saved Per Vaccination. Table 1 presents two estimates of b, the number of life-days-saved (LDS) per vaccination in an immunization program based on Ghanaian data and assumptions as presented by the Ghana Health Assessment Team (1981).[131 The first estimate of 75.4 LDS per<sup>vaccination</sup> at the bottom of column (7) is based on the theoretical distribution of the various vaccinations in that column. The second estimate of _53.8_ LDS per vaccinatioon at the bottom of column (8) is based on an empirical distrioution of vaccinations observed in neighboring Ivory Coast. Apparently<sup>it is difficult</sup> to maintain the proper ratio of measles vaccines to other vaccines<sup>and to deliver the third doses of the</sup> polio and DPT vaccines. Since the third doses add less<sup>than the average to</sup> LDS, reducing their proportions increases the average of the program. However, since measles vaccination has at least thirty times more impact<sup>on</sup> LDS per vaccination than any of the others, reducing its proportion even slightly has a large negative effect<sup>on the average LDS per vaccine.</sup>

Table 2 presents in columns (8)<sup>and (9) the raw material for developing a</sup> comparable estimate of b based on Javanese data and assumptions as developed and analyzed by a University of Michigan study (Grosse et al, 1979).(14] In e rural population of 50,000, the<sup>Michigan study estimated that</sup> an immunization program consisting of 27,000 administered doses per year would reduce mortality and morbidity to a degree which<sup>is calculated here to</sup> save 1,790 life years through averted deaths and 22,500 days of partial or total disability. Thus on average the Javanese vaccination program is estimated to save 25.0 healthy-life-days per vaccination, a figure which is of the same order of magnitude as the<sup>eatimates for Ghana from Table 1.</sup> However the Javanese immunization program considered by the Michigan study differs in three ways from the immunization program<sup>presented in Table</sup> 1. The Javanese program includes a vaccination of 2100 mothers per year for neonatal tetanus but excludes vaccinations against measles and polio. By referring to the Michigan report,<sup>it is possible to estimate the value of b that</sup> would obtain in Java if the vaccination program resembled that in Table<sup>1.</sup>
page 13 Table 1. Estimation of the Average Number of Life-Days Saved Per Vaccination from Ghanaian Data

|Vaccination/|Life-<br>Days-|Prop.<br>at|Poten-<br>tial|Prop.<br>Prdcng|LDS<br>Per|Distribut<br>Vaccina|ions<br>of<br>tions:|
|---|---|---|---|---|---|---|---|
|Dose|Lost|Risk|LDS|Im'ty|Vac.|Theory|Obsrvd.|
|(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|
|1. Measles|23.36|.039|599.0|.60|359.38|.191|.128|
|2. Tuberculosis|11.01|1.00|11.01|.90|10.45|.142|.152|
|3. Polio/l|1.20|.038|15.8|.90|.57|.111|.180|
|4. Polio/2|||7.9|.90|.29|.111|.096|
|5. Polio/3|||7.9|.90|.29|.111|.084|
|6. Diptheria/l|.014|.077|.086|.90|7.08|.037|.060|
|7. Diptheria/2|||.078|.90|6.65|.037|.032|
|8. Dipthena/3|||.018|.90|1.57|.037|.028|
|9. Pertussis/l|4.65|.078|23.8|.90|21.46|.037|.060|
|10.Pertussis/2|||23.8|.90|21.46|.037|.032|
|ll.Pertussis/3|||11.9|.90|10.73|.037|.028|
|12.Tetanus/1|4.47|.961|2.2|.90|1.99|.037|.060|
|13.Tetanus/2|||2.2|.90|.22|.037|.032|
|14.Tetanus/3|||.2|.90|.22|.037|.028|
|TOTALS|44.70||706.0|||75.4|53.8|

- SOURCES: Table 1 of Ghana Health Assessment Team (GHAT) (1981) and the appendix to it distributed by R. Morrow, WHO, Geneva.

- Column (2): Expected life-days-lost per capita in entire population from GHAT, Table 1, column (10).

- Column (3): Proportion of entire population which is at risk from this disease and thus can benefit from the vaccination. Measles - pop. 1-2 assumed 39/1000 (GHAT Appendix); TB - entire population; polio - pop. 2-3 assumed 38/1000 (GHAT Appendix); Dip. - pop. 1-3 assumed 77/1000; pert. - pop. 0-2 assumed 78/1000; Non-neonatal tet. - pop. older than 1 yr. assumed 961/1000.

- Column (4): Column (2) / columr (3). Quotient is allocated 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%. (Morrow, 1984, personal communication!

- Column (5): Makinen (1982) and Shepard, Sanoh and Coffi (1982a) have estimated the effectiveness of measles vaccine under field conditions in Cameroun and the Ivory Coast at 48.5% and 60% respectively. The second and more optimistic figure is used here. The other effectiveness proportions are conjectured to be obtainable in a well-managed EPI system.

- Calumn (6): Column (5) x column (4). The diptheria, pertussis and non-neonatal tetanus vaccines are administered in a single vaccine called "DPT."

- Column (7): The eight distinct applications of a vaccine to a "fully immunized" individual are: one each of measles and BC G, three of polio and three of DPT. The theoretical distribution of vaccinations across these eight distinct vaccination events is based on the calculations by P. Knebel of the Sahel Development Planning Team, Bamako, Mali as presented in Agency for International Development (1983). It assumes that all children receive all six vaccinations.

- Column (8): This distribution of vaccination types can be deduced from the data presented by Sanoh (1983) on aggregate vaccinations performed in the Abengourou region in 1981 and on estimated coverage of this rural population by each of the eight vaccination events.
**page** 14

Table 2. Estimation of Life-Days Saved Per Year in a Population of 50,000 in Rural Java When an ImmunizatLon Program is Added to an Existing Health Center.

||With|out Immu|nization|||With Immu|nization||
|---|---|---|---|---|---|---|---|---|
|Age Group<br>(1)|Pop.<br>in<br>Thous<br>(2)|Life<br>Expect.<br>(3)|Death<br>Rate<br>(4)|Disa-<br>bility<br>Rate<br>(5)|Death<br>Rate<br>(6)|Disa-<br>bility<br>Rate<br>(7)|Life-<br>Y ears<br>Saved<br>;8)|Thousands<br>Days<br>Saved<br>(9)|
|0-1 Years Old|1.5|48|104.0|*|85.9|*|1301|*|
|1-4 Years|7.0|52|28.3|21.0|27.4|19.9|298|22.5|
|5-14 Years|13.0|50|2.7|*|2.4|*|176|*|
|15-44 Years|21.5|35|5.6|3.6|5.6|3.6|15|0.0|
|45 Years Old<br>**and**Older|7.0|15|*|5.5|*|5.5|*|0.0|
|TOTALS|50.0||11.0|11.4|10.23|10.9|1790|22.5|

- SOURCE: Unless otherwise indicated, all references to pages, tables or appendices in the following notes are to R.N. Grouse, J.L.deVries, R.L.Tilden, A.Dievler,S.R.Day, "A aealth Development Model Applicatdon to Rural Java," Final Report of Grant No. AID/otr-G-1651, Department of Health Planiing and Administration, School of Public Health, University of Michigan, October, 1979.

- NOTES: Immunization program consists of 27,000 shots per year against tuberculosis (6600 doses BC G vaccine), diptheria, pertussis, and both neonatal and postnatal tetanos (18300 doses DPT vaccine plus 2100 doses tetanos toxoid), but excludes measles. See pages 30, 34 and pages 2 and 3 of Appendix A in Grosse et a.

- 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 from base run with a health center but no additional health programs. See alternative 1, PV I in the first line of Table 7 on page 47 or of any table in Appendix F. Since these tables do not provide the mortality rates of for the two groups over 15, an overall rate for both groups is interpolated.

- Column (5): Days of disability per person per year. Source is same as column (4) except interpolation is required for those under 15.

- Column (6): From Table 7, alternative 1, PV 3 with interpolation as for column (4). Column (7): Same as (6) with interpolation as in (5). Column (8): Using C4 to represent column (4), etc. the formula for this column is: 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).
page 15 First, consider the numbet of addicional life years that would be saved if mea.sles vaccination were added to the Javanese program. The Michigan study estimated the incidence rate at zero for infants less than one and only 200 per chousand among children aged one to four. In the latter group the study assumed the case fatality rate to be 4.8% (0.5Z among the 20X treated and 5% among the 80% untreated). If measles vaccine is 60% effective as assumed in Table 1, then it will save 5.76 lives per thousand vaccinated (200 x .048 x .6). Assuming that 1,500 children are vaccinated per year just as they are entering the 1-4 age bracket where their life-expectancy is 52 years (from Table 2, column 3), the addition of measles vaccination would save an additional 449 life years per year in this Javanese rural population of 50,000 (5.76 x 1.5 x 52).

However, the incidence of neona.al tetanus in Java was estimated at 21.3 per thousand with a case fatality rate of 90%. Thus, removing the 2100 doses of t,.tanus toxoid given to the pregnant mothers (assumed 95% effective by Grosse et al, Appendix A, V.3) would increase deaths in the zero to one age group by 18.2 per thousand. For the 1,500 in this age group whose life expectancy is 48 years, the life-years lost would be 1,310 (18.2 x 1.5 x 48). The Michigan study did not include polio among the 31 diseases analyzed, possibly because its impact on mortality and morbidity was deemed small. Indeed in Ghana polio does not even rank among the top 25 contributors to life-days-lost (Ghana Health Assessment Teram, 1981, Table 2). As a rough approximation, assume that the Ghanaian figure of 1.2 days of life lost per person per year applies to Java as well. Then adding polio vaccination would save an additional 164 life years in the population of 50,000 Javanese (1.2 x 50,000 / 365.25), while requiring an a-iditional 18,300 vaccinations on the assuaption that the children getting DPT get polio vaccinations at the same time. Thus the net effect of these three adjustments to the Javanese - immunization program would be a loss of 697 life-years (449 + 164 1310) and an increase in the number of vaccinations by 17,700 (1500 + 18,300 - 2100). To arrive at an estimate of b for Java, subtract 697 from 1790, multiply the result by the number of days in a year and add 22,500 days of averted disability (from column 9 of Table 2) for a total of 421,700 LDS. Then divide this total by the 44,700 (27,000 + 17,700) vaccinations that would be required to achieve it. The resulting estimate is 9.4, a substantial reduction in average impact from the program defined by the Michigan study.[15] 2. Estimates of Life-Days-Saved Per Encounter. The impact of an immunization program is inherently easier to estimate than that of a VHW program, because effective immunization produces a measureable change in blood chemistry which accurately predicts whether an individual will ever contract the disease in question. In some cases sero-conversion correlates highly with an even more visible sign, a scar at the vaccination site. In contrast, the impact of VHWs on health can only be measured by observing a change in health status associated with their activites. Nevertheless the absence of information on the impact of VI W services on health status is surprising in light of the available experience with VHW projects. A review published in 1982, which limited itself to primary health care projects funded by the United States Agency for International Development, identified 52 such projects of which 42 used a VH W of one variety or another. However, the reviewers could find only "only five evaluations of health status located in
page 16 the project documents reviewed" (American Public Health Association, 1982, p. 81). One of these was for a project without VHWs. Two of the<sup>other four cited</sup> evidence of positive impacts of VH W activities on health status and the other two demonstrated no rignificant effect. Although "nearly all the projects plan to evaluate outcome by measuring changes in health status, . . . many evaluation components are initiated but never completed ; others are executed late; and s1l others are never initiated" (ibid., pp. 79, 80).

As a result of this lack of information on the effectiveness of VHW activity, any estimate of a, the number of life-days-saved per VHW encounter, must be proposed even more tentatively than the estimates of b, above. However, by using expert judgements of VH W effectiveness, two independent estimates of a are possible, one from Ghanaian and the other<sup>from Javanese</sup> data and assumptions. Table 3 develops estimates of the number of life-days saved per VH W encounter based on primarily Ghanaian rough estimates of the effectiveness of the Ghanaian VH W at treating 13 different disease categories. Column (6) gives an estimate of the number of "needed" encounters witi a VHW per yt. , assuming that all of this need generates effective dem.. d by villagers for treatment outside the home and that no traditional healers, pharmacists or other providers substitute for the VH W. Based on this undoubtedly .high estimate of encounters per year, column (7) computes the average number of LDS per encounter to be 14.9.

The extent to which demand for the services of a VHW will fall short<sup>of</sup> "need" is difficult to estimate until a study such as those of Heller (1982)<sup>and</sup> M wabu (1983) on Kenya is available for VHWs in a country similar<sup>to that under</sup> consideration. Column (8) of Table (3) gives a rough estimate of such<sup>demand</sup> based on the assumption that the villagers will not accept any preventive or screening services from the VHW and that they do not<sup>demand "enough" care</sup> from the VHW for colds, diarrhea, schistosomiasis and childhood pneumonia, because they seek other sources of care or because tney consider these symptoms to be insufficiently serious to warrant treatment. (It has been reported that blood in ttie urine, a symptom of schistosomiasis, is considered to be a mark of manhood in some cultures.) These assumptions<sup>reduce by half</sup> the total number of encounters by the VHW, but reduce the<sup>number of LDS by</sup> three-quarters so that the average LDS per encounter also drops by half to about 7.5, sdil a substantial number even under these admittedly pessimistic assumptions.

While the Ghanaian analysts computed total life-days lost under the current health system Cor 48 diseases and the impact that VHWs could be hoped to have on nine of those, the Michigan study considered<sup>each of only 31</sup> diseases at a much more disaggregated leveL Working from estimates of the incidence of each of these 31 diseases for each of six age-sex categories under each of eight different combinations of immunization, sanitation and nutrition programs, the Michigan study developed estimates of the impact of the VH Ws and of five other treatment combinations on mortality and morbidity in the rural Javanese population of 50,000.

Table 4 extracts from this work the information necessary to estimate the number of LDS per VHtW encounter in Java. Converting the<sup>estimated</sup> number of life-years saved from column (8) to days and adding the number of disability days from column (9) gives a total savings of 3,531,200 LDS. Dividing this total by the estimated number of encounters of 235,000 gives an estimated number of LDS per encounter of 15.0.
page 17 Table 3. Estimation of the Average Number of Life-Days Saved Per Encounter with a Village Health Worker.

|<br>Disease<br>(1)|Life-Days<br>Lost<br>If Sick<br>(2)|VH W<br>Effectiv-<br>ness<br>(3)|Life-Day<br>Saved/<br>Encntr<br>(4)|s<br>Incidence<br>Per Thou.<br>(5)|Est'ed<br>"Need"<br>(6)|Life-<br>Days<br>Svd.<br>(7)|Est'ed<br>"Demand"<br> <br>(8)|Life-<br>Days<br>Savad<br>(9)|
|---|---|---|---|---|---|---|---|---|
|1. Cold|0.6|0.10*|0.04|1000.0|1600|0.02|800|0.02|
|2. Skin|||||||||
|Tnfection|6|0.10*|0.4|470.0|752|0.09|752|0.17|
|3. Malanra|815|0.26|29.3|40.0|289|2.58|0|0.00|
|4. Malnutrition,<br>Severe|11667|0.63|1016.8|1.5|11|3.40|0|0.00|
|5. Gastro-<br>enteritis|207|0.38|49.2|70.0|112|1.68|56|1.68|
|6. Accidenrs|1935|0.20*|241.9|7.7|12|0.91|12|1.82|
|7. Schisto-<br>somiasis|629|0.69|271.3|7.0|11|0.92|6|0.93|
|8. Pneumonia<br>- Child|7750|0.37|1792.2|2.4|4|2.09|2|2.10|
|9. Pneumonia<br>- Adult|1300|0.15|121.9|7.0|11|0.42|11|0.83|
|10. Premature<br>Birth|1750|0.10|18.7|9.6|90|0.51|0|0.00|
|11. Complication<br>of Pregnancy|s<br> <br>1229|0.39|51.1|4.8|45|0.70|0|0.00|
|12. Birth<br>Injury|10250|0.21|229.6|1.6|15|1.05|0|0.00|
|13. Other<br>Diseases|786|0.01*|4.9|209.0|334|0.50|0|0.00|
|TOTALS|38,325|||1,830.6|3,287|14.86|1,639|7.53|

- NOTES: Column (2): Denved by dividing the life-days-losc calculated by the Ghana Health Assesment Project (1981) by the estimated incidence rate from column (5).

- Column (3): The National Health Planning Unit (1978, Table 6) of Ghana estimated healthy days of life currently lost from each disease, LDL, the life days that would be saved by the fully implemented primary health care system including VHWs, LDS, and the portion of these savings that would be achieved without the VHW system, LDSt. Figures without asterisks are derived by the formula: (LDS-LDSt)/(LDL-LDSt). Figures with asterisks are the author's estimates for diseases omitted in the National Health Planning Unit document.

- Column (4): Column (2) x Column (3) divided by an estimate of number of encounters per episode, which is given by the ratio of column (6) to column (5).

- Column (5): From Ghana Health Assessment Project (1981).

- Column (6): Prevention of malaria and malnutrition on the one hand and birth problems on the other requires frequent encouters (e.g. five per year) between the VHW and the target groups of children under three and pregnant women respectively. Assuming there are 60 children under three and 30 pregnant women per thousand population, the two groups would require 300 encounters and 150 encounters respectively. These totals are distributed &cross diseases 3 and 4 on the one hand and diseases 10, 11 and 12 on the other according to the incidence ratios. Other diseases are assumed to average 1.6 encounters per episode, the ratio observed in a sample of VH W huts in Senegal in 1979 (Over, 1980).

- 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, for lack 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).
page 18 Table 4. Estimarion of Life-Days Saved Per Year in a Population of 50,000 in Rural Java When 200 Village Health Workers are Added to an Exiscing Health Cencer.

||W|ithout V|HWs|||With V|HWs||
|---|---|---|---|---|---|---|---|---|
|Age Greup<br>(1)|P op.<br>in<br>Thous<br>(2)|Life<br>Expect.<br>(3)|Death<br>Rate<br>(4)|Disa-<br>bility.<br>Rate<br>(5)|Death<br>Rate<br>(6)|Disa-<br>bility<br>Rate<br>(7)|Life-<br>Y ears<br>Saved<br>(8)|Thousands<br>Days<br>Saved<br>(9)|
|0-1 Years Old|1.5|48|104.0|*|67.2|*|2647|*|
|1-4 Years|7|52|28.3|21.0|13.4|17.2|5424|81.4|
|5-14 Years|13|50|2.7|*|1.6|*|696|*|
|15-44 Years|21.5|35|5.6|3.6|4.6|3.2|639|9.2|
|45 Years Old<br>and Older|7|15|*|5.5|*|4.7|*|5.3|
|TOTALS|50||11.0|11.4|6.9|9.4|9405|96.0|

- SOURCE: R.N. Grosse, J.L.deVries, R.L.Tilden, A.Dievler,S.R.Day, "A Health Development Model Appladon to Rural Java," Final Report of Grant No. ATD/otr-G-1651, Department of Health Planning and Administration, School of Public Health, University of Michigan, October, 1979.

- NOTES:- Village Health Worker Program as defined by Grosse et al (ibid., pp. 5-7 of Appendix D) consists of one VHW per 250 people (or per 50 households) handling 4.7 encounters per person per year, for a total of 235,000 encounters in the population of 50,000. Of the 31 disease categories included in their analysis, Grosse et al assume that treatment at a rural health center can have a beneficial effect on either morbidity or mortality in 20 of these, but that a VHW has some impact in every 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 from the bottom of page 4 of Appendix F of Grosse et al (1979). Interpolated as for column (4).

Columns (7) through (9): Same notes as for Table 2 this paper.
page 19 Unlike the estimate of need in column (7) of Table 3, the Michigan study explicitly incorporates assumptions on the proportion of cases in each age group for each disease that wil seek treatment from the VHW (Grosse et l. Appendix B). These proportions range from .90 for severe diarrhea and upper respiratory infection down to .30 for intestinal parasites and .10 for complicatdons of childbirth and pregancy. While some of these fLgures seem rather high, the face that these adjustments have been made makes the Javanese estimate more comparable to the Ghanaian estimate based on "demand" than to that based on "need." Thus the Javanese estimate is twice as large as the comparable one for Ghana.

An examination of the the details of the Michigan study calculations reveal that they were more optimisitic than were the Ghanaian analysts regarding the productivity of the VH W. The Michigan analysts assumed the VUW vould have some effect on mortality or morbidity for 20 of the 31 diseases analyzed, whereas the Ghanaian analysts hoped for such an impact on only nine diseases. Furthermore, for those problems which both studies assumed the VHW would influence, the Michigan study assumed a greater VhW effectiveness. Column (6) of Table 5 presents the implied effectiveness of the VHW in the Michigan study which compares most directly with each of **the** values from column (3) of Table 3. Setting aside colds and skin infections as not having been considered by Ghanaian analysts (and in any event of trivial consequence for total LDS), the column (6) effectiveness fliure for Java **is** typically greater than the corresponding Ghanaian figure. These greater effectiveness estimates, together with the larger number of diseases the Javanese VHW is assumed to influence and the higher level of assumed demand combine to make the estimate of 15 LDS per encounter a relatively optimistic one. Nevertheless, it is encouraging that it is of the same order of magnitude as the estimate for Ghana.

3. Estimates of Parameters of the Cost Functions. Turning now to the dight-hand-sLde of decision rule (9), consider the parameter Ilf This parameter was defined in section m above as the ratio of two numbers. The denominator of this ratio is the number of vaccinations that a fixed center operating on budget C* could deliver on site in one year, if it has no responsibility for VHW support and supervision. (In section ml, this number was called V*.) The numerator is the number oZ encounters that the same fixed center could support on the same budget through the supervision of outlying VHWs. To determine this number with any confidence will require detailed cost and management studies of fixed centers with outreach and VH W supervision activities in several developing countries.

However suppose that the cost (net of vaccine costs) of traveling to within reach of Q people is directly proportional to Q to the power s, where s is the degree of returns to scale in the cost function (and bears the same interpretation as the returns to scale parameter introduced in equation (2) of section **I).** Suppose the cost function is roughly the same whether the purpose of travel is to vaccinate the target group within Q by a mobile team or to supervise the VHWs aho serve Q by a fixed center, provided that only one of these two tasks is performed. Under these assumptions, Table 6 develops an estimate of Pf for each of several values of s based on preliminary estimates of the costs of a mobile vaccination team operating in Abengourou, Ivory Coast, in 1981 (Sanoh, 1983). (16]
**page** 20

# Table **5.** The tstimated EffectLveness of the Javanese VIHW on the Twelve Disease Problems of Table 2 of the Text.

|Ghanaian<br> <br>**Di"as**<br> <br>Category<br>t<br>(1)|Ghanaia<br>Effec-<br>dvuess<br>(2)|n<br>Ghanaian<br>Incidence<br>(3)|Javanese<br>A<br>Diseas<br>Ja<br>Category<br>A<br>(4)|ggregated<br>vanese<br>geGroup<br>(5)|Percentage<br>Improveme<br>in Case<br>Fatality<br>Rate<br>(6)|nt<br>Javanese<br>Incidence<br>(7)|
|---|---|---|---|---|---|---|
|1.C old|102|1000|2. URI|0-15<br>15+|02<br>02|2000<br>1000|
|2. Skin Inf.|102|470|4. Sidn Dii.|0-15<br>15+|0Z<br>0Z|50<br>100|
|3.M alria|262|40|8. Malaisi|0-15|962|20|
|||||15+|1002|50|
|4. MalnutritLon|632|1.5|not included||||
|5.Gastroenteritis|382|70|5.MildDiarrhea|0-15<br>15+|02<br>0|2000<br>1000|
||||6.Severe Di&.|0-15|692|250|
|||||15+|40 2|80|
|6. Accidents|20Z|7.7|13. Burns|0-15<br>|542<br>|30|
|||||15+|0|10|
||||14. Fractures|0-15|442|1|
|||||15+|292|1|
||||15. C uts|0-15|632|15|
|||||15+|70 Z|15|
|7. Schistosomiasus|692|7|not included||||
|8. Pneumonia, Child|37X|2.4|1. LRI|0-15|792|50|
|9. Pneumonia, Adult|152|7|1. LRI|15+|792|10|
|10.&12. Prem. Brth|<br>10Z|9.6|21. Comp. Brth|0-1|85Z|90|
|&Birth Injury|21S|1.6|<br>&Pregnancy||||
|11. Comp. of Preg.|392|4.8|21. Comp. Brth|Wom. 15-4|4<br>212|24|

SOURCES: Grosse et **aL** (1979), Ghana Realth Assessment Team (1981) and Naciol Health Planning Unit (1978).

NOTES: Columns (2) and (3): From Table 2 in the text.

Column (3): Incidence per thousand in overall population from Table 1 of Ghana Health Assessment Team (1981).

Column (4): Appendix A of Grosse et al (1979). Column (5): Aggregates of the _ssx_ age-sex categories used in Appendices A and C of Grosse et al (1979).

Column (6): Calculated from the last two columns of Appendix C of Grows. et al (1979) by the formula (CFNRX-CFRX)/CFRX, where CFNRX is the case fataiicty rate without treatment, CFRX is the case fatality rate with treatment by a VHW.

Column (7): Derived from the incidence rates by age-sex group in Appendix A of Grosse et al by choosing a value in the mi4dle of the range of incidence races given in that source.
**page** 21

Table 6. EsCimation of If in Abengourou, Ivory Coast Under Constanc and Increasing Returns to Scale

|Constant<br>Returns<br>Incre<br>to Scale<br>to|asing Ret<br>Scale|urns|
|---|---|---|
|**(s-l.0)**<br>**(su.9)**|(s. 8)|**(su.7)**|
|1. Population covered by V8Ws attached<br>to a sngle fixed center.<br>7,900<br>5,750|3,860|2,320|
|2. Number of fixed centers "needed" to srve<br>the entire region of Abengourou:<br>17<br>24|36|60|
|3. Eimated<br>number of encounters by VHWs attached<br>to a. single flxed center with budget given under<br>Asumption F2 below (ie. pf V*):<br>37,100<br>27,000|18,200|10,900|
|4. Estimate of the parameter pf.<br>10.6<br>7.7<br>Data and Asumptions Used:|5.2|<br>3.1|
|Abengourou Mobile Team:<br>Fixed Centers as VaW Super|visors:||
|Ml. Estimated rural population<br>F1. Number of vaccinations<br>of Abengourou:<br>138,000<br>with no encounters,<br>V*:||3500|
|42. Total cost of mobile<br>F2. Budget for V* vaccinatio<br>team for one year. 5,293,814<br>F3. Assumed number of supe<br>M43. Cost of vaccine:<br>1,009,600<br>trips per year to each V|ns,<br>**C*:**<br>rvision<br>aW:|735,700<br>3|
|44. Cost to reach rural pop.<br>_F4._Maximum cost per spvsn<br>w/o vaccinating:<br>4,284,210<br>that stays within budget,|trip<br>C*:|245,233|
|M5. Average Cost per Cap<br>F5. Assumed number of enco<br>to reach rural pop.:<br>31.0'<br>with VHW per capita per|unters<br>year|4.7|

NOTES: Row 1: Asume the dLmple model of transport and supervision cost C - A Qs, where a is the returns to scale parameter with a similar interpretation to the s introduced in equatLon (2) of section m of the text, Q is the quantity of rural residents to vhom the traveling health professionals come sufficiently close to either vaccinate almost all of the target group among them or to supervise the VHW who **treats** them, and C represents all costs except drugs and/or vaccines. Then the ratio of two values of Q is equal to the ratio of the two corresponding costs to the power l/s. The entries in this row are thus equal 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 F1 Ite Ml: The rural population **is estimated at** about 69% of the total population of Abengourou 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 study by L. Sanoh of CIRES, Abidjan and the Boston University Strengthening Health Delivery Services Project, and are measured in 1981 CFA francs. (Approx. 260 CPA francs/dollar in 1981). (Sanoh, 1983) Item M5: Item M4/item Ml.

(Notes continued on next **page.)**
page 22 Suppose aul, implying constant returns to scale in trarsport. Then the asaumptions of Table 6 yield an estimate of Uf %qual to 10.6. If -!n the other hand the mobile team achieves substantial economies of scale in transport that would not be available for smaller amounts of travel by a VH W supervisor attached to a fLxed center, then the value Of Po' is estimated to be **as** low as 3.1 when s - 0.7. At this value of s, total transport costs rise only seven percent for every tan percent increase in Q. If the commercial trucking industry in an LDC benefited from economies of scale as great as this, one would not expect to find any small independent truckers left in the country.

According to the decision rule, if b/a is greater than the ratio of Uf to a function of B (or of d), Strategy M is more cost-effective than Strategy F. However, the functicn of a vanes between one (when B approaches infirity) and two (when B approaches one). Thus if b/s is greater than Pf, or less than p /2 the value of B has no effect on the decision. In the former case, Strategy h lis more cost-effective and in the latter case Strategy F dominates. Only iE b/a is between these two bcunds is B important.

4. Applications of the Decision Rule. Table 7 presents four estimates of b/a across the top and four estimates of uf down the left side. The cells of the table are divided into three sections by aotted lines. Cels to the northwest, where b/a is less than P<sup>1</sup> f/<sup>2</sup> , are marked with an F to indicate that **these** parameter values lead to the choice of Strategy F regardless of **the** degree of complementarity of the f;xed center cost function. Cells to the southeast contain an M to indicate the reverse. Only in the cells between the two dotted lines does the strategy choice depend on the value of B. Instead of an F or an M, these cells contain the critical value of B (and in parentheses the critical value of 6) above which (below which) the decision rule would prescribe Strategy F.

For reasons explained above, column (2) for Java ard column (4) for Ghana seem more plausible than columns (1) and (3) respectively. Also constant or only mildly increasing .,eturns to scale, as represented by rows (A) and (B) seem more plausible than the more extreme economies of scale as represented by rows (C) and (D). Within these cells, Strategy F unequivocally dominates Strategy M in Java, regardless of the complementarity in the Javanese fixed centers.

NOTES TO TABLE 6 (continued):

- Item Fl: The average number of vaccinations per year performed by the two of the fourteen rural fixed health centers in Abengourou which perform such vaccinations as reported by Sanoh (1983, Table 6).

- Item F2: The average total cost for producing these vaccinations. (Sanoh, 1983, Table 3). Item F3: In West African VHW worker projects, 3 supervisions per year is a minimum recommendation. See for example Over (1980, 1982).

Item F4: Item F2/item F3.

- Item F5: The assumption used in Grosse et al (1979). At one VEW per 500 inhabitants, this figure implies 45 encounters per week. In a sample of nine Senegalese villages visited in the summer of 1979, Over (1980) found the average VUW was seeing 6.5 villagers a day, with a standard devaation of 3.9. This small sample thus supports the estimate from Grosse et aL
page 23 However, for Ghanaian assumptions on the health impacts of vaccinations and encounters, the degree of complementarity plays an important role. If e and v can be produced as perfect joint products so that the isocost curve looks like Figure ld, then B is very large _(6_ approaches zero) and Strategy F is preferable for a > .9. If, on the other hand, the opportunity cost of superuviung VH Ws from a frxed center is substantial in terms of foregone vaccinations so that the Strategy F iscoat curve resembles Figure la, then B approaches one (d approaches infinity) and Strategy M is preferable for s < 1.0.

Based on these illustrative parameter esatmates, the choice of primary health care integration strategy seems to be quite sensitive to the particularities of the epidemiologLcal situation and the costs of production in a specific region. Where the relative impacts of vaccination and basic health services and the **relative** costs of the two strategies resemble the West African data and assumptions used to generate rows (A) and (B) of column (4), the degree of complementarity of the joint production of vaccinatdons and encounters in fixed centers is an imporcant input to the strategy choice.

# V. Concluding Remarks

With only two parameters for the objective function and three from each cost function, the model presented here is extremely parsimonious. The advantages of this parsimony are that the coefficients of the model are relatdvely easy to estimate and that the model can be relatLvely easily understood by decision-mnakers. Of course, the parsimony is purchased at the expense of several strong assumptions. Most important among these is the assumption that the choice between the fixed and mobile integration strategLes is the important policy decision and is separable from other government policies and programs within and without the health sector. A second critical assumption is that the units of analysis can be the "average encounter" and the "average vaccination" and that the chosen integration strategy is independent of the mix or impacts of these average events. A third assumption is that the national health objective in rural areas is to maximize healthy-life-days.

Given these assumptions and the additional assumption that the effects of **diseases** and health interventions are additive, the parameters of the objective function can be "guess-timated" from fundamental epidemiologiLal data organized according to the pattern of the Ghana Health Assessment Team study, as is done here in Tables 1 and 3. Since each of the objective function parameters (a and b) represents the net impact of an intervention **oi** an index of overall health status, rather than its impact on any single disease, it would be feasible to estimate the objective function for a region by setting up two experimental groups, one with only the vaccination program and
page 24 Table 7. Cost-Effectiv;n Choice of an Integration Strategy for Various Parameter Estimates

|Estimates<br>of the<br>Average Impacr on<br>Healthy Life Days of:|Java<br>with<br>EPI<br>(1)|Java<br>Orig.<br>Assum.<br>(2)|Ghana<br>Theory<br>(3)|Ghana<br>Demand/<br>Obsrvd<br>(4)|
|---|---|---|---|---|
|.A vaccination<br>(parameter<br>b)|9.4|25.0|75.4|53.8|
|A VHW encounter<br>(parameter<br>a)|15.0|15.0|14.9|7.5|
|Ratio of b/a:|.6|1.7|5.1|7.2|
|Cost Function<br>Parameters<br>s andpf|||||

Constant Returns to Scale:

|(A) For s<br>1, If .<br>10.6|F<br>F|F<br>,|3.2<br>(0.5)|
|---|---|---|---|
|Increasing<br>Returns<br>to Scale:||-<br>j-<br>J||
|(B) For s -0.9,<br>Pf.<br>7.7|F<br>F|;<br>2.9<br>(0.5)|20 3<br>(0.05)|
|(C) Fors<br>0.8, hf<br>- 5.2<br>(D) Fors90.7,f- 3.1|F<br>F<br>**I**~<br>F<br>a<br>1.7<br>|<br>(1.4)|71.2<br>(0.01)<br>I<br>_Ji--_<br>-<br>*M|--<br>H<br>M|

NOTES: Column (1): The estimate of b is derived in the text. The estimate of a is based on Table 4. Column (2): The estimate of b is based on Table 2, that of a on Table 4. Columns (3) and (4): The estimates of b and a are from Tables 1 and 3. Rows (A) throough (D): The estimates of pf are from Table 6. The numerical entries in cells A4, B3, B4, C3 and D2 are the values of 13 which solve the equation: b hf a (2[3/(>1)]1<sup>)(hl)/B</sup> The values in parentheses are the values of the elasticity of complementarity, defined as 8 - _1/(-1)._ In these cells, if 13 is above the specified value (or if 6 is below the specified value in parentheses) then Strategy F is the cost-effective choice. Otherwise Strategy M is the cost-effective choice.
page 25 one with only the VH Ws, and measuring the impact of each intervention on health status relative to a control group where neither intervention is introduced.[17] Alternatively and less satisfactorily, the parameters a and b could be estimated at relatively little cost by multiple regression on nonexperimental data from the region of interest. Either of these estimation techniques has the additional advantage over "guess-timation" of correcting for the problems of disease interdependence and competing risk, and thus allowing relaxation of the unpalatable assumption that health effects are additive.

The cost function parameters could be "gvess-timated" in a specific country by working with experienced health ministry managers and depending on their judgement as to the costs of various combinations of activities.[l8] Here too it would be feadLble and preferable to estimate these parameters statistcally using a sample of mobile teams and fixed centers that are performing some or all of the vaccination and VHW supervision functions. With enough observations, a moie flexible functional form could be chosen in lieu of the constant elasticity form used here. With increased flexibility, changes in average unit cost could be attributed to changes in coverage and intensity as well as to changes in output mix as modeled here. [19] It is useful to contraet the present study with two other cost-effectiveness studies of primary health care in developing countries, both of which were led by economists from the University of Michigan. A team based at the School of Public Health constructed the linear-programming model referenced in Tables 2 and 4 above, which depends on 3,696 different parameters in place of the two parameters in the objective function used here (Grosse et al, 1979, Appendices A, B and C). Although the SPH model deals with separ4te packages of interventions as discrete administrative entities just as the present paper treats Strategy F and Strategy X as distinct - the SPH model is completely linear and thus would require modification to address the problem of strategy choice with joint costs.

An independent team based at Michigan's Center for Research on Economic Development constructed a programming model which has a non-linear objective function, but linear cost constraints (Barnum et al, 1980). Although more parsimonious than the SPH model, the CRED model neveztheless includes 221 parameters. With modification to incorporate nonlinear cost constraints, this model could also be used to address the strategy choice problem. Given the available computer time and resources, models patterned after the SPH and CRED models would be useful tools for health planners in developing countries to address almost any health planning problem. However, the suze and complexity of these models makes thess costly and unwieldy and may reduce the degree to which they are understood, believed and used by decisionmakers. Until these models are generally available, understood and believed, smaller, special purpose models such as the present one may play an important role in guiding policy decisions and generating demand among decision-makers for modelling exercises.

A consideration which is difficult to introduce explicitly into the model, but must be addressed in the choice of primary health care integration strategy is the degree of uncertainty in the present about various aspects of the future. Two variables are particularly importanc in this regard and act in opposite directions on the preferrred strategy choice.
page 26 First, suppose there is uncertainty regarding the population likely to inhabit the region under consideradon in five or ten years. Even if fixed centers appear optimal given today's estimates of cost and health impact parameters, creating them may be unjustified if a large proportion of the population might migrate either out of the region or to new population centers within the region. In this situation the flexibility of the mobile teams is a substantial argument in their favor.

A second dimension of uncertainty is the regional rural health budget cotstraint. If this budpet is often cut markedly from programmed levels, then the effect on healthy-life-days of operating both strategies at this much lower level of funding must be considered. The best strategy in .his situation is the one that saves the most healthy-life-days over a series of years when the budget varies back and forth at random from its full level .o its lowest level. Even if the mobile strategy seems best based on the model presented here and the assumption of full funding, its absolute need for fuel may make its productivity much more sensitive to recurrent cost crises than would be the fixed center, and thus the less preferred option when such crises are considered likely.

In view of the tentaciveness of the Section IV estimates, the need for research is evident. But which parameters should be the focus of priority efforts? Which parameter estimates would provide the greatest benefit **at** the least cost?

The benefits of immunization, represented here by the parameter b, are the best known portion of the model and of the data, so they are not at the top of the list of research priorities. As discussed in Section IV, the benefits of VHW services are less well-understood, and thus in greater need of research effort. However, the statistdcal and political problems inherent in estimating these benefits are immense. This research is necessary, Ut must proceed deliberately, without the expectation of a quick payoff. In contrast to these two areas, research on the joint cost function for multiple primary health care services in rural areas is both lacking and relatively easy to perform. Thus the top research priority in the health sector of developing countries should be estimation of a set of these cost functions, so that planning models can better serve as practical guides to policy.
page 27

# NOTES

- (1] While an LDC might choose Strategy F in one region of the country and Strategy M in another region, it is hard to see how a combination of both strategies could be implemented cost-effectively in the same region, because such a mixture of strategies would require the MOH to provide expensive transport and management time to reach each village more often than would otherwise be necessary.

- t21 One argument for different weights is that atding healthy-life-days to the life of a productively employed adult may save additional life-days of his or her dependents. The political sensitivity of such relative weights is an argument for establishing them within the decision-making apparatus of the country in question.

- [31 For some purposes it would be desirable to disaggragate further among consultations for different preventive and curative problems. Such a further disaggregation is a straightforward generalization of the three-fold diaggregation presented here. Over and Smith (1980) and Smith and Over (1981) present an approach to the creation of homogeneous aggregates of patient problems in an ambulatory setting.

- [41 To the extent that the initial investment cost and the eventual replacement cost of the project's capital have a positive opportunity cost to the country, the relevant cost constraint for the planner includes the value of aU these capital expenses plus the value of all discounted future recurrent expenses. Then it would be necessary to modify the objective function to capture the stream of all future healthy-life-days, also discounted to the present. However, donors frequently make funds available for the investment costs of health projects which are not available for other expenditures in the same country. Furthermore, many developing countries behave as if replacement capital will be provided by donors, an expectation that has often been fulfiled. The assumption here is that the opportunity cost of capital expenditures is zero so that the only relevant cost constraint for the developing country is the recurrent cost function. This assumption makes every year the same so that the intertemporal aspect of the problem can be ignored and there is no need to discount future capital expenditures or future healthy-life-days. See Gray and Martens (1980) aad Over (1980) on the recurrent cost problem in LDCs.

- [5l Although not derived from profit maximizing assumptions, these cost functions represent best sustainable managerial practice and thus should be estimated by the technique developed for "frontier production functions". If the production technology is defined for only a limited number of discrete points in the space spanned by vectors e and v, then a continuous curve fitted to these points may be inappropriate. The integer-programming approach that must be turned to in this situation can, of course, capture joint production and other nonlinearides. For an example of the representation of a nonlinear production technology by a piace-wise linear integer-programming model in health, see Smith and Over (1981).

- [61 The problem of joint cost allocation raises its head again if there **is** jointness in the production of e and v with other health sector activities (such as the other activities of the fixed centers). If the amount of total recurrent costs incurred jointly in the production of these other activities with e and v is small
page 28 then standard allocation rules can be used as suggested in deFeranti (1983, pp. 31-33). However if joint costs are so large chat different allocation rules alter the choice between the fixed and mobile strategy, then the scope of the model must be expanded to include a vector of these other activities in the objecdLve function as veU as in the cost functions.

- (7] In fact h(e, v, x) is likely to be nonlinear both because the health impact of any given intervention typically diminishes with increased coverage or intensity and because a reduction in the morbidity or mortality from one disease typically influences the morbidity and mortality from other diseases. Barnum et al (1980, Chapters 2, 3) specify a programming model with a nonlinear objective function to capture these problems, though for lack of appropriate data they are forced to estimate its 221 parameters from the survey responses of 16 experts. Section V and its notes discuss a nonlinear version of h(e, v, x) in the present modeL

- (8] The functional form of equation (2) is that of tae constant elasticity of substitution production function with the sign of its exponent, and thus its curvature, reversed. The elasticity of product transformation (or elasticity of complementarity) is given by o - 1/(3 - 1) and can be interpreted as the percentage increase in the optimal ratio of vaccinations to encounters (v/e) resulting from a one percent increase in the ratio of the effectiveness of vaccinations to that of encounters (b/a). By assumption the cost function is separable in prices and output.

- L9] Under this hypothesis:

Thus for given p, Af(j), A (2), s and s , V is an ifcreaFng function of C Under constant returns to scale A4j) - 2 Am(5) and V - C /Af(p).

- (10] For example, Walker and Gish (1977) found mobile services to be substantially less cost-effective than fixed services at the delivery of curative care.

- (111 See note 9.

- (121 The assumption of complementatity in the Strategy M production process woould likewise render that strategy more competitive.

- (131 The Ghaci Health Assessment Team presents estimates of total healthy-life-days-lost due to each disease.(1981, Tables 1, 2) Whether measured by ageand disease-specific mortality rates or by healthy-lifedays-lost in the populacton, the total burdea of a disease on society cannot be used directly to prioritize disease interventions. Instead it is necessary to estimate the marginal number of life-days-saved by an intervention and its marginal cost and then allocate resources so that the number of life-days-saved per unit cost is equalized across all interventions. (ibid., pp. 76, 77; Creese, 1979, pp. 24, 25). Tables 1 and 3 of this paper provide examples of possible approaches to translating the healthy-days-of-life-lost estimates from Ghana into impact measures of this sort.

- [141 The programming model of rural orimary health care in developing countries by Barnum et al (1980) has the advantage of modeling disease interdependence.
page 29 However, escimates of the parameters a and b cannot be easily deduced from the results reported for that model.

- [151 Assuming the costs of this revised program would be larger than that of the program analyzed by Michigan, the smaller total LDS would make it less cost-effective than a program like that analyzed for Ghana. However, the low incidence of measles assumed by the Michigan study for unvaccinated Javanese children would have to be carefully substantiated.

- (16] All figures drawn from Sanoh (1983) are preliminary and, like the other figures presented here, are for illustrative purposes only.

- (17] With the addition of one more experimental group, one receiving both vaccination and VHW services, an interaction term could be introduced into the objective function. Equation (1) of the model would then be modified to read:

H - 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 (1979) costing guidelines would be helpfuL The unit of analysis should be changed from the "fully-im munised-child' to the healthy-life-day and procedures should be suggested for allowing encounters and vaccinations to be treated as joint products.

- [191 For example, Chiang and Friedlander (1984) use a translog function to specify a general multiproduct cost function.