Econometric estimation of country-specific hospital costs

1478-7547-1-3 1478-7547 Methodology Econometric estimation of country-specific hospital costs Adam Taghreed adamt@who.int Evans B David evansd@who.int Murray JL Christopher murrayc@who.int

Global Programme on Evidence for Health Policy (GPE/EQC), World Health Organization, CH-1211 Geneva 27, Switzerland

Cost Effectiveness and Resource Allocation 1478-7547 2003 1 1 3 http://www.resource-allocation.com/content/1/1/3 10.1186/1478-7547-1-3 12773218 24 2 2003 26 2 2003 26 2 2003 2003 Adam et al; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.

Abstract

Information on the unit cost of inpatient and outpatient care is an essential element for costing, budgeting and economic-evaluation exercises. Many countries lack reliable estimates, however. WHO has recently undertaken an extensive effort to collect and collate data on the unit cost of hospitals and health centres from as many countries as possible; so far, data have been assembled from 49 countries, for various years during the period 1973–2000. The database covers a total of 2173 country-years of observations. Large gaps remain, however, particularly for developing countries. Although the long-term solution is that all countries perform their own costing studies, the question arises whether it is possible to predict unit costs for different countries in a standardized way for short-term use. The purpose of the work described in this paper, a modelling exercise, was to use the data collected across countries to predict unit costs in countries for which data are not yet available, with the appropriate uncertainty intervals.

The model presented here forms part of a series of models used to estimate unit costs for the WHO-CHOICE project. The methods and the results of the model, however, may be used to predict a number of different types of country-specific unit costs, depending on the purpose of the exercise. They may be used, for instance, to estimate the costs per bed-day at different capacity levels; the "hotel" component of cost per bed-day; or unit costs net of particular components such as drugs.

In addition to reporting estimates for selected countries, the paper shows that unit costs of hospitals vary within countries, sometimes by an order of magnitude. Basing cost-effectiveness studies or budgeting exercises on the results of a study of a single facility, or even a small group of facilities, is likely to be misleading.

Introduction

Information on hospital unit costs is valuable to health decision-makers and researchers for at least three purposes: budgeting (now receiving more attention with the availability of additional funds for health in poor countries through the Global Fund to Fight AIDS, Tuberculosis and Malaria); the assessment of hospital efficiency; and the assessment, by means of either cost-benefit or cost-effectiveness analysis, of the efficiency of different health interventions. Recognizing the need to make this information available on a country-specific basis, WHO has undertaken as part of the work programme WHO-CHOICE (CHOosing Interventions that are Cost-Effective – see http://www.who.int/evidence/cea), an extensive effort to collate all sources of data on unit costs from as many countries as possible 1. Large gaps remain, however, particularly for developing countries. Although the long-term solution is that all countries perform their own costing studies, the question arises whether it is possible to predict unit costs for different countries in a standardized way for short-term use. The purpose of the work described in this paper is to use the data collected across countries to predict unit costs in countries for which data are not yet available (both point estimates and uncertainty intervals are reported).

Health economics has a long tradition of estimating hospital-cost functions econometrically 2345678910. Econometric models explain how total costs change in response to differences in service mix, inputs, input prices, and scale of operations. They allow cost and production functions to be specified with sufficient flexibility that a non-linear relationship can be demonstrated between costs and quantity of inputs: total costs can rise at a lower rate than prices2.

Previous studies have commonly used microeconomic data to analyse and estimate hospital-cost functions. This literature indicates two main approaches: behavioural cost functions and cost minimization functions 23911. Behavioural cost functions have been used to explain the variations in cost per unit of output among hospitals. They have used as determinants all variables for which a causal relationship to hospital costs is hypothesized and data are available – e.g., bed size, global indicators of hospital activity such as average length of stay and occupancy rate, dummy variables for teaching status, etc. On the other hand, the literature on cost minimization has described the minimum cost of providing a given volume of output as a function of an exogenous vector of input prices and the volume of output. The purpose is to determine whether hospitals are cost-minimizers (profit maximizers).

When testing the hypothesis of cost-minimization, the explanatory variables typically comprise only of output quantities (e.g., number of bed days) and input prices. The remaining variables used in the behavioural cost function specification are not part of the cost minimization question but can be used to explain deviation of observed unit costs from the theoretical minimum functions – e.g., possible reasons for inefficiency 3.

To our knowledge, all previous studies have used within-country data sets; we know of none that has attempted to estimate hospital-cost functions across countries. Such studies require a large number of observations from as many countries as possible.

The model described here follows the tradition of the behavioural cost function literature because its purpose is to estimate country-specific costs per bed-day, not to test the hypothesis of cost-minimization. The analysis controls for across-country price-level differences by using unit costs adjusted for purchasing-power parity, namely in international dollars; and for differences in quantity and complexity of resource use by using macro-level indicators such as per capita GDP 121314. The model forms part of a series of models that can be used to predict country-specific unit costs for a number of purposes. They may be used, for instance, to estimate: (i) unit costs at different capacity levels for the purposes of efficiency analysis or economic evaluation of health interventions; (ii) the "hotel" component of average cost per bed-day for budgeting exercises; or (iii) unit costs excluding components that might be funded from other sources, such as drugs. The specific objectives of this paper are to:

• explain the observed differences in hospital inpatient cost per bed-day across and within countries; and

• use the results to predict cost per bed-day for countries for which these data are not yet available.

Methods

Data

The search sources used to obtain the data were: Medline, Econlit, Social Science Citation Index, regional Index Medicus, Eldis (for developing-country data), Commonwealth Agricultural Bureau (CAB), and the British Library for Development Studies Databases. The range of years was set at 1960 to the present. Data covering costs and charges were included.

The search terms used were: "costs and cost analysis" and hospital costs or health centre or the abbreviations HC (health centre) or PHC (primary health centre) or outpatient care. The language sources searched were English, French, Spanish and Arabic; no Arabic study was found. In addition, a number of studies were found in the grey literature, from such sources as electronic databases, government regulatory bodies, research institutions, and individual health economists known to the authors 215161718192021222324252627282930313233343536373839404142434445464748495051525354. Also included were data from a number of WHO-commissioned studies on unit costs.

A standard template was used for extracting data from all sources. Database variables include: ownership; level of facility (see Additional file 1: Annex 1 for a definition of facility types as coded in the unit cost database); number of beds; number of inpatient and outpatient specialties; cost data (cost per bed-day, outpatient visit, and admission); utilization data (bed-days, outpatient visits, admissions); types of cost included in the cost analysis (capital, drugs, ancillary, food) and whether they were based on costs or charges; capacity utilization (occupancy rate, average length of stay, bed turnover, and average number of visits per doctor per day); reference year for cost data; currency, and methods of allocation of joint costs. The database consists of unit-cost data from 49 countries for various years between 1973–2000, totalling 2173 country-years of observations. Some studies provided information on 100% of the variables described above; at the other extreme, some provided information on less than 15%. The number of observations used in this analysis was 1171 (see Additional file 1: Annex 2 for the percentage of missing data in the model variables and Additional file 1: Annex 3 for the list of countries).

Additional File 1

Annex 1: Definition of facility types as coded in the unit cost database.

Annex 2: Percentage of missing data in the model variables prior to data imputation.

Annex 3: Countries and number of unit cost observations included in the model.

Click here for file

Data cleaning comprised consistency checks and direct derivation of some of the missing variables, when possible, from other variables from the same observation (e.g., occupancy rate was calculated from number of beds and number of bed-days). STATA software was used for data analysis 55.

Cost data were converted to 1998 International dollars by means of GDP deflators 56 and purchasing-power-parity exchange rates used for WHO's national health accounts estimates (PPP exchange rates used in this analysis are available from the WHO-CHOICE website: http://www.who.int/evidence/cea).

Data Imputation

Most statistical procedures rely on complete-data methods of analysis: computational programs require that all cases contain values for all variables to be analyzed. Thus, as default, most software programs exclude from the analysis observations with missing data on any of the variables (list-wise deletion). This can give rise to two problems: compromised analytical power, and estimation bias. The latter occurs, for example, if the probability that a particular value is missing is correlated with certain determinants. For example, if the complete observation sets tend to be from observations with unit costs that are systematically higher or lower than average, the conclusions for out-of sample estimation drawn from an analysis based on list-wise deletion will be biased upwards or downwards 57.

There is a growing literature on how to deal with missing data in a way that does not require incomplete observation sets to be deleted, and several software programs have been developed for this purpose. If data are not missing in a systematic way, missing data can be imputed using the observed values for complete sets of observations as covariates for prediction purposes. Multiple imputation is an effective method for general-purpose handling of missing data in multivariate analysis; it allows subsequent analysis to take account of the level of uncertainty surrounding each imputed value, as described below 58596061. The statistical model used for multiple imputation is the joint multivariate normal distribution. One of its main advantages is that it produces reliable estimates of standard errors: single imputation methods do not allow for the additional error introduced by imputation. In addition, the introduction of random error into the imputation process makes it possible to obtain largely unbiased estimates of all parameters 58.

In this study, multiple imputation was performed with Amelia, a statistical software program designed specifically for multiple imputation of missing data 57596263. First, five completed-data sets are created by imputing the unobserved data five times, using five independent draws from an imputation model. The model is constructed to approximate the true distributional relationship between the unobserved data and the available information. This reduces potential bias due to systematic difference between the observed and the unobserved data. Second, five complete-data analyses are performed by treating each completed-data set as an actual complete-data set; this permits standard complete-data procedures and software to be utilized directly. Third, the results from the five complete-data analyses are combined 64 to obtain the so-called repeated-imputation inference, which takes into account the uncertainty in the imputed values.

Model specifications

From the tradition of using cost functions to explain observed variations in unit costs, we estimate a long-run cost-function by means of Ordinary Least Squares regression analysis (OLS); the dependent variable is the natural log of cost per bed-day 2367865. The primary reason for using unit cost rather than total cost as the dependent variable is to avoid the higher error terms due to non-uniform variance (heteroscedasticity) in the estimated regression. This could arise if total cost were used as the dependent variable, as the error term could be correlated with hospital size 23. The reason for using cost per bed-day rather than cost per admission is that "bed-days" are better than "admissions" as a proxy for such hospital services as nursing, accommodation and other "hotel services" 3, permitting more flexibility in the use of estimated unit costs.

As the relationship between unit costs and the explanatory variables are expected to be non-linear, the Cobb-Douglas transformation was used to approximate the normal distribution of the model variables. Natural logs were used. The Cobb-Douglas functional form can be written as follows:

Equation 1

or,

Equation 2

ln (Y) = δ + α₁ln (X₁) + α₂ln (X₂)

where δ = ln (α₀). This function is non-linear in the variables Y, X₁and X₂, but it is linear in the parameters δ, α₁, α₂, and can be readily estimated using Ordinary Least Squares66.

Log transformation has the added advantage that coefficients can be readily interpreted as elasticities366.

Therefore, the cost function specification of the OLS regression model may be written as:

Equation 3

Where UC_iis the natural log (ln) of cost per bed-day in 1998 I $ in the ith hospital; X₁is ln of GDP per capita in 1998 I $; X₂is ln of occupancy rate; X_3,4are dummy variables indicating the inclusion of drug or food costs (included = 1); X_5,6are dummy variables for hospital levels 1–2 (the comparator is level 3 hospital); X_7,8are dummy variables indicating facility ownership (comparator is private not-for-profit hospitals); X₉is a dummy variable controlling for USA data (USA = 1); and e denotes the error term.

The choice of explanatory variables is partly related to economic theory and partly determined by the purpose of the exercise, which is to estimate unit costs for countries where the data are not available. In this case, the chosen explanatory variables must be available in the out-of-sample countries. Country-specific – or in the case of large countries such as China, province-specific – GDP per capita in international dollars (I $) is used as a proxy for level of technology 121314; occupancy rate as a proxy for level of capacity utilization; and hospital level as a proxy for case mix. Unit costs are expected to be correlated positively with GDP per capita and case mix and negatively with capacity utilization.

The inclusion of the seven control variables makes it possible to estimate unit cost for different purposes to suit different types of analysis – for example, cost per bed-day in a primary-level hospital, which does not provide drugs or food; or the cost in a tertiary level hospital, with drugs and food included.

The dummy for the USA was included because all data were charges rather than costs and because there were a large number of observations from that country. Dummies for countries other than the USA with a large number of observations, such as China and the United Kingdom, were also tested as was the use of dummy variables to capture whether the cost estimates included capital or ancillary costs. These variables were not included in the model which best fit the data. Utilization variables, such as number of bed-days or outpatient visits, and hospital indicators, such as average length of stay, were not included as explanatory variables because most out-of-sample countries do not have data on these variables, and prediction of unit costs would, therefore, be impossible.

Model-fit

Regression diagnostics were used to judge the goodness-of-fit of the model. They included the tolerance test for multicollinearity, its reciprocal variance inflation factors and estimates of adjusted R square and F statistics of the regression model.

Predicted values and uncertainty analysis

Two types of uncertainty arise from using statistical modes: estimation uncertainty arising from not knowing β and α perfectly – an unavoidable consequence of having a finite number of observations; and fundamental uncertainty represented by the stochastic component as a result of unobservable factors that may influence the dependent variable but are not included in the explanatory variables 62. To account for both types of uncertainty, statistical simulation was used to compute the quantities of interest, namely average cost per bed-day and the uncertainty around these estimates. Statistical simulation uses the logic of survey sampling to learn about any feature of the probability distribution of the quantities of interest, such as its mean or variance 62.

It does so in two steps. First, simulated parameter values are obtained by drawing random values from the data set to obtain a new value of the parameter estimate. This is repeated 1000 times. Then the mean, standard deviation, and 95% confidence interval around the parameter estimates are computed. Second, simulated predicted values of ŷ (the quantity of interest) are calculated, as follows: (1) one value is set for each explanatory variable; (2) taking the simulated coefficients from the previous step, the systematic component (g) of the statistical model is estimated, where g= f (X,B); (3) the predicted value is simulated by taking a random draw from the systematic component of the statistical model; (4) these steps are repeated 1000 times to produce 1000 predicted values, thus approximating the entire probability distribution of ŷ. From these simulations, the mean predicted value, standard deviation, and 95% confidence interval around the predicted values are computed. In this way, this analysis accounts for both fundamental and parameter uncertainty.

The predicted log of cost per bed day, ln , can then be calculated from:

Equation 4

where and are the estimated parameters, and X_i..nare the independent variables. If and , back-transforming Equation 4 (reduced to 1 independent log-transformed variable for simplicity) gives the power function.

Equation 5

where denotes a biased estimate of the mean cost per bed-day due to back-transformation. This is because one of the implicit assumptions of using log-transformed models is that the least-squares regression residuals in the transformed space are normally distributed. In this case, back-transforming to estimate unit costs gives the median and not the mean. To estimate the mean it is necessary to use a bias correction technique. The smearing method described by Duan (1983) was used to correct for the back-transformation bias 67. The smearing method is non-parametric, since it does not require the regression errors to have any specified distribution (e.g., normality). If the n residuals in log space are denoted by r_i, and b is the base of logarithm used, the smearing correction factor, , for the logarithmic transformation is given by:

Equation 6

Multiplying the right side of Equation 5 by Equation 6 almost removes the bias, so that:

Equation 7

The smearing correction factor () for our model was 1.25.

Results

Table 1 shows the variable names, description, mean and standard error, estimated after combining the results of the five datasets of the multiple imputation estimates. Table 2 presents the results of the best-fit regression model. The adjusted R square of the combined regressions is 0.80, with an F statistic of 509 (p < 0.0001), indicating that the model explains a large part of the variation of the cost per bed-day across countries 68. The signs of the coefficients are consistent with the earlier hypotheses. For example, the GDP per capita is positively correlated with cost per bed-day, while the lower the occupancy rate the higher is the cost per bed-day. Unit costs are lower in level-one hospitals than in those of levels two and three. The coefficients for the two main explanatory variables (GDP per capita and occupancy rate) are highly significant (p < 0.0001), as well as most of the control dummies, e.g., hospital level. The coefficient for food costs is not significant at the 5% level but was included in the model because it added to its explanatory power.

Table 1

Descriptive statistics of the multiple imputation estimates N = 1171

Variable

Description

Mean

Ln cost per bed day

Natural log of cost per bed day in 1998 I $

4.98

1.63

Ln GDP per capita

Natural log of GDP per capita in 1998 I $

8.90

1.06

Ln occupancy rate

Natural log of occupancy rate

-0.41

0.61

Drug costs

Dummy variable for inclusion of drug costs. Included = 1

0.96

0.18

Food costs

Dummy variable for inclusion of food costs. Included = 1

0.93

0.25

Level 1 hospital

Dummy variable for level 1 hospital ⁽¹⁾

0.33

0.47

Level 2 hospital

Dummy variable for level 2 hospital

0.41

0.49

Public

Dummy variable for level public hospitals ⁽²⁾

0.84

0.36

Private for profit

Dummy variable for level private for profit hospitals

0.08

0.27

USA

Dummy variable for USA. USA = 1

0.17

0.37

(1) Dummies for levels of hospital are compared with level 3 hospitals (2) Dummies for hospital ownership are compared with public not-for-profit hospitals

Table 2

Multiple Imputation regression coefficients and SE Dependent variable: Natural log of cost per bed-day in 1998 I $ N: 1171

Adjusted R²= 0.80

F statistic = 509

p of F statistic <0.00001

Variable

Coefficient

Ln GDP per capita

0.7624

0.0295

25.813

<0.0001

Ln occupancy rate

-0.2318

0.0474

-4.886

<0.0001

Drug costs

0.6410

0.1769

3.624

<0.0001

Food costs

0.2116

0.1394

1.518

0.152

Level 1 hospital

-0.5777

0.0742

-7.787

<0.0001

Level 2 hospital

-0.3118

0.0594

-5.253

<0.0001

Public

-0.2722

0.1172

-2.323

0.021

Private for profit

0.2444

0.1316

1.857

0.064

USA

1.7471

0.1022

17.104

0.000

Constant

-2.5036

0.3264

-7.672

0.026

The tolerance test and its reciprocal variance inflation factors (VIF) showed no evidence for multicollinearity between the model variables (tolerance ranged between 0.20 and 0.89, mean VIF 1.97; tolerance less than 0.05 and VIF more than 20 indicate the presence of multicollinearity).

The only country dummy that was included in the final model was for the USA. The most plausible explanation for the positive, highly significant coefficient for the USA dummy is that USA was the only large data set where charges were reported rather than costs. In this case, the coefficient for the USA could be interpreted as a cost-to-charge ratio, estimated as 1:1.74. In other words, costs represent 57% of the charge on average. This is consistent with published national reports on the average cost-to-charge ratio for the USA such as that published by the United States General Accounting Office (63%) 69.

Figure 1 shows the three regression lines of levels one, two and three hospitals, respectively, plotted against the log of GDP per capita (the Y-axis is log of cost per bed-day). The regression lines were estimated for public hospitals, with occupancy rate of 80%, including food costs and excluding drugs. Because the original data had a lower average occupancy rate (mean 71%, SD 39%), and most observations included drug costs, it is to be expected that the regression lines will be slightly lower than the actual data points in the database. The regression lines do not pass through the USA data points situated at the upper right side of the graph because they have been calculated for the case where the US dummy was set at zero.

Figure 1

Regression lines for level one, two and three hospitals against the natural log of GDP per capita

Regression lines for level one, two and three hospitals against the natural log of GDP per capita. (The Y-axis is the dependent variable: natural log of cost per bed day) Cost in 1998 I$ N = 1171

Overall, Figure 1 shows that the regression lines have a good fit with the data used to develop the model. They not only illustrate the relationship between cost per bed-day, hospital level and GDP per capita, but also show that there remains substantial variation in unit costs for any given level of GDP per capita. It would be inadvisable, therefore, to base cost estimates on a single estimate of hospital costs in a particular setting, something that is a common feature of cost-effectiveness studies.

To use the equation reported in Table 2 to predict unit costs for a number of in and out-of-sample countries, with the appropriate uncertainty interval, requires consideration of the probability distributions of the predicted unit costs, given a specified level of the model variables. In order to derive these distributions, simulation techniques were used following the steps described in the Methods section. Table 3 presents for selected countries in different regions of the world the average simulated predicted values and 95% uncertainty intervals. The estimates are presented in 2000 I $, based on the 2000 GDP per capita in I $ and assuming that the estimated coefficients will remain constant over a short time period. They are specific to public hospitals, at an occupancy rate of 80%, excluding drug, but including food costs. Regional estimates of cost per bed day, with the same characteristics described above, are available from the WHO-CHOICE website: http://www.who.int\evidence\cea.

Table 3

Predicted cost per bed-day ⁽ⁱ⁾in 2000 I $

Country

GDP per capita (I$)

In or out-of-sample

Hospital level

Cost per bed day

Mean (I $)

95% uncertainty interval Low

95% uncertainty interval high

Mali

581

Out

7.39

5.46

9.80

1.36

9.64

7.07

12.73

1.74

III

13.14

9.58

17.40

2.44

Mozambique

720

Out

8.70

6.45

11.43

1.58

11.35

8.32

15.01

2.03

III

15.46

11.31

20.42

2.85

Algeria

1,449

Out

14.82

10.95

19.45

2.65

19.35

14.26

25.45

3.39

III

26.34

19.41

34.63

4.72

Indonesia

3,167

Out

26.90

19.86

35.19

4.77

35.12

26.05

46.12

6.11

III

47.80

35.38

63.28

8.44

Ecuador

3,260

27.50

20.30

35.95

4.88

35.90

26.63

47.17

6.25

III

48.87

36.17

64.71

8.63

Romania

3,634

Out

29.88

22.05

39.11

5.30

39.00

28.86

51.25

6.79

III

53.09

39.23

70.35

9.37

Greece

6,192

Out

44.88

33.02

59.23

8.03

58.58

43.25

76.84

10.28

III

79.73

59.01

104.62

14.10

Russian Federation

8,035

54.75

40.17

72.43

9.86

71.48

52.73

94.24

12.62

III

97.27

71.79

127.92

17.27

Bahrain

14,159

Out

84.41

61.48

112.10

15.52

110.19

80.27

146.22

19.85

III

149.93

110.19

198.97

27.01

United Arab Emirates

20,330

Out

111.30

80.27

148.59

20.81

145.28

105.96

191.58

26.62

III

197.66

144.13

263.01

36.09

United Kingdom

24,348

127.76

91.83

170.79

24.11

166.77

121.08

221.00

30.85

III

226.87

164.90

302.91

41.76

Canada

28,087

Out

142.51

102.03

190.22

27.11

186.02

134.55

247.23

34.69

III

253.05

183.16

337.26

46.89

⁽ⁱ⁾Cost per bed day is estimated for public hospitals with 80% occupancy rate, excluding drug costs and including food costs.

Discussion

This paper describes recent work on developing models to predict country-specific hospital unit costs, by level of hospital and ownership, for countries where these data are not available. The main purpose of this work was to feed into estimates of the costs and effects of many types of health interventions in different settings. Estimates are typically available for variables such as the number of days in hospital, or the number of outpatient visits, for certain types of interventions, but unit prices are not available for many countries. The model presented in this paper used all data on unit costs that could be collected after a thorough search to estimate costs for countries where this information does not exist. Data imputation techniques were used to impute missing data, which has the advantage of eliminating the bias introduced by list-wise deletion of observations in cases where information for some of the variables required by the model is missing.

The goodness-of-fit of the model was tested by various regression diagnostic techniques including the tolerance test for multicollinearity, adjusted R square and F statistic. All suggested a good fit of the model with the data and that GDP per capita could be used to capture different levels of technology use across countries. Although this is the first time that costs have been compared across countries, the signs of the coefficients are consistent with results from previous microeconomic studies within countries. For example, these studies have found that occupancy rate was negatively correlated with cost per bed-day while hospital level had the opposite relationship, something also found in the model presented in this paper 7071. This adds confidence to the estimated results.

In addition, the estimates produced by this model were sent to health economists and researchers in different countries to check their face validity. Experts from countries in all WHO regions, covering wide differences in GDP per capita and in technologies typically found in hospitals were consulted, including Benin, Canada, Ecuador, Egypt, Kenya, Netherlands and Thailand. They were provided with a description of the estimated unit cost (e.g., which costs were included) and were asked whether they thought they approximated the average cost per bed-day in their countries. All indicated that the results had face validity.

It is of particular note that the model incorporates a more extensive database on unit costs by hospital level and ownership than has previously been available. Increasing the range of observations will increase the validity of extrapolations of cost estimates for countries in which these data are not available. Additional sources of data are being sought for this purpose and to assist countries to develop their own studies. As this body of information grows, the predictive power of unit-cost models will continue to increase.

There are other possible uses of this model such as estimating the possible costs of scaling-up health interventions for the poor, which is receiving increasing attention with the activities of such bodies as the Global Fund to Fight AIDS, Tuberculosis and Malaria. This can be done in many ways, according to the objectives of the analysis. It may be used, for instance, to estimate:

- unit costs at different capacity levels for purposes of efficiency analysis or economic evaluation of health interventions;

- the "hotel" component of average cost per bed-day;

- unit costs, excluding specific items such as drugs or food costs.

Finally, it must be emphasized that there is wide variation in the unit costs estimated from studies within a particular country (Figure 1). These differences are sometimes of an order of magnitude, and cannot always be attributed to different methods. This implies that analysts cannot simply take the cost estimates from a single study in a country to guide their assessment of the cost-effectiveness of interventions, or the costs of scaling-up. In some cases, they could be wrong by an order of magnitude.

Conflict of Interest

None.

Authors' contributions

TA was responsible for data collection, management and analysis, participated in the development of the methodology and drafted the manuscript. DE contributed to the development of the methodology, as well as data analysis and reporting. CM participated in the development and coordination of the methodology. All authors read and approved the final manuscript.

Acknowledgements

The authors express their gratitude to Carolyn Kakundwa and Margaret Squadrani for their work in compiling and processing the data necessary for this exercise; to Bian Ying, Viroj Tangcharoensathien, Walaiporn Patcharanarumol, Jiangbo Bao, Aparnaa Somanathan, Elena Potaptchik and Ruth Lucio for their efforts in gathering data at the country level; Ajay Tandon, Ke Xu and Gary King for their input in the development of the methods used; and to Xingzhu Liu and Jan Oostenbrink for the valuable comments during the review process. This work represents the views of the authors and not necessarily those of the organization they represent.

Generalised cost-effectiveness analysis: an aid to decision making in health. Hutubessy RCW Baltussen RMPM Tan Torres-Edejer T Evans DB Applied Health Economics and Health Policy 2002 1 89 95 14619255 Public hospitals in developing countries: resource use, cost, financing. Barnum H Kutzin J Baltimore, The Johns Hopkins University Press for the World Bank 1993 The specification of a hospital cost function. A comment on the recent literature. Breyer F J Health Econ 1987 6 147 157 10.1016/0167-6296(87)90004-X 10312165 A multiple-output multiple-input model of the hospital industry in North Carolina. Conrad RF Strauss RP Appl Econ 1983 15 341 352 Omitted variable bias and hospital costs. Cremieux PY Ouellette P J Health Econ 2001 20 271 282 10.1016/S0167-6296(00)00085-0 11252374 Estimating hospital costs. A multiple-output analysis. Grannemann TW Brown RS Pauly MV J Health Econ 1986 5 107 127 10.1016/0167-6296(86)90001-9 10287222 Hospital cost functions. Lave JR Lave LB Annu Rev Public Health 1984 5 193 213 10.1146/annurev.pu.05.050184.001205 6426487 On the estimation of hospital cost functions. Vitaliano DF J Health Econ 1987 6 305 318 10.1016/0167-6296(87)90018-X 10285440 Estimating hospital costs with a generalized Leontief function. Li T Rosenman R Health Econ 2001 10 523 538 10.1002/hec.605 11550293 Hospital cost functions for developing countries. Wagstaff A Barnum H WPS 1044. Washington, D.C, World Bank 1992 The impact of teaching status on average costs in Spanish hospitals. Lopez-Casasnovas G Saez M Health Econ 1999 8 641 651 10.1002/(SICI)1099-1050(199911)8:7<641::AID-HEC475>3.0.CO;2-L 10544329 The cost escalation of social health insurance plans in China: its implication for public policy. Liu X Hsiao WC Soc Sci Med 1995 41 1095 1101 10.1016/0277-9536(94)00423-Q 8578332 Medical care costs: how much welfare loss? Newhouse JP J Econ Perspect 1992 6 3 21 10128078 Insurance effects on US medical spending (1960–1993). Peden EA Freeland MS Health Econ 1998 7 671 687 10.1002/(SICI)1099-1050(199812)7:8<671::AID-HEC379>3.3.CO;2-0 9890329 A model for calculating costs of hospital wards: an Italian experience. Garattini L Giuliani G Pagano E J Manag Med 1999 13 71 82 10.1108/02689239910249619 10747452 The cost of treating paediatric malaria admissions and the potential impact of insecticide-treated mosquito nets on hospital expenditure. Kirigia JM Snow RW Fox-Rushby J Mills A Trop Med Int Health 1998 3 145 150 9537277 The cost of rural health services in Papua New Guinea. Mitchell M Thomason J Donaldson D Garner P P N G Med J 1991 34 276 284 1799090 A study of unit cost of out-patient and in-patient service of Khon Kaen Hospital in the fiscal year 1996. Patcharanarumol W Bangkok, Chulalongkorn University 1997 Dzongkhag costing study for Tashigang Dzongkhag. Huff-Rousselle M Royal Government of Bhutan, Department of Health Services, Ministry of Social Services 1992 Bangladesh facility efficiency survey. Rannan-Eliya R Somanathan A Working Paper No. 16. Dhaka, Health Economics Unit, Ministry of Health and Family Welfare, Government of the People's Republic of Bangladesh and Health Policy Programme, Institute of Policy Studies of Sri Lanka 1999 Development of a revised FIF user fee schedule. Report July 1996. Musau S Kilonzo M Newbrander W Kenya Health Care Financing Project: Contract No. 623-0245-C-00-0040-00. Boston, Management Sciences for Health 2000 Review of literature on costs of health services in developing countries. Robertson RL PHN Technical Note 85-21. Washington, Population, Health and Nutrition Department, World Bank 1985 Access and financing. Hospital services in Australia National Health Strategy Issues Paper No. 2. Canberra, Department of Health, Housing and Community Services 1991 Economic and management perspectives of Windhoek state hospital complex. Ojo K Windhoek, Ministry of Health and Social Services 1995 Costs, effects and cost-effectiveness analysis of a mobile maternal health care service in West Kiang, The Gambia. Fox-Rushby JA Foord F Health Policy 1996 35 123 143 10.1016/0168-8510(95)00774-1 10156650 Cost of selected health institutions in the Central Region 1972–1973. Brooks RG Ghana Med J 1975 14 209 214 1234683 Household participation in financing of health care in government health centres in Rwanda. Shepard DS Carrin G Nyandagazi P In: Health economics research in developing countries Oxford University Press Lee K, Mills A 1990 140 164 The costs of hospital services: a case study of Evangelical Lutheran Church hospitals in Tanzania. Flessa S Health Policy Plan 1998 13 397 407 10.1093/heapol/13.4.397 10346031 Cost analysis of the health care sector in The Gambia. Volume 1. Ministry of Health The Gambia World Health Organization Ministry of Health 1995 1 Functional expenditure analysis. Final Report for Queen Elizabeth II Hospital, Maseru, Lesotho. Puglisi R Bicknell WJ Boston University, Health Policy Institute 1990 I Cost analysis of Niamey hospital. Wong H USAID Project No. 683-0254. Bethesda, MD, Abt Associates Inc 1989 Cost analysis of health services in Sierra Leone. A case study of Connaught hospital and Waterloo Community Health Centre. Annex III. Ojo K Foley J Renner A Kamara FM Sierra Leone, Ministry of Health 1995 Technical and economic efficiency of the Asella regional hospital in Ethiopia. De Virgilio G Haile M Lemma A Mariani D La Medicina Tropicale nelle Cooperazione allo Sviluppo 1990 6 1 7 Costs, resource utilisation and financing of public and private hospitals in Uganda. Omar AO Komakech W Hassan AH Singh CH Imoko J East Afr Med J 1995 72 591 598 7498048 The costs of HIV/AIDS care at government hospitals in Zimbabwe. Hansen K Chapman G Chitsike I Kasilo O Mwaluko G Health Policy Plan 2000 15 432 440 10.1093/heapol/15.4.432 11124247 Hospital or health centre? A comparison of the costs and quality of urban outpatient services in Maseru, Lesotho. Pepperall J Garner P Fox-Rushby J Moji N Harpham T Int J Health Plann Manage 1995 10 59 71 10142123 On measuring the hospital cost/quality trade-off. Carey K Burgess JF Jr Health Econ 1999 8 509 520 10.1002/(SICI)1099-1050(199909)8:6<509::AID-HEC460>3.3.CO;2-S 10544316 Financing and costs of health services in Belize. Raymond SU Lewis B Meissner P Norris J HCFLAC Research Report no. 2. Stony Brook, State University of New York 1987 Measuring public hospital costs: empirical evidence from the Dominican Republic. Lewis MA La Forgia GM Sulvetta MB Soc Sci Med 1996 43 221 234 10.1016/0277-9536(95)00364-9 8844926 Unit cost and financial analysis for the hospital 12 de Abril in Bolivia. Olave M Montano Z Small Applied Research Report No. 11. Bethesda, Abt Associates Inc 1993 Hospital costing study Glendon Hospital – Montserrat. Gill L Percy A Report No.15. Organisation of Eastern Caribbean States, Health Policy & Management Unit 1994 Health care financing in St Lucia and costs of Victoria Hospital. Russell SS Gwynne G Trisolini M HCFLAC Research Report no. 5. Stony Brook, State University of New York 1988 Papua New Guinea: health sector financing study project. Final Report – volume II hospital cost study Snow J Prepared for the Papua New Guinea Department of Health under contract with the Asian Development Bank, TA No. 1091-PNG 1990 Unit cost estimation for outpatient and inpatient departments in Nakleoung District Hospital, Cambodia. Chan S Bangkok, Chulalongkorn University 1997 Implementing hospital autonomy in Jordan: an economic cost analysis of Princess Raya Hospital. Banks DA As-Sayaideh ASK Shafei ARSH Muhtash A Bethesda, MD, The Partners for Health Reformplus Project, Abt Associates Inc 2002 The new NHS – 2001 reference costs. Department of Health London, Department of Health 2001 Cost analysis and efficiency indicators for health care: report number 1 summary output for Bani Suef General Hospital, 1994–1994. Department of Planning Ministry of Health and Population Data for Decision Making, Harvard School of Public Health, University of California, Berkeley, School of Public Health Boston, Harvard University Press 1997 Cost analysis and efficiency indicators for health care: report number 2 summary output for Suez General Hospital, 1993–1994. Department of Planning, Ministry of Health and Population, Data for Decision Making, Harvard School of Public Health, University of California, Berkeley, School of Public Health Boston, Harvard University Press 1997 Cost analysis and efficiency indicators for health care: report number 3 summary output for El Gamhuria General Hospital, 1993–1994. Department of Planning, Ministry of Health and Population, Data for Decision Making, Harvard School of Public Health, University of California, Berkeley, School of Public Health Boston, Harvard University Press 1997 Cost analysis and efficiency indicators for health care: report number 4 summary output for 19 primary health care facilities in Alexandria, Bani Suef and Suez, 1993–1994. Department of Planning, Ministry of Health and Population, Data for Decision Making, Harvard School of Public Health, University of California, Berkeley, School of Public Health Boston, Harvard University Press 1997 Application of activity-based costing (ABC) for a Peruvian NGO healthcare provider. Waters H Abdallah H Santillan D Int J Health Plann Manage 2001 16 3 18 10.1002/hpm.606.abs 11326572 Hospital cost accounting and analysis: the case of Candelaria. Robertson RL Barona B Pabon R J Community Health 1977 3 61 79 Health reform and hospital financing in Georgia. Jorbenadze A Zoidze A Gzirirshvili D Gotsadze G Croat Med J 1999 40 221 236 10234066 The cost of the district hospital. A case study from Malawi. Mills AJ WPS 742. Washington,D.C, World Bank 1991 Stata Statistical Software: Release 7.0. StataCorp College Station, TX, Stata Corporation 2001 World Development Indicators 2000. World Bank Washington, DC, World Bank 2000 List-wise deletion is evil: what to do about missing data in political science. King G Honaker J Joseph A Scheve K Paper presented at the Annual Meeting of the American Political Science Association, Boston 1998 Multiple imputation for missing data. A cautionary tale. Allison PD Sociological Methods & Research 2000 28 301 309 Amelia: A Program for Missing Data (Windows Version). Honaker J Joseph A King G Scheve K Singh N Cambridge, MA, Harvard University 1999 Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure. Lu K Tsiatis AA Biometrics 2001 57 1191 1197 11764260 Multiple imputation for missing data. Patrician PA Res Nurs Health 2002 25 76 84 10.1002/nur.10015 11807922 Making the most of statistical analyses: improving interpretation and presentation. King G Tomz M Wittenberg J Am J Pol Sci 2000 44 341 355 Analyzing incomplete political science data: An alternative algorithm for multiple imputation. King G Honaker J Joseph A Scheve K Am Polit Sci Rev 2000 Multiple imputation for survey nonresponse. Rubin DB New York, Wiley 1986 Hospital cost analysis: a survey and evaluation of recent studies. Cowing TG Holtmann AG Powers S Adv Health Econ Health Serv Res 1983 4 257 303 10299466 Basic econometrics. Gujarati DN New York, McGraw-Hill, Inc 3 1995 Smearing estimate: a nonparametric retransformation method. Duan N J Amer Statistical Assoc 1983 78 605 610 How not to lie with statistics: avoiding common mistakes in quantitative political science. King G Am J Pol Sci 1986 30 666 687 Military health care. Savings to CHAMPUS from using a prospective payment system. US General Accounting Office Fact Sheet for Congressional Requesters GAO HRD-90-136FS. Washington D.C., United States General Accounting Office 1990 The cost and efficiency of public and private health care facilities in Ogun State, Nigeria. Wouters A Health Econ 1993 2 31 42 8269045 A statistical cost function study of public general hospitals in Kenya. Anderson DL Journal of Developing Areas 1980 14 223 235