Performance evaluation of exPenditure in Primary care : the case of Brazil ’ s southeastern cities

This study aimed to analyze the performance of cities of Brazil’s southeastern region on primary care expenditure, from 2007 to 2010. In order to do the performance analysis we used the technical efficiency scores produced by the Data Envelopment Analysis (DEA) methodology and the Ray and Desli Malmquist Index as the quantitative metrics. Before starting the cities’ efficiency analysis, the cluster analysis was applied to group similar cities. This study proposes an analytical model of the comparative performance of 1097 cities, based on the National Primary Care Policy. The efficiency scores obtained highlights the disparities in the allocation of resources and lost in productivity through the years analyzed. This fact could be justified due the absence of procedures of relative comparison between cities and the decentralization of public expenses in public healthcare. The results shed light on the possibility to improve the quantity of primary care services, given the current level of expenditure.


Introduction
I n order for SUS to become effective, primary care needs to be strengthened.It is being capable of solving around 80% of the health needs and problems, also highlighting the importance of prevention and immunization in this care level.(BRASIL, 2007;ELIAS et al., 2006) However, in Brazil there are still citizens which do not possess access to primary care service, for various reasons, among them the low relation between supply and demand for these services.The limitation of public resources may be considered as a restricting factor to the increase in the offer of healthcare services, requiring that the public administrator allocate efficiently his resources instead of seeking the increase of budget sources.(FLEURY;BARIS, 2001;FLEURY;BAHIA, AMARANTE, 2007) According to the Brasil (2008) the results which Brazil has obtained in the healthcare area are below the expected results considering the invested amount of money.Little by little, the public policy makers begin to admit that money may not have been well invested.Among the main possible solutions for the problem we can state: increase the amount of financial resources -probably unviable due to the resource limitation -or increase the efficiency in resource allocation.
Focusing on the above highlighted problems and seen the increasing of efficiency as a feasible solution for the improvement of the results which Brazil has obtained in healthcare area, this study was carried out to answer the following question: what is the comparative performance of cities in the southeastern region of Brazil in primary care expenditure?According to Selden and Sowa (2004) and Scott and Davis (2007), the idea of performance is focused, typically, in the outputs and outcomes of programs or policies.According to Farrel (1957) and Charnes, Cooper and Rhodes (1978) technical efficiency is the ability to produce more outputs with a given amount of inputs and according Scott and Davis (2007) could be applied as a performance assessments.
It is justified that the evaluation of efficiency in public resources allocation may serve as an instrument to support public managers' decision making as well as identifying benchmark cities so that the inefficient cities may looking for the best practices from efficient cities.In performance analysis, according to Greiling (2006), benchmarking is designed to make learning easier as a continuum and systematic process of measuring products, services and practices aiming at correcting failures and improving results.This idea of a comparison between units of analysis by relative efficiency scores is found in the performance analysis literature.(BEHN, 2003;GREILING, 2006;SELDEN;SOWA, 2004;SCOTT;DAVIS, 2007) Given the problems proposed and the justifications for conducting this study, this study was carried out to analyze the comparative performance of cities in the southeastern region of Brazil in primary care expenditure, from 2007 to 2010.More specifically, we separated the groups of the most similar cities according to characteristics which could have influence on expenditure efficiency scores and then applied the proposed efficiency model by Data Envelopment Analysis and Ray and Desli Malmquist Index. Ibañez and others (2006) state that is important to say that rescuing primary care is a part of the current issue of the feasibility of health systems.The increasing healthcare costs have brought governments and private institutions which work in this field to place primary care as a central point aiming to preventing health problems and treating them in a more efficient manner.Again, the improvement of the expenditure efficiency in primary care could be a good solution to health results.Likewise, this study propose an efficiency model to assess the expenditure efficiency on Brazilian primary care.The research and data collection strategy From the population of 1668 cities in Southeastern region of Brazil we chose only cities which had at least one Family Health Team -the group of physician, nurses, nurse assistants and other professionals -classified as the main strategy according the National Primary Care Policy.Afterwards, after an exploratory analysis of the data, we excluded from the sample those with inconsistent variables and with the absence of some observation for one or more analyzed years (2007)(2008)(2009)(2010).It was excluded 570 cities because of that.
The final sample was comprised of about 70% of the cities in Minas Gerais, 60% of the cities in the State of Espírito Santo, 50% of the cities in Rio de Janeiro and 52% of the cities in São Paulo.In some cases, existing secondary data create an opportunity for evaluative and simplified comparisons.The performance measures may contribute not only to indicate the organizations are making mistakes but also to indicate when they are doing well.Performance measures provide justification for the existence of the organizations.(BEHN, 2003;GREILING, 2006;HALACHMI, 2005) For data collection and analysis, the National Primary Care Policy from 2006 was established as the reference public policy.By this definition, the analysis period was from 2007 -the first year of this policy -to 2010, due to this being the last year with available data in the researched databanks.All of these variables were collected during the period from July to September 2011.

Analysis procedures
In order to do the performance analysis as the quantitative measure we used in this study the technical efficiency scores produced by the Data Envelopment Analysis (DEA) methodology.But, before starting the cities' efficiency analysis the cluster analysis was applied to group similar cities according to Short and others (2007) and Ferguson, Deephouse and Ferguson (2000).It becomes necessary that the compared units were similar in order to avoid spurious comparisons and group the most similar cities and separating the most distinct.Therefore, it will be possible to compare similar measures according to the discussion which approaches the concepts of benchmarking in the literature.(BEHN, 2003;GREILING, 2006) In the cluster analysis we used the non-hierarchical k-means method quoted in Maroco (2003) and Hair and others (2005) for partitioning the city groups.This method was utilized due to the fact that it is an advantage in relation to the hierarchical methods because to the ease which it can be applied to very sizable data matrixes and there is no need to calculate and store a new dissimilarity matrix in each step of the algorithm.According to Maroco (2003) the probability of a wrong classification of a given subject in a given cluster is lower in the non-hierarchical methods.(MAROCO, 2003) According to Sugar and James (2003), a fundamental problem in cluster analysis is to determine the best number of groups.In order to determine this number that shall be used in the study we employed the Calinski and Harabaz index whose equations are in Milligan and Cooper (1985) and Sugar and James (2003).According to Milligan and Cooper (1985), the Calinski and Harabaz index is considered a robust index for defining the number of clusters.
After the definition of the clusters, the measuring of efficiency was performed through the use of the Data Envelopment Analysis (DEA) methodology, output-oriented supposing variable returns to scale (CHARNES;COOPER;RHODES, 1978;BANKER;CHARNES;COOPER, 1984)  In the Equation 1 the Decision making units (DMU) represented by the cities use m inputs, s products; j is associated with the analyzed DMU 0 and n corresponds to the total number of DMU; x ij is the consumed quantity of the input i (i = 1,2, ..., m) by DMU j ; y rj is the quantity produced of the product r (r = 1,2,3 …s) for DMUj; j l is the weight of the composition of the analyzed DMU 0 virtual (projection on the efficient frontier); VRS q is the efficiency score output-oriented supposing variable return to scale.
The output orientation was applied because the objective of the cities must be to increase the primary care services production and not to reduce the budget allocated in the field.Also, quoted authors have discussed the scarcity of resources for this sector, indicating that the increase in expenditure efficiency is necessary.(FLEURY;BARIS, 2001;WORLD BANK, 2007;BRASIL, 2008) The Data Envelopment Analysis is able to classify the analyzed units by indexes from 0 to 100% through mathematical programming.So it was possible to rank the cities and compare them.The structures of the classic models are found in Charnes, Cooper and Rhodes (1978), Banker, Cooper and Rhodes (1984) and Banker and Thrall (1992) that show the classic models in Data Envelopment Analysis.
The supposition of variable return to scale was tested by the Theorem 2 of Banker (1996) quoted by Ray (2004) which has shown itself to be a consistent analysis.After the application of the above mentioned test, comparing the scores according to Ray (2004), we did not notice a prevalence of only one type of return to scale.In this case, the quoted authors recommend the assumption of variable returns to scale (VRS).
In this study we have a panel of efficiency scores for verifying both changes in the productivity and difference in efficiency scores over the years.According to Banker et al. (2005) the Malmquist index was proposed by Caves, Christensen and Diewet (1982) with the objective of measuring changes in productivity between two periods of time by the distance between a DMU and the frontier of production for each period.This calculation to measure the productivity changes are interesting in a context in which multiple inputs and outputs, as well as longitudinal dependent panel coexist.Ray and Desli (1997)  indicates the change in technical efficiency, i.e., how far the DMU is from the maximum production observed, between year t and t+1.The geometric mean of two ratios in brackets x practicable regarding the frontier of period t+1.
In the situation of in which there has been no change in the inputs and outputs through the periods, the signal of productivity index does not change and The CRS and VRS symbols are the abbreviation of constant returns to scale and variable returns to scale, respectively.According Fare and others (1994) productivity gain is found when the Malmquist index is greater than 1.The deterioration of performance over time is associated with the Malmquist index less than 1.To calculate productivity change among DMUs is necessary to calculate the eight different linear programming problems: ) , ( all assuming constant returns to scale and variable returns to scale.
In the analysis of this study's results, all the statistic tests are found at the end of each table.In these tables we shall also describe the results of the sample distribution normality tests, in order to justify the application of parametric or non-parametric hypotheses tests.

Analytical model for performance evaluation in Primary Care resource allocation
This study agrees with Elias and others (2006) and Brasil (2008) when they discuss that the analysis of health must take into consideration the "Social Space", considering that society has different access to the consumption of goods, including health services.In this discussion we include the fact that the characteristics of the analyzed regions such as the demographic and epidemiologic profile should be taken into consideration.
The grouping of similar cities make possible for a given inefficient city in its expenditure to be compared to other cities with similar characteristics, or the most similar possible.Another advantage of obtaining groups of cities with the most similar characteristics possible is the fact that this comparison offers better benchmarking for the inefficient cities.
What will define how similar the groups are internally are the variables inserted to characterize them.In this study, the model for ranking the cities was built from four dimensions considered to be important for primary care in health and may have impact on the expenditure of distinct cities: private coverage, development, size and poverty.Figure 1 describes the four dimensions.
Private health coverage was considered the most important dimension for the separation between the groups.In order to explain the importance of this dimension we quote the arguments of Wibulpolprasert, Tangcharoensathien and Kanchanachitra (2008) who state that most of the population in development countries do not have any access to private health services, which makes the access to health, immunization and medicine more difficult.In this direction, individuals with private health coverage may need less the services offered by Brazilian Unified Health System than individuals who do not have any access to private services.The arguments of Ibañez and others (2006), Henrique and Calvo (2009) and Machado, Lima and Viana (2008) converge towards the existence of a relation between poverty and access to health services.The individuals who do not possess any private coverage will need to refer themselves to the public primary care services.
As a manner of giving a higher weight to this dimension, the cities were divided in 2 groups according to that city's percentage of private coverage before introducing the further dimensions.Through the exploratory data analysis we established that it would be feasible to build two groups with an approximate number of cities.
Therefore, the first group -labeled group A -was comprised by cities with 10% or less of the population registered by the Family Health Team covered by the private services.The other group -labeled group B -was formed by the cities with more than 10% of the population with private coverage.It is considered that the first group has a higher dependency on public primary care services than the second one.After the separation approximately 56% of the cities were put in group A and 44% were in group B.
Between the four dimensions inserted for characterizing the groups, poverty was represented by the proportion of population benefited by the Conditional Cash Transfer program called "Bolsa Família".These are people who seek public health services according Ibañez and others (2006), Conill (2008) and Henrique and Calvo (2009).These quoted authors consider that this part of the population is found in areas with higher nutrition risk, lower education, living and basic sanitation conditions and which will depend with a higher frequency on the public health services.
Size was another variable to be considered.This is because according to Henrique and Calvo (2009) and Conill (2008) the implantation of primary care programs were predominant in smaller cities, in which high complexity care did not fulfill the population's needs.So, we expect that cities with a smaller population size will have a more developed primary care system than those in bigger cities.
The last dimension to be considered was development represented by the Human Development Index (HDI).This variable was chosen because it took into consideration, in composing the index, not only GDP, but longevity and education.This variable allows for the identification of cities with a more structured health system highlighting the relation between longevity and health.It is necessary to state that education is an important component for prevention and promotion of health (BRASIL.Ministério da Saúde, 2007;ELIAS et al., 2006;IBAÑEZ, 2006) After the definition of the clusters we inserted some more variables available by Ministry of Health for additional characterization the cities.These variables are related to the cities' infrastructures as the following ones: According to the World Bank (2007) these variables were used because other factors such as the access to drinking water and sanitation may also have an influence on comparisons between expenditures and results.Wibulpolprasert and others (2008) affirm that apart from the reduction in child mortality and immunization for achieving the objectives of primary care it is necessary the access to drinking water and basic sanitation.
It was possible to perform the relative technical efficiency analysis after group the similar cities.According to Brasil (2007) primary care resources should be allocated for paying the Family Health Team and maintaining the primary health units.In this direction, the allocation of resources for the primary care will be represented by the number of Family Health Teams and number of health establishments.These two variables according to National Primary Care Policy represent the primary care main expenditure i.e resource allocation.
In the new organization of primary care, the cities became managers of the local systems, responsible for fulfilling the Primary Care principles, organizing and executing actions in its territory.The resource allocation model for performance evaluation in Figure 2 was built by two inputs and three outputs.For allocating resources, the National Primary Care Policy quoted by the Brasil (2007) proposes that cities should be responsible for maintaining the Family Health Team -the main strategy -and the necessary infrastructure including material resources, equipment and sufficient inputs for the set of proposed actions.Therefore, the expenditure efficiency model was represented by the number of Family Health Team and the number of health establishments as inputs.

Lucas Maia dos Santos, Márcio Augusto Gonçalves & Marco Aurélio Marques Ferreira
Relating to the justification for formulating this model we may quote as a reference the work of Starfield (1998) which characterized primary care as the "entrance door" which gives accessibility to population health needs.So, the first output was characterized by the number of people registered by the Family Health Team.According to Henrique and Calvo (2009), this variable is important for resource allocation because primary care coverage is just around a third of the country's population.Also, according to Elias and others (2006) and Brasil (2007) the population registration has the importance of enabling the program to know about morbidity characteristics and thus act towards prevention and promotion of health.According to Brasil (2007) at least the Health Family Team are comprised of a doctor, a nurse, a nursing assistant and community health agents.The Health Family Team are responsible for maintaining the family and individual records updated and using the data for analyzing the health situation taking into consideration the social, economical, cultural, demographic and epidemiologic characteristics of the territory.Starfield (1998) and Brasil (2007) state that the primary care evaluation has to encompass the regular use of the primary care services which is represented by the number of home visits by the Health Family team.Also, Starfield (1998) affirms that primary care should supply the minimum range of adequate services to the population which is represented by the ambulatory production in primary care.In this production we include the primary care procedures performed according to the Table of Procedures, Medicine, Orthesis, Prosthetics and Special Material of Brazilian Unified Health System.

Analysis of the results
In the division of the city groups for the cluster analysis, we labeled as Group A the one with the lower private health coverage, i.e, cities with less than 10% of the population with private coverage.Table 1 shows the division of Group A in two groups of cities as follow: Group 1 and Group 2. As previously mentioned, in the tables we can find the results of the tests performed for choosing and differentiating the groups.
Comparing groups we can affirm that, in general, Group 2, shown in Table 1, presented lower averages for all the variables used to rank them, except for proportion of the population covered by the Conditional Cash Transfer program.
Relatively, Group 2 has the smallest cities, with a population average of 9,929 inhabitants against 27,584 inhabitants of Group 1. Analyzing the quartiles, Group 2 has more cities with lower basic sanitation coverage and infrastructure as well as the dimensions used to split the groups.We observe that Group 2 was formed by cities with at most 53 thousand inhabitants, while Group 1 has cities with up to approximately 830 thousand inhabitants.Analyzing the quartiles, 75% of the cities in Group 1 have less than 23 thousand inhabitants while in Group 2 there are less than 12 thousand.
We highlight that these differences do not imply that in Group 2 there will be only smaller cities and in Group 1 only the bigger cities.As we inserted 4 dimensions in the cluster analysis, it is possible to have, in a same group, bigger and smaller cities which are then similar by the other dimensions.Regarding the cities' infrastructure and basic sanitation, Group 1 has higher water network coverage for the houses (76% versus 60% of Group 2), higher garbage collection (81% versus 54% of Group 2), sewage piping (68% versus 41% of Group 2), brick houses (96% versus 93% of Group 2) and electricity coverage (97% versus 90% of Group 2).These values indicate a higher basic sanitation and infrastructure coverage for the cities in Group 1, when comparing to Group 2.
Regarding the beneficiaries of Conditional Cash Transfer we notice a higher average for Group 2 with, approximately, 10% of the population versus 6% in Group 1.The other analyzed variables indicated a higher proportion of poor population in Group 2.

Lucas Maia dos Santos, Márcio Augusto Gonçalves & Marco Aurélio Marques Ferreira
Due to the opposing characteristics observed in the groups, it was expected that because of the higher averages attained for infrastructure coverage and the lower ones for poverty, Group 1 would show a higher HDI average.Therefore, we found an average of the index of 0.76 versus Group 2 which presented an average index of 0.67.
About the splitting of Group B, according to the pseudo-F criteria, we should choose the solution comprised by 5 clusters, with the highest value of 276.84 for a pseudo-F, due to them being more distinct.However, when analyzing the amount of cities in each group, we noticed that one of them was formed by only 2 cities.These were the cities of São Paulo and Rio de Janeiro.Knowing the characteristics of these cities as the biggest cities and the most important financial centers, it was expected that these cities would be grouped separately, for a better distinction among the groups.We opted, then, for considering these two as outliers in the study and taking them out of the analyses due to their distinct characteristics when comparing to other cities.
With the exclusion of the two cities a new cluster analysis was performed and, as we can see in Table 2, the highest Calinski Harabaz pseudo-F value of 314.02 was shown to be the best division with two groups.
Group B was partitioned into Groups 3 and 4 after the Cluster analysis.Analyzing the descriptive statistics of the variables which integrate the groups, we may notice that Group 3 has a higher average for the infrastructure variables such as water piping coverage (90% versus 78%), garbage collection (94% versus 80%), sewage (83% versus 69%), brick housing (96% versus 95%) and electric energy (99% versus 57%).The quartile analysis also shows that most cities in Group 3 have higher values observed for the variables of infrastructure and sanitation.
As for the private coverage, Group 3 has the cities with higher private coverage average (19% versus 13%) as the observation shows.Apart from having a higher private health coverage than Group 4, this group has a lower number of people dependent on Conditional Cash Transfer program (4% versus 7%).
Regarding size, Group 3 hasw a higher average population and a higher range than Group 4. Group 3 has an average 98,929 inhabitants versus 23,369 inhabitants of Group 4. Analyzing the quartiles, 75% of the cities in Group 3 have less than 95 thousand inhabitants, while this value is less than 20 thousand inhabitants for Group 4. It was possible to see that, for the analyzed dimensions, groups 1, 2, 3 and 4 were formed with cities of different sizes, but similar by other dimensions.Despite this fact, Group 2, with the lowest private coverage has the cities with the lowest population and, by analyzing the quartiles, 75% of these have less than 12 thousand inhabitants.This group also showed the smallest averages for the other variables, indicating the presence of the smallest cities and also the poorest of the sample.
Group 1 and Group 4 have similar characteristics, except for the private coverage percentage.While Group 1 has 75% of the cities with less than 23 thousand inhabitants, Group 4 has 75% of the cities with less than 20 thousand inhabitants.As to development, they are close in HDI indexes, Group 1 having an HDI index average of 0.76 and Group 4 has 0.74.
Group 3 showed itself to be opposed to Group 2, presenting the highest averages for variables analyzed.This group may be considered as the one formed by the biggest cities in the sample and, at the same time, being in average the most developed.
In general, the 4 groups presented the best possible distinction for the four proposed dimensions which could have influence over the expenditure efficiency in primary care.The formation of these groups will enable to perform the analysis of technical efficiency to identify better benchmark cities.
Placing the groups in an imaginary line which measures the dimensions stated for ranking the cities, we may say that Groups 2 and 3 are at the extremities of this imaginary line, while Groups 1 and 4 are in intermediate positions.The list of efficient cities by groups are available in the appendix of this study after the references.

Technical efficiency analysis
The descriptive statistics of technical efficiency in allocating primary care resources for Group 1 are set out in Table 3 through the four years.We may notice that the average efficiency of resource allocation was, respectively and approximately, 58%, 59%, 65% and 62% from 2007 to 2010.Analyzing the quartiles of the technical efficiency scores we can observe that in all years 75% of the cities had efficiency scores lower to 75% approximately.As to the inferior quartile, 80% of the cities have indexes higher than 44%.Relatively, we may say that these results are far from 100% efficiency.
Analyzing these results we may infer that most of the analyzed cities could increase the service offer for the population in primary care, for being below the limit of efficient cities.This score and efficiency dispersion was expected due to the autonomy in expenditures of the city governments in primary care as discussions of Fleury andBaris (2001), Brasil (2008) and La Forgia and Couttolenc (2009).If each city allocates its resources without relative comparison parameters, it is expected that the results will be so spread.Therefore, this study proposes to bring these differences into evidence, in order to motivate the decision maker for controlling the resource allocation in these cities.About the differences in efficiency through the years was not possible to verify significant changes in productivity (Malmquist) in the range 2009-2010.For the other years, it can be inferred that the cities had Malmquist indexes different from 1 (one).From Table 2 it can be seen that more than half of the cities in Group 1 showed a lost in productivity in the ranges of 2007-2008 and 2008-2009.In the interval 2009-2010 there were no significant changes.According to the average there was a loss of 1% in productivity in the range from 2007 to 2008 and the same amount for 2008-2009.Group 2, formed by 255 cities, forms Group A of cities with lower coverage of private health insurance.The technical efficiency scores and scale of this group are presented in Table 4.
For the respective analyzed years, the average technical efficiency scores were, approximately, 58%, 48%, 56% and 60%.We may see by the scores' descriptive statistics a considerable range for efficiency which has a minimum of 20% for year 2007; approximately 16% for year 2008; 28% for year 2009; 29% for year 2010.Similar ranges were observed when analyzing Group 1, reinforcing the hypothesis that the analyzed cities are different in primary care expenditure efficiency.The efficiency of the cities are low when we analyze that 75% of the sample have efficiency scores below 73% between the four years analyzed.If we analyze only year 2008, this value falls to 60%.
Looking at Table 4 we could see that most cities in Group 2 showed lost in productivity in the range 2007-2008 and 2009-2010.On average there was a gain in productivity by 1% from 2007 to 2008 and an average reduction of 2% in 2009-2010.Even with the average increase in the interval 2007-2008, most municipalities have reduced productivity as seen in quartiles.As can be seen in Table 5, there was a lost in the productivity for most cities.In Group 3, from the first to the second year (2007)(2008) no significant change in productivity was found.In the rest of the intervals analyzed, it was observed that most cities lost expenditure productivity in primary care, although the averaged gain of 1% from 2008 to 2009.
We can observe through the descriptive statistics that 50% of the cities have efficiency scores below 60% over all the years analyzed.Thus, we expect a higher percentage increase in the outputs generated by these cities so that they may improve technical efficiency.
In Table 6 we have available the efficiency scores for Group 4, formed by 176 cities.The average efficiency found was of 65%, 70%, 67% and 50%, respectively, for the years analyzed.Technical efficiency for the year 2010 was inferior to the other years, contrary to the averages of years 2007 to 2009.By analyzing the quartiles, for the year of 2010 it is possible to infer on the presence of cities with low scores for the year of 2010.Again Table 6 shows that most cities lost expenditure productivity.In other years there was no significant change in the median productivity.Analyzing the quartiles, we notice that 75% of the cities have efficiency indexes above 50%, except for year 2010.In the same direction, except for the year of 2010, 75% of the analyzed cities have efficiency scores below 75%.
Overall, it can be inferred that most of the cities analyzed showed lost in productivity in primary care expenditure over the years analyzed.This result can be inferred by analyzing median of Malmquist Index of Ray and Desly (1997).It may be possible that the reduction of this productivity is related to stabilization of Primary Care National Policy since the early years there may be greater effort by governments to promote policy and this effort would be reduced over the year.This is a hypothesis not tested in this study and it is not possible to tell if this is the cause of most lost in productivity.
The analysis posted here meet the performance studies, such as Behn (2003) and Greiling (2006) who claim that the performance measures that diverge from the expected can create opportunity for learning and that these measures may suggest topics for research.

Conclusions
This study was developed aiming at being utilized by the city managers and researchers as an instrument for supporting the decision making, so that the inefficient cities can look for their benchmarks (100% efficient cities) of the best public resource allocation practices seeking to increase the primary care services offer for the population.We have attached the list of efficient cities in the appendix of this study that could offer more services in primary care with the same level of resource allocation.
One of this study's main contributions was the proposal of the analytic model of performance in primary care expenditures.This model take in account the main variables described by literature.Furthermore, this study took into consideration a longitudinal analysis which is not taken into consideration in most studies which use efficiency indexes in Brazil.
Analyzing the most similar possible cities, in four different groups, the efficiency scores evidenced the disparities in resource allocation in the southeastern region because of the differences in the efficiency scores, a fact which could be justified by their autonomy in allocating their resources and the absence of relative comparison procedures between them for these expenditures.The 1988 Federal Constitution gave attributions to municipalities and states besides the federal government by the decentralization process in the public management.This study proposes a model to solve this problem a lack relative comparisons.According this study there is space for increase the primary care service offer.
As a proposal for a performance analysis, this model should be applied continuously, so that it may be justified as a performance study.This study is the initial proposal of a model so that the measuring is not restricted only the period of this study.The building of reference units or benchmarks may be an instrument to direct the decision-making of city managers, as well as other higher public management levels.
It was important to incorporate all possible cities from southeast region to create a practical frontier.We indicate not exclude or look for outlier in these frontiers assuming that all cities are under the same conditions to manage his resources because of the decentralization of primary care resource allocation.That is why we did not apply the super-efficiency of Banker and Chang (2006) for identifying outliers in the production frontier.Maybe exceptional efficient cities should be taken into account to know why that could be so different in offering more services with some level of investments.By the way the inefficient cities should try to reach these exceptional efficient cities and not those with the same productivity level.That was one of the reasons to apply a non parametric metric to analyze the expenditure efficiency.
Therefore, this study follows Greiling (2006) in the supposition that performance measures which diverge from what was expected may create an opportunity for learning.But the measures themselves tend more to suggest themes for investigation than to directly transmit main operational lessons.So do this study.In order to improve performance, public managers need to understand how they can influence people's behavior inside their cities which produce their results, and how they can influence the citizens' behavior, which is converted into results from these outputs.We questioned whether there were changes in productivity from 2007 to 2010 and we found that there was no gain in productivity in any of the four groups obtained.For most cities there were no statistically significant changes in productivity or when it was found, these were caused by lost in productivity.The analysis of the cause of productive lost is not in this study but there are a main hypothesis about that: the rise in the difference between the efficient cities and inefficient cities.In this case, we could analyze in future studies if this difference was caused by the improvement of efficient cities or worse of inefficient cities.
Since the importance cited in this study, the need to increase efficiency at the expense of the budget increase for the sector, it is important to try seek the causes of reduced productivity and work so that resources can be allocated more productively.
Besides analyses of productivity lost, future studies could analyze and compare the validity among different models that could incorporate other variables as number of physicians, number of nurses and epidemiological and mortality variables (as childhood mortality, frequency of diabetes and arterial hypertension).The purpose of studies like that are beyond this study purpose and could incorporate statistical analysis as structural equation modeling and path analysis to test which model could be more appropriate to rank the efficiency of cities.

Figure 1 -
Figure 1 -Dimensions for characterizing the cities

Figure 2 -
Figure 2 -The model of technical efficiency in expenditure on primary care

(
x10 2 ); BRICK -proportion of houses made of bricks (x10 2 ); ELECTRICITY -proportion of houses which have electricity (x10 2 ); PRIVATE -proportion of population covered by private healthcare assistance (x10 -3 ); TRANSFER -proportion of population benefited by the "Conditional Cash Transfer" program (x10 2 ); POPULATION -population living in the city (x10 -3 ); HDI -Human Development index; Gr -group.Tests results: highest pseudo-F of Calinski and Harabaz: 362.71; p-value<0.01for univariate normality asymmetry and kurtosis test and bivariate and multivariate normality of Doornik-Hansen; p-value<0.01for differences between the groups G1 and G2 by the Kruskal-Wallis non-parametric test.Source: research results.

Table 2 Descriptive Analysis -Group B split in Groups 3 and 4 *
Source: research results.

Table 4 Technical efficiency and productivity changing for Group 2
Group 3, formed by 306 cities, has its efficiency scores presented in Table5.As we can observe, the technical efficiency scores were, approximately, 61%, 54%, 60% and 60% for the years analyzed.Regarding range, this group shows cities with lower efficiency scores, namely 15% for2007 and 14% for 2008.
Source: research results.

Table 5 Technical efficiency and productivity changing for Group 3
Observations: p-value<0.05for univariate normality asymmetry and kurtosis test and bivariate and multivariate normality of Doornik-Hansen; * significant at 5% by the nonparametric Wilcoxon test for the theoretical value of the median equal to 1.
Source: research results.

Table 6 Technical efficiency and productivity changing for Group 4
Source: research results.