Policy, Planning, and Resarch
WORKING PAPERS
Population, Health, and Nutrition
Population and Human Resou ces
Department
The World Bank
July 198
WPS 23
Cost-Effective
Integration of Immunization
and Basic Health Services
in Developing Countries:
The Problem of Joint Costs
Mead Over
The debate between those who favor delivering comprehensive
primary health care from fixed health centers and those who
favor delivering selective primary care from mobile health
teams can be decided, in principle, on empirical grounds. Key
requirements for choosing the more cost-effective approach in a
given developing country are (1) an effectiveness measure
common to both types of health care programs and (2) an
approach to modeling joint costs.
The Pdicy. Plning, nd Research Canplex distibutes PPR Woddng Papers to disseminte the findings of work in progress and to
anoreg the exchange of ideas amng Bank staff and all othens interested in development issues. These papesca ry the nafmes of
the author, reflect only teir views, and should be used and cited accordingly. The fndings, interpretations, and conclusions are the
uthors own.They should not be awtibuted totheWorld Bank. its Board of Directors, itsmanagement. or any of its membercountries.



Polcy aPtning, and R rech  |
Population, Health, and Nutrition
With limited budgets for rural primary health       joint costs of simultaneously producing more
care, developing countries are under pressure to    than one health care service. In some situations
intcgrate the basic medical services that govem-    the degree of "jointness" of the cost structure
ment health centers provide with the vaccination     and the associated production technology have
programs that mobile immunization tearns             an important impact on thc relative cost-effec-
handle. For health planners, the question is        tiveness of the two altemative approaches.
whether to organize the integrated services
around the fixed health centers or around the           Using the Liethod described here, econo-
mobile health teams. Implicit in this decision is   mists can address this problem in a way that
a choice between more comprehensive health          does justice to both the superior efficiency of the
care from the fixed center versus more selective    mobile teams and the superior comprehensive-
care from the mobile teams.                         ness of the fixed centers. Special purpose
models such as this one can guide policy deci-
Application of cost-effectiveness analysis is   sions since they are less complex than more
complicated by two inherent difficulties. First,    general models and can be easily understood by
because the two types of health care programs       decisionmakers.
improve the health of different target groups,
some common measure of the effectiveness of             This paper is a product of the Population,
the two programs must be agreed upon. Here          Health, and Nutrition Division, Population and
the healthy-life-years saved by the two altema-      Human Resources DepartmenL Copies are
tive programs is proposed and implemented as a      available free from the World Bank, 1818 H
useful common measure of effectiveness.             Street NW, Washington, DC 20433. Please
contact Noni Jose, room S6-105, extension
The second difficulty is that of modeling the    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



Cost-Effective Integration of Immunization and Basic Health Services in
Developing Countries:
The Problem of Joint Costs
by
Mead Over
Table of Contents
Page
I.     Introduction .................................................1
II.    The Planner's Decision Problem .........................2.................. 2
m.    A Rule for Choosing the Cost-Effective Integration Strategy..          4
IV.    Application and Interpretations of the Decision Rule   . .            12
1. Estlmates of Healthy Life-Days-Saved Per Vaccination ...          12
2. Estimates of Life-Days-Saved Per Encounter ...................    15
3. Estimates of Parameters of the Cost Functions ...............     19
4. Applications of the Decision Rule ....................................  22
V.     Concluding Remarks ................................................  23
Notes .27
Refereices .30



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, e) - A(p) ((/u)13 + 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/(B- 1
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:
v    [ C/A(p) Il/s .                                    (3)
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
e             e               e             e
(a)             (b)           (c)            (d)
Figure 1. The Effect - Varying R3 on the Production
Possibility Yrontier
e
Strategy F
P-mV, | | i. /              ICombinod Feasible Region
m | . 0 | > /for Budget C
| , S | E K ~Strategy 11
V*                 2v*
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 1im 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:
Strategty F:       a   a 1/a 
[ (ehlf) + V       V                                   (4)
Strategy H:                      *
2 (e/pm) + v - 2 V                                     (5)
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
Hf w                                                    (6)
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
e
F±1vre 3a.\                            tt9 
scrat.gy~~strtey 
Strateg-y l1                    Object*ive Function
domina tesh(s,,x)
\ ~Strategy U
_e          ~s                 i 2V  V
e
Figure 3b,   ,L-fV*        H        F
Strategy F
dominates    PuImV              hev , x)m
:  v   +_ b/a
V      2v*
Figu.e 3c.                  A
Neither      IJmV*                  F
strategy                        h(e,,x)
dominates                                M
V-    * 2      V      K



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/2. 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
e
9%~~
IJfV i
V*      2V*         V
Figure 4a. Strategy F suffers from
zero complementarity
e
IJf V*  A~                      m~
i         SlopoZ  2a
Figure 4b. Strategy F favored by
perfect complementarity



page 12
IV. Applications and Interpretations of the Decision Rule.
If the values of the four parameters in decision rule (9) were known with
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. Thls section applies information from
three studies, on Ghana, Java, and the Ivory Coast, in order to arrive 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 together to illustrate
the application and interpreeation of the decision rule in Table 7 at the end of
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 vaccination 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 it is difficult to maintain the proper ratio
of measles vaccines to other vaccines and to deliver the third doses of the
polio and DPT vaccines. Since the third doses add less than the average to
LDS, reducing their proportions increases the average of the program.
However, since measles vaccination has at least thirty times more impact on
LDS per vaccination  than any of the others, reducing  its proportion even
slightly has a large negative effect on the average LDS per vaccine.
Table 2 presents in columns (8) and (9) the raw material for developing a
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 Michigan study estimated that
an immunization program consisting of 27,000 administered doses per year
would reduce mortality and morbidity to a degree which is calculated here to
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 eatimates for Ghana from Table 1.
However the Javanese immunization program considered by the Michigan
study differs in three ways from the immunization program presented in Table
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, it is possible to estimate the value of b that
would obtain in Java if the vaccination program resembled that in Table 1.



page 13
Table 1. Estimation of the Average Number of Life-Days Saved
Per Vaccination from Ghanaian Data
Life-    Prop.   Poten-  Prop.        LDS          Distributions of
Vaccination/     Days-    at        tial    Prdcng      Per          Vaccinations:
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.
Without Immunization              With Immunization
Pop.                   Disa-           Disa-    Life-   Thousands
in    Life    Death  bility   Death   bility    Y ears  Days
Age Group      Thous  Expect. Rate   Rate   Rate    Rate    Saved  Saved
(1)           (2)    (3)    (4)    (5)    (6)         (7)    ;8)   (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
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 other four cited
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 from Javanese
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 of
"need" is difficult to estimate until a study such as those of Heller (1982) and
M wabu (1983) on Kenya is available for VHWs in a country similar to that under
consideration.  Column (8) of Table (3) gives a rough estimate of such demand
based on the assumption that the villagers will not accept any preventive or
screening services from the VHW and that they do not demand "enough" care
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 reduce by half
the total number of encounters by the VHW, but reduce the number of LDS by
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 each of only 31
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 estimated 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.
Life-Days    VH W    Life-Days                    Life-           Life-
Lost    Effectiv-   Saved/ Incidence  Est'ed   Days  Est'ed    Days
Disease      If Sick    ness      Encntr Per Thou. "Need"  Svd. "Demand"  Savad
(1)         (2)       (3)        (4)      (5)       (6)      (7)       (8)   (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,
Severe       11667     0.63    1016.8         1.5      11     3.40       0    0.00
5. Gastro-
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-
somiasis       629      0.69    271.3         7.0      11     0.92        6    0.93
8. Pneumonia
- Child       7750      0.37    1792.2        2.4       4      2.09       2    2.10
9. Pneumonia
- Adult        1300     0.15     121.9        7.0      11      0.42      11    0.83
10. Premature
Birth        1750      0.10      18.7        9.6      90     0.51       0    0.00
11. Complications
of Pregnancy 1229      0.39      51.1        4.8      45      0.70       0    0.00
12. Birth
Injury       10250     0.21     229.6        1.6      15      1.05       0    0.00
13. Other
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.
Without VHWs                      With VHWs
P op.                  Disa-            Disa-    Life-   Thousands
in    Life    Death  bility.  Death   bility    Y ears  Days
Age Greup      Thous  Expect. Rate   Rate   Rate    Rate    Saved  Saved
(1)           (2)    (3)    (4)    (5)   (6)          (7)    (8)    (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
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.
Percentage
Improvement
Ghanaian           Ghanaian           Javanese      Aggregated   in Case
Di"as              Effec-  Ghanaian  Diseas         Javanese      Fatality     Javanese
Category          tdvuess Incidence  Category       Age Group        Rate      Incidence
(1)                (2)      (3)        (4)            (5)          (6)           (7)
1. C old              10 2    1000    2. URI           0-15           02          2000
15+            02         1000
2. Skin Inf.          102     470     4. Sidn Dii.     0-15            0Z           50
15+            0Z          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. Mild Diarrhea 0-15            02         2000
15+           0          1000
6. Severe Di&.   0-15          692          250
15+           40 2          80
6. Accidents          20Z       7.7   13. Burns        0-15           542           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  10Z       9.6   21. Comp. Brth  0-1            85Z            90
& Birth Injury     21S        1.6    & Pregnancy
11. Comp. of Preg.   392        4.8   21. Comp. Brth  Wom. 15-44   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
Returns    Increasing Returns
to Scale      to Scale
(s-l.0)  (su.9)    (s. 8)  (su.7)
1. Population covered by V8Ws attached
to a sngle fixed center.                           7,900    5,750     3,860    2,320
2. Number of fixed centers "needed" to srve
the entire region of Abengourou:                      17       24        36      60
3. Eimated number of encounters by VHWs attached
to a. single flxed center with budget given under
Asumption F2 below (ie. pf V*):                   37,100   27,000    18,200   10,900
4. Estimate of the parameter pf.                        10.6       7.7       5.2     3.1
Data and Asumptions Used:
Abengourou Mobile Team:                    Fixed Centers as VaW Supervisors:
Ml. Estimated rural population             F1. Number of vaccinations
of Abengourou:      138,000                with no encounters, V*:                3500
42. Total cost of mobile                   F2. Budget for V* vaccinations, C*:   735,700
team for one year. 5,293,814            F3. Assumed number of supervision
M43. Cost of vaccine:  1,009,600               trips per year to each VaW:              3
44. Cost to reach rural pop.               F4. Maximum cost per spvsn trip
w/o vaccinating:  4,284,210                that stays within budget, C *:      245,233
M5. Average Cost per Cap                   F5. Assumed number of encounters
to reach rural pop.:     31.0'              with VHW per capita per 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 P1f/2, 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
Java       Java      Ghana    Ghana
Estimates of the                            with        Orig.    Theory    Demand/
Average Impacr on                            EPI        Assum.              Obsrvd
Healthy Life Days of:                        (1)        (2)        (3)        (4)
.A vaccination  (parameter b)                 9.4       25.0       75.4       53.8
A VHW encounter (parameter a)               15.0        15.0      14.9         7.5
Ratio of b/a:                                 .6         1.7       5.1         7.2
Cost Function Parameters s and pf
Constant Returns to Scale:
(A) For s   1, If .  10.6                     F          F         F    ,    3.2
(0.5)
Increasing Returns to Scale:                                     -      j-  J
(B) For s -0.9, Pf. 7.7                       F          F      ;  2.9        20 3
(0.5)      (0.05)
(C) For s  0.8, hf - 5.2                      F          F        71.2      -- H
(0.01)  I
I   ~   Ji-- - 
(D) For s9  0.7, f - 3.1                      F    a    1.7      *M            M
|   ( 1.4)
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)(hl)/B
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:
/ ~ *   v/sf)       *              (1/Sm)
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 age- and disease-specific mortality rates or by healthy-life-
days-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.



page 30
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WPS5    Comparisons of Real Output in
Manufacturing                              Angus Maddison            April 1988         E. Zamora
Bart van Ark                                33706
WPS6    Farm-Nonfarm Linkages in Rural Sub-
Saharan Africa                             Steven Haggblade          April 1988         C. Spooner
Peter B. Hazell                              37570
James Brown
WPS7    Institutional Analysis of Credit
Cooperatives                               Avishay Braverman         April 1988         C. Spooner
J. Luis Guasch                              37570
WPS8    Prospects for Equitable Growth in
Rural Sub-Saharan Africa                   Steven Haggblade          April 1988         C. Spooner
Peter B. Hazell                              37570
WPS9    Can We Return to Rapid Growth?              Andrea Boltho             June 1988          J. Israel
31285
WPS1O   Optimal Export Taxes for Exporters
of Perennial Crops                         Mudassar lmran            June 1988          A. Kitson-Walters
Ron Duncan                                  33712
WPS11   The Selection and Use of Pesticides
in Bank Financed Public Health
Projects                                   Norman Gratz              June 1988          C. Knorr
Bernhard Liese                               33611
WPS12   Teacher-NonTeacher Pay Differences
in Cote d'lvoire                           Andre Komenan             June 1988          R. Vartanian
Christiaan Grootaert                         34678



PPR Working Paper Series
Title                             Author                    Date             Contact
WPS13  Objectives and Methods of a World
Health Survey                              Trudy Harph.,m           June 1988          A. Menciano
Ian Timaeus                                 33612
WPS14   The Optimal Currency Composition of
External Debt                              Stijn Claes-c's          June 1988          S. Bertelsme
33768
WPS15   Stimulating Agricultural Growth and
Rural Development in Sub-Saharan
Africa                                     Vijay S. Vyas            June 1988          H. Vallanasco
Dennis Casley                               37591
WPS16   Antidumping Laws and Developing
CtA ifre                                   Patr.ck .s.c_r!          Juno 1988          S. T.orr}J
33709
WPS17   Economic Development and the Debt
Crisis                                     Stanley Fischer          June 1988          C. Papik
33792
WPS18   China's Vocational and Technical
Training                                   Harold Noah              June 1988          W. Ketema
John Middleton                              33651
WPS19   Coie d'ivoire's Vocational and
Technical Education                        Christiaan Grootaert    June 1988           R. Vartanian
34678
WPS20   Imports and Growth in Africa               Ramon Lopez               June 1988         61679
Vinod Thomas
WPS21   Effects of European VERs on Japanese
Autos                                      Jaime de Melo            June 1988          S. Fallon
Patrick Messerlin                           61680
WPS22   Methodological Problems in Cross-
Country Analyses of Economic Growth        jean-Paul Azam           June 1988          E. Zamora
Patrick Guillaumont                         33706
Sylvi3ne Guillaumont
WPS23   Cost-Effective Integration of
Immunization and Basic Health Services
in Developing Countries: The Problem
of Joint Costs                             A. Mead Over, Jr.        July 1988          N. Jose
33688