VI. ANALISIS ECONÓMICO DEL SECTOR PÚBLICO DEL P.A
VI.1. Análisis específico de ayuntamientos
VI.2.2. De los entes dependientes
THE CORE MODEL w
The number of new infections averted by each intervention i for a budget level x is calculated with the following formula:
q
∆Ii (x) = αi(x) *
∑
Ia(o) * min [(Ni(x) * Pia), (Popa *fa)] / Popa ] a=1where:
∆Ii (x) is the number of new infections averted by each intervention i for budget level x
αi(x) is the effectiveness of a prevention program i as a function of the budget allocation x. It
represents the percentage of new HIV infections that can be prevented within the total population reached by a given intervention i with a defined budget level x assigned to that intervention. αi(x) is estimated in Step 7 of the model (see Chapter 3).
q is the total number of population groups. q is defined in Step 1a.
Ia(o) is the baseline number of infections in group a. Ia(o) is the sum of primary and secondary
infections, as estimated in Steps 2 and 3 respectively.
Ni(x) is the total number of people reached by intervention i at budget level x.
Ni(x) = (total available budget) / (unit cost of the intervention)
The unit cost of the intervention is an average cost, which is estimated in Step 6. This simplification was used due to data limitations that prevented an estimation of the marginal cost of each intervention (see Chapter 2, Caveats).
Pia is the percentage of the population reached by intervention i that corresponds to group a.
Pia is estimated in Step 5.
Popa is the total population of group a. Popa is estimated in Step 1b.
fa is the maximum proportion of group a that can be reached. fa is estimated in Step 1c.
and (Ni(x) * Pia) = (Popa *fa)
We seek to maximize the number of infections averted across all interventions under a budget constraint. This problem can be represented as follows:
n q
Max
∑
∑ (
αi(x) *Ia(o) * [ (Ni(x) * Pia) / Popa ])
i =1 a=1
s.t.
∑
xi = Bwhere:
n is the total number of interventions. These are defined in Step 4. xi is the budget allocated to each intervention
B is the total Budget available for HIV/AIDS prevention programs
ADDITIONS TO THE CORE MODEL
Reserved Spending
To account for reserved spending for a particular intervention, in the constrained maximization problem, we fix:
xi = ri for i = 1,2,3,…, n.
where ri is the guaranteed allocation for each group.
Correction for Effects of Concurrent Interventions
Effects of positive or negative synergy aside, the effectiveness of an intervention in isolation is always different than its effectiveness in coexistence with other interventions. For example, six interventions, which in isolation would each prevent 20% of all new infections, will not prevent 120% of all new infections when acting together. The model corrects for this using the following formulas:
(i) The corrected number of infections averted by all interventions acting on group a is:
n n
Corrected ∑ ∆Iia = ∑ ∆Iia * {1-[(1-Eff.1a)* (1-Eff.2a)*...* (1-Eff.na)]} i=1 i=1
where:
∆Iia is the number of new infections averted by each intervention i in group a, based on the
assumption of isolated effectiveness n is the total number of interventions
Eff.ia is the % effectiveness of intervention i in averting overall infections in group a
(ii) Similarly, the corrected total number of infections prevented by intervention i is:
q q
Corrected ∑∆Iia = ∑ ∆Iia * {1-[(1-Eff.1a)* (1-Eff.2a)*...* (1-Eff.na)]} a=1 a=1
(iii) The corrected total number of infections prevented by all interventions is given by:
n q
∑ ∑ ∆Iia * {1-[(1-Eff.1a)* (1-Eff.2a)*...* (1-Eff.na)]} i =1 a=1
Secondary Infections
The expected number of secondary infections in the general population that arise from one primary infection in a given subgroup (S) was calculated using the following Bernoulli formulax:
S =m*(1-P)*[1-(1-An) n (1-Ak) k ] Where:
S is the expected number of secondary infections that arise from one primary infection m is the average number of sexual partners for a person in the population group under
analysis
P is the mean HIV prevalence among the sexual partners of a person in the population group under analysis
An is the transmission probability per unprotected contact
Ak is the transmission probability per protected contact where Ak = (1-e)*An
e is condom effectiveness
n is the average number of unprotected sex acts per partner k is the average number of protected sex acts per partner
In addition, the effect on the transmission probability per contact of a co-infection with an
ulcerous or non-ulcerous STD was included in the model using the following formula to calculate the transmission probability per unprotected contact An :
An = T * (PSTDu*Mu + PSTDnu*Mnu) + T * (1 - PSTDu - PSTDnu)
Where:
T is the transmission probability with no STD co-infection PSTDu is the prevalence of ulcerous STDs in the subgroup
PSTDnu is the prevalence of non ulcerous STDs in the subgroup
Mu is the infectivity modification factor for ulcerous STDs
Mnu is the infectivity modification factor for non-ulcerous STDs
All the parameters for the calculation of S are presented in Step 3 of the Model.
APPENDIX II: THE EFFECT OF SUBGROUP SATURATION ON
COST-EFFECTIVENESS
Basing resource allocation decisions on specific subgroups of the population rather than interventions greatly simplifies the calculations involved. This is, however, not very useful for the policymaker since assigning certain amounts of resources to a subgroup does not solve the allocation question unambiguously; resources allocated to any specific subgroup can be spent in many different ways with different results. The approach adopted here is to base allocation on interventions and to define the composition of the population reached by each intervention. Both the interventions and their mapping onto subgroups must be defined to prevent ambiguity in the interpretation of the results of the model.
By using interventions (which reach more than one subgroup) rather than subgroups as the basis for resource allocation, certain corrections have to be made to ensure a correct optimization process. An intervention, say counseling and access to rapid testing (see step 4), has a given composition of subgroups as its target population. As more money is allocated to this intervention, the smaller subgroups begin to get saturated. This means that the intervention has already reached the accessible population in the smaller subgroups (e.g., CSWs, MSM, prisoners). Budget increases for this intervention do not permit reaching more people in those subgroups. In other words, given enough resources, each intervention can reach a theoretical point where it cannot attain a single additional member out of a number of subgroups.
The saturation of subgroups as explained above implies that the composition of the population attained by an intervention can change as the budget increases. The table below illustrates this point for a fictitious intervention that benefits three subgroups, two of which are small (1,500 CSW and 4,500 MSM) and the general population. The unit cost for the intervention is supposed to be US$10 per person. With $100,000, therefore, the intervention reaches 10,000 beneficiaries, of whic h 1,500 are CSWs and 1,500 are MSM. This means that the CSW population is saturated at this budget level, and as more funds become available for this intervention, they do not benefit the CSW population any longer. The same happens for MSM when $300,000 are allocated to the intervention.
The Changing Composition of Population Reached: The Effects of Subgroup Saturation
Number of Individuals Reached Percentage of Population Targeted by Intervention Reached
Budget Level CSWs MSM General
Population CSWs MSM General Population $100,000 1,500 1,500 7,000 15% 15% 70% $200,000 1,500 3,000 15,500 8% 15% 78% $300,000 1,500 4,500 24,000 5% 15% 80% $400,000 1,500 4,500 34,000 4% 11% 85% $500,000 1,500 4,500 44,000 3% 9% 88%
Note: Shaded cells indicate a subgroup at or beyond saturation point.
As the budget increases, the model accounts for this by calculating the proportion of target population “not filled” by saturated subgroups, and increasing the composition by other subgroups to attain the correct number of individuals for that budget level.
The implication for the optimization exercise is that the cost-effectiveness of an intervention changes (usually decreases) as the budget allocated to the intervention increases. Indeed, the effectiveness of the intervention is subgroup specific (see step 7); since the composition of the population benefiting from an intervention changes as the budget increases, the cost-effectiveness of the intervention also changes. The cost-effectiveness of the intervention tends to decrease because small, high-risk subgroups form a decreasing part of the population reached and thus the relative difficulty and cost of preventing each infection tends to increase.