a comparison of the technical efficiencies of health districts and hospitals in botswana

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A comparison of the technicalefficiencies of health districts andhospitals in BotswanaThekke V Ramanathan , Koni Suresh Chandra & Wilson M ThupengPublished online: 01 Jul 2010.

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Development Southern Africa Vol. 20, No. 2, June 2003

A comparison of the technicalefficiencies of health districts andhospitals in Botswana

Thekke V Ramanathan, Koni Suresh Chandra &Wilson M Thupeng1

An attempt is made here to construct and present relative efficiency indices for the servicesrendered by health districts and specific hospitals in Botswana, using Stochastic FrontierRegression analysis and Data Envelopment Analysis. The analysis indicated that three districts– Kweneng East, Kgalagadi and Boteti – have efficiency scores below the optimum level. Amongthe 13 hospitals considered, Tsabong Primary Hospital was found to have an efficiency score ofless than one. Since the health services involve a number of factors, these indices ought to serveas indicators for further scrutiny of those units (health districts and hospitals) that fall below theoptimum efficiency level. The data used for the analysis are from the published material by theCentral Statistics Office, Botswana for the year 1997. Health is considered one of the majorconcerns of the government of Botswana. As a consequence, the authors feel that this study willbe useful to policy makers and health planners in giving them some kind of relative rankingamong health districts and hospitals.

1. INTRODUCTION

Any production activity envisages maximum output for a given level of inputs or itscomplementary objective of minimising the levels of inputs to achieve a productiontarget. Health services may be regarded as a production process wherein the healthpersonnel and infrastructures form the inputs and the services rendered to patients serveas outputs. The departure from the optimal production level is an indicator ofinefficiency in the system. In this application, there is a need to interpret the term‘inefficiency’ from a different angle. The patients themselves, when they arrive, can betreated as input in the production process and the output is the value of the servicesrendered (in terms of the relief they obtain after treatment). Such minute classificationsmay create some methodological issues. Moreover, it is difficult to gather quantitativedata on customer satisfaction from available hospital records.

Keeping the issues raised above in mind, the best way to interpret inefficiency ispossibly as the surplus input in the health centre as far as a chosen output is concerned.Such information may be meaningful to health planners in terms of the reallocation ofsurplus inputs to nearby and needy health centres. Furthermore, as there is no methodof identifying the optimal level of production, and in the absence of any model for suchan exercise, it would be desirable to set these inefficiency indices in relative terms, i.e.with reference to the ‘best’ production unit among the given units. Several approachesto the measurement of technical efficiency in production have been developed sinceFarrell (1957) provided basic definitions for technical efficiency. In the case of a singleoutput, Stochastic Frontier Analysis (SFA) is one of the well-known techniques for

1 Respectively, Senior Lecturer, Professor and Lecturer, Department of Statistics, University ofBotswana, Gaborone, Botswana.

ISSN 0376-835X print/ISSN 1470-3637 online/03/020307-14 2003 Development Bank of Southern AfricaDOI: 10.1080/0376835032000085965

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308 TV Ramanathan et al.

identifying and estimating the relative efficiencies of several decision-making units(DMUs). Data Envelopment Analysis (DEA) is yet another method for estimating therelative inefficiencies in DMUs, which has an added advantage of analysing severaloutputs simultaneously. It is well known in the literature that the results of these twoapproaches cannot be compared, since they are based on different sets of assumptions.There are two more popular methods – the Thick Frontier Approach (TFA) and theDistribution-Free Approach (DFA) – available in the literature for estimating thefrontier efficiency of a DMU. However, we will consider only SFA and DEA here.

In this article, an attempt is made to compare the activities of the 22 health districts inBotswana based on the data available for the year 1997. In such studies, it would bemore appropriate to make a relative comparison hospital-wise, since some districts havemore than one hospital. Since data across hospitals are not available (this is one of themajor limitations of the data used here), we have compared 13 hospitals usingdistrict-level data, as there is one hospital in each district.

The methodology of SFA is reviewed in Section 2. Sections 3 and 4 contain the mainfindings of this study, district-wise and hospital-wise respectively. A brief descriptionof DEA is given in Section 5, along with the corresponding empirical results pertainingto the present data. Information about the output slackness and input surplus is alsoprovided. Here, too, we have made district-wise and hospital-wise analyses. The articleconcludes with some remarks in the last section.

2. METHODOLOGY

The use of stochastic frontier regression in the determination of production efficienciesis widely discussed in the literature. Applications to the evaluation of health centreshave been dealt with in the study by Burgess & Wilson (1993). However, these authorsused DEA for their analysis.

With reference to a single output y and k inputs x � (x1, x2, … ,xk), the productionfunction f(x1, x2, … , xk) provides the maximum output of the product Y, under a giventechnology. Let y be the realised output level. The difference between y and f(.) wouldbe an indicator of the degree of inefficiency in the production process. Since thedifference is always non-negative, it is introduced in the model as a non-negativerandom variable with the support as a subset of [0, � ). Linearising such a model withan inclusion of a statistical error, one has the general form of a linear frontierregression:

yt � �0 � �1x1t � �2x2t � … � �kxkt � vt � ut; t � 1,2, …, n (2.1)

where {vt} are statistical errors that are assumed to be independent and identicallydistributed random variables with a common mean of zero and a variance of �2

v . Also,{ut} are independent and identically distributed random variables, indicating theinefficiency factor, independent of vs and having distributions over a subset of [0, � ).While the normal distribution is preferred for modelling the distribution of vs, thedistribution of any non-negative random variable appears to be a plausible choice forus. A half-normal distribution appears to be the first choice for the distribution of us,which has the density:

f(u, �u) ��2

��2u

e

� u2

2�2u , �u � 0,0 � u � � (2.2)

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Technical efficiencies of health districts and hospitals in Botswana 309

We note that E(ui) measures the average inefficiency for the entire set of DMUs.However, we are interested in identifying the inefficiency factor for each DMU.Towards this end, one can estimate the conditional expectation E(uii) for each i,where i � ui � vi, the details of which are found in the literature. Jondrow et al (1982)have provided the expression for this conditional expectation under the half-normalassumption, and it is given by:

E(u1|i) �� 1 � 2��zi �

(zi)

�(zi)� (2.3)

where zi �t�

, �2 � �2u � �2

v and � �u/�v. The functions and � are respectively the

cumulative distribution and the density function of a standard normal variable.

Statistical issues and inference aspects related to model (2.1) have been widelydiscussed in the literature. However, the works of Farrell (1957), Schmidt (1976, 1985),Greene (1993) and Aigner et al (1977) seem adequate for acquiring an immediateunderstanding of the theory. For the sake of brevity we are omitting the details, as theyare readily available in the literature. Coelli (1992) has developed software calledFrontier 4.1, a recent version of which can be downloaded from a public domain(http://www.une.edu.au/econometrics/cepa.htm). This software provides not only theestimates of the coefficients in (2.1), but also the unit-wise relative efficiencies underthe assumptions of normality of vs and half-normality of us. We have used thissoftware for our study.

3. EVALUATION OF BOTSWANA HEALTH CENTRES: DISTRICT-WISECOMPARISONS

For the present study, the data published in the Health Statistics Report of 1997 (CSO,1997) were used. There are 22 health districts in Botswana, as listed in Table 1.

Different types of ailments are grouped into various categories, such as typhoid andrelated diseases (TYPHO), malnutrition and related diseases (MALN), etc. There are 11such groups. These groupings are exactly those maintained by the Central StatisticsOffice, Botswana. However, for the sake of immediate information, the ailmentsincluded in these groups are listed in Table 2.

We have considered seven inputs and 15 outputs for our analysis. The inputs include

Table 1: Health districts of Botswana

No. Health district No. Health district No. Health district

1 Gaborone 9 South East 17 Lobatse

2 Serowe/Palapye 10 Selebi Phikwe 18 Goodhope

3 Francistown 11 Kgatleng 19 Kweneng West

4 North West 12 Boteti 20 Kgalagadi

5 Mahalapye 13 Okavango 21 Chobe

6 Kweneng East 14 Bobirwa 22 Hukuntsi

7 Tutume 15 Gantsi

8 Southern 16 North East

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Table 2: List of ailments included in the disease groups considered in this study

Group Label Ailments

1 TYPHO Typhoid, diarrhoea, tuberculosis, whooping cough, chicken pox, measles, hepatitis,

mumps, malaria confirmed, malaria unconfirmed, fungus, worms, scabies, other

infectious/parasitic diseases, exposure to rabies, pneumonia, diphtheria, bilharzias,

meningitis, rabies, tetanus

2 MALN Malnutrition, other nutritional deficiencies

3 BLOOD Diseases of blood and blood-forming organs, diseases of the heart, blood pressure

problems, diseases of the vascular system

4 MENTL Mental disorders, diseases of the nervous system, tonsillitis, asthma, other diseases

of the respiratory system, coughs and colds

5 ORAL Oral health problems, dental extraction (procedure), other diseases of the digestive

system

6 PREG Pregnancy, childbirth and the puerperium, diseases of the female genital organs,

disorders of the menstrual cycle

7 MALGEN Diseases of the male genital organs, other skin conditions, abscesses

8 MUSC Diseases of the musculoskeletal system, congenital abnormalities, signs, symptoms

and other conditions, burns, poisoning and bites, accidents and injuries, allergic

reactions, road traffic accidents

9 EYE Eye infections, foreign body in eye, other eye diseases (excluding infection),

trachoma

10 EAR Ear infections, foreign body in ear, other ear diseases (excluding infection)

11 FERT Fertility problems, diseases of the urinary system, alcohol and drug abuse, medical

examinations, tumours, diseases of the breast

numbers of hospitals, clinics, health posts in each district and the information onnumbers of beds, doctors, nurses and other health staff (from all hospitals). The outputsinclude the number of outpatients from 11 different ailment groups, the total numberof outpatients, number of inpatients discharged alive, new births discharged alive andpatient days. A detailed list of inputs and outputs with appropriate labels are given inTable 3. The data on the above mentioned variables were consolidated from the HealthStatistics Report (CSO, 1997).

Using the software mentioned earlier, the output-wise efficiencies of 22 health districtsand the related rankings were worked out, as set out in Table 4.

Before proceeding with the comparisons, it is pertinent to note that the efficiency scoresthemselves do not portray the facts. The outputs in the case of health services shouldnot be considered as outputs in economics of production. A score of less than unitydoes not indicate the inefficiency of the DMU in question, since there are so manyhidden and unseen factors that contribute to this score. In health services, the patientsas well as health personnel are aware of the realities on the ground. This aspect has alsobeen rightly stressed in the earlier works of Burgess & Wilson (1993: 349). What theyreveal ought to be treated as pointers that require a closer scrutiny in the activities ofspecific health centres. Furthermore, one must remember that the efficiency scoresgiven are relative measures — relative with respect to the ‘best’ among the givenDMUs. Also, it may be cautioned that we have carried out the analysis using secondarydata, and thus the natural limitations apply.

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Table 3: Inputs and outputs selected for this study

Inputs Outputs Outputs

1. Hospitals in the district 1. Outpatients in Group 1 diseases 9. Outpatients Group 9 diseases (eye,

(HOSP) (typhoid, etc.) (TYPHO) etc.) (EYE)

2. Clinics in the district 2. Outpatients Group 2 diseases 10. Outpatients Group 10 diseases

(CLIN) (malnutrition, etc.) (MALN) (ears, etc.) (EAR)

3. Health posts in the 3. Outpatients Group 3 diseases 11. Outpatients Group 11 diseases

hospitals(s) (HPOST) (blood related) (BLOOD) (fertility, etc.) (FERT)

4. Beds (BEDS) 4. Outpatients Group 4 diseases 12. Outpatients (all groups) (TOTAL)

(mental, etc.) (MENTL)

5. Doctors (DOCS) 5. Outpatients Group 5 diseases 13. New births discharged alive

(oral, etc.) (ORAL) (DISNB)

6. Nurses (NURS) 6. Outpatients Group 6 diseases 14. Inpatients discharged alive

(pregnancy, etc.) (PREG) (DISALIV)

7. Health staff (OTHERS) 7. Outpatients Group 7 diseases 15. Patient days (PATDAY)

(male genitals, etc.)(MALGEN)

8. Outpatients Group 8 diseases

(muscular, etc.) (MUSC)

Note: All inputs and outputs are counted in that category.

Table 4 shows some interesting features. Districts like Hukuntsi, which rank low withrespect to many outputs, stand out in treating outpatients suffering from ailments underthe group ORAL. Likewise, the North East, Serowe/Palapye and Kweneng EastDistricts seem to have performed relatively better in treating patients in the groupsMUSC, EYE and TOTAL. It would be rewarding to study why this has been exposedsingularly. Finally, the top rankings of Gaborone and Francistown are as expected,since they are strategically important to Botswana for various reasons. One can, for thesake of easy comparison, consider the average ranks in the groups TOTAL, DISNB,DISALIV and PATDAY, and even here Gaborone leads the others with Serowe/Palapye, Francistown and North West following behind the capital city. The overallrankings based on the average of ranks are given in Table 5.

4. EVALUATION OF INDIVIDUAL HOSPITALS

In this section we present the findings relating to individual hospitals for which datawere available. It was possible to consider only 13 hospitals in Botswana (listed inTable 6) for which the individual data could be identified in the Health Statistics Reportof 1997.

The technical efficiency and the rankings for these hospitals are presented in Table 7.

The remarks made earlier in Section 3 on the interpretation of the efficiency score holdeven in this case. While deeper studies are indicated in the case of hospitals with lowerranks, the specific disease group-wise performance of hospitals like S.D.A. Kanye inMUSC and PREG, Goodhope in MALGEN, Deborah in BLOOD and Maun inTYPHO, appears to be significantly higher, compared with their other activities. Theoverall ranking, as done in Section 3, gave the final placement as given in Table 8.

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Tab

le4:

Out

put-

wis

eef

ficie

ncie

san

dre

late

dra

nkin

gof

heal

thdi

stri

cts

Dis

tric

tT

YP

HO

MA

LN

BL

OO

DM

EN

TL

OR

AL

PR

EG

MA

LG

EN

MU

SCE

YE

EA

RF

ER

TT

OT

AL

DIS

NB

DIS

AL

IVP

AT

DA

Y

Nor

thW

est

0,94

77(6

)0,

9806

(8)

0,96

55(9

)0,

9429

(4)

0,97

34(6

)0,

9676

(9)

0,94

73(6

)0,

9666

(10)

0,94

28(1

5)0.

9348

(14)

0,92

44(7

)0,

9814

(6)

0,96

50(3

)0,

9657

(8)

0,91

95(4

)

Nor

thE

ast

0,91

77(1

3)0,

9568

(16)

0,86

95(2

1)0,

3426

(22)

0,60

85(2

1)0,

9472

(16)

0,70

11(2

1)0,

9443

(16)

1,00

00(1

)0.

8397

(19)

0,91

44(8

)0,

9535

(18)

0,90

74(1

2)0,

9387

(16)

0,50

01(2

1)

Sero

we/

0,95

23(4

)0,

9864

(2)

0,97

76(4

)0,

9660

(3)

0,98

32(4

)0,

9838

(4)

0,94

84(5

)0,

9855

(1)

0,96

36(7

)0.

9724

(4)

0,90

54(9

)0,

9859

(2)

0,95

52(5

)0,

9812

(4)

0,94

82(3

)

Pala

pye

Bob

irw

a0,

9316

(10)

0,96

86(1

3)0,

9610

(13)

0,86

60(1

3)0,

9587

(14)

0,95

81(1

2)0,

9356

(9)

0,96

69(8

)0,

9564

(10)

0.92

30(1

6)0,

6436

(18)

0,96

95(1

1)0,

7040

(20)

0,95

68(1

1)0,

8347

(14)

Kw

anen

g0,

9529

(3)

0,98

40(4

)0,

9806

(3)

0,87

14(1

2)0,

9824

(5)

0,98

41(3

)0,

9583

(3)

0,98

19(3

)0,

9684

(5)

0.96

17(9

)0,

8572

(12)

0,98

32(3

)0,

9078

(11)

0,98

40(2

)0,

8827

(10)

Eas

t

Sout

hern

0,94

13(8

)0,

9830

(6)

0,97

66(5

)0,

8749

(10)

0,97

33(7

)0,

9847

(2)

0,94

22(8

)0,

9798

(5)

0,96

61(6

)0.

9786

(3)

0,73

46(1

6)0,

9805

(7)

0,90

00(1

4)0,

9782

(5)

0,91

51(5

)

Gan

tsi

0,91

35(1

5)0,

9562

(17)

0,94

17(1

6)0,

8159

(15)

0,88

72(1

8)0,

9288

(18)

0,88

39(1

6)0,

9423

(17)

0,91

50(1

8)0.

8816

(18)

0,44

79(2

2)0,

9569

(15)

0,82

39(1

6)0,

9330

(17)

0,85

82(1

3)

Mah

alap

ye0,

9435

(7)

0,98

31(5

)0,

9747

(8)

0,92

83(5

)0,

9721

(8)

0,98

17(5

)0,

9207

(11)

0,98

10(4

)0,

9565

(9)

0.95

97(1

1)0,

9956

(1)

0,98

17(5

)0,

9619

(4)

0,98

16(3

)0,

8977

(9)

Kga

tleng

0,91

52(1

4)0,

9691

(11)

0,95

79(1

4)0,

9149

(7)

0,96

20(1

2)0,

9630

(10)

0,90

35(1

3)0,

9586

(14)

0,94

38(1

4)0.

9653

(7)

0,87

84(1

0)0,

9659

(13)

0,89

53(1

5)0,

9591

(10)

0,90

07(7

)

Cho

be0,

8916

(20)

0,93

25(2

1)0,

9247

(19)

0,76

97(1

7)�

0,66

30(2

2)0,

8581

(21)

0,85

47(1

8)0,

9084

(21)

0,88

79(2

0)�

0.31

87(2

2)0,

7884

(15)

0,93

54(2

1)0,

6950

(21)

0,87

90(2

1)0,

5924

(19)

Kga

laga

di0,

9037

(18)

0,94

82(2

0)0,

9331

(17)

0,71

15(1

9)0,

8903

(17)

0,92

11(1

9)0,

8925

(14)

0,93

62(1

8)0,

9182

(17)

0.88

90(1

7)0,

4510

(21)

0,94

84(2

0)0,

6726

(22)

0,92

40(1

9)0,

7284

(17)

Tut

ume

0,95

16(5

)0,

9825

(7)

0,96

47(1

0)0,

8091

(16)

0,95

63(1

5)0,

9736

(7)

0,93

23(1

0)0,

9734

(6)

0,95

19(1

1)0.

9599

(10)

0,96

59(5

)0,

9798

(8)

0,98

08(1

)0,

9714

(7)

0,76

97(1

5)

Bot

eti

0,91

86(1

1)0,

9687

(12)

0,96

15(1

2)0,

8737

(11)

0,96

42(1

0)0,

9573

(13)

0,83

88(1

9)0,

9661

(11)

0,94

92(1

2)0.

9620

(8)

0,70

51(1

7)0,

9703

(10)

0,94

39(7

)0,

9464

(13)

0,88

23(1

1)

Oka

vang

o0,

9392

(9)

0,96

72(1

4)0,

9491

(15)

0,85

03(1

4)0,

8234

(19)

0,93

14(1

7)0,

8650

(17)

0,96

11(1

3)0,

8960

(19)

0.75

89(2

1)0,

8109

(13)

0,96

26(1

4)0,

9086

(10)

0,94

49(1

4)0,

7528

(16)

Gab

oron

e0,

9599

(1)

0,99

09(1

)0,

9944

(1)

0,97

57(1

)0,

9879

(3)

0,98

91(1

)0,

9652

(1)

0,98

34(2

)0,

9885

(2)

0.98

68(1

)0,

9773

(3)

0,99

10(1

)0,

9797

(2)

0,98

76(1

)0,

9751

(2)

Fran

cist

own

0,95

44(2

)0,

9843

(3)

0,98

50(2

)0,

9720

(2)

0,98

94(2

)0,

9755

(6)

0,94

69(7

)0,

9730

(7)

0,97

71(4

)0.

9866

(2)

0,97

54(4

)0,

9831

(4)

0,93

67(9

)0,

9769

(6)

0,97

98(1

)

Sout

hE

ast

0,91

79(1

2)0,

9739

(10)

0,97

54(7

)0,

8916

(8)

0,95

96(1

3)0,

9681

(8)

0,96

37(2

)0,

9667

(9)

0,96

36(8

)0.

9558

(12)

0,87

69(1

1)0,

9690

(12)

0,95

18(6

)0,

9629

(9)

0,90

47(6

)

Lob

atse

0,77

56(2

2)0,

9542

(18)

0,96

24(1

1)0,

8887

(9)

0,96

38(1

1)0,

9553

(14)

0,88

43(1

5)0,

9101

(20)

0,94

77(1

3)0.

9711

(6)

0,97

86(2

)0,

9551

(16)

0,90

54(1

3)0,

9073

(20)

0,89

86(8

)

Sele

bi0,

9111

(16)

0,97

54(9

)0,

9761

(6)

0,91

95(6

)0,

9652

(9)

0,95

34(1

5)0,

9491

(4)

0,96

47(1

2)0,

9844

(3)

0.97

19(5

)0,

9548

(6)

0,97

42(9

)0,

9399

(8)

0,95

67(1

2)0,

8696

(12)

Phik

we

Kw

anen

g0,

9014

(19)

0,95

24(1

9)0,

9288

(18)

0,44

66(2

1)0,

8207

(20)

0,90

78(2

0)0,

9193

(12)

0,93

50(1

9)0,

9317

(16)

0.92

89(1

5)0,

6402

(19)

0,95

03(1

9)0,

7646

(18)

0,92

45(1

8)0,

5555

(20)

Wes

t

Goo

dhop

e0,

9110

(17)

0,95

80(1

5)0,

9164

(20)

0,71

75(1

8)0,

9212

(16)

0,96

08(1

1)0,

6849

(22)

0,94

81(1

5)0,

8570

(21)

0.95

54(1

3)0,

5112

(20)

0,95

36(1

7)0,

7272

(19)

0,94

37(1

5)0,

7208

(18)

Huk

unts

i0,

8494

(21)

0,87

84(2

2)0,

8199

(22)

0,63

28(2

0)1,

0000

(1)

0,50

31(2

2)0,

8247

(20)

0,66

48(2

2)0,

6766

(22)

0.77

84(2

0)0,

7981

(14)

0,87

98(2

2)0,

8007

(17)

0,52

70(2

2)0,

3152

(22)

Not

e:B

yde

finiti

on,

anef

ficie

ncy

scor

eca

nnot

bene

gativ

e.Su

chsc

ores

,w

hen

obta

ined

,ha

vebe

engi

ven

the

leas

tra

nk.

Ran

king

appe

ars

inbr

acke

ts.

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Table 5: Ranking of health districts based on average rankings

Health district Rank Health district Rank Health district Rank

Gaborone 1 South East 9 Lobatse 17

Serowe/Palapye 2 Selebi Phikwe 10 Goodhope 18

Francistown 3 Kgatleng 11 Kweneng West 19

North West 4 Boteti 12 Kgalagadi 20

Mahalapye 5 Okavango 13 Chobe 21

Kweneng East 6 Bobirwa 14 Hukuntsi 22

Tutume 7 Gantsi 15

Southern 8 North East 16

These rankings appear to be in line with the general findings in Section 3 as far as these13 hospitals (districts) are concerned.

5. DATA ENVELOPMENT ANALYSIS

As mentioned in the introduction, we also consider DEA, which takes into account allthe outputs in assessing the technical efficiencies of DMUs. We provide a briefintroduction to this methodology below.

Let the input vector x be used to produce the output vector y. The objective is tomeasure the performance of each district or hospital relative to the best observed in thesample. Let X and Y be the corresponding matrices of inputs and outputs. Let a DMUuse the input level x0 to produce an output y0. Its efficiency score, indicated by �, isobtained by solving the following linear programming problem:

Min�,

�

subject to� y0 � Y � 0�x0 � X � 0 � 0

where � is a scalar and a vector of constants. The technical efficiency score �measures the deviation in performance from that of the best practice DMU on theefficient frontier. It will satisfy � 1, with a value of 1 indicating a point on theefficient frontier and hence a technically efficient DMU, according to Farrell’s (1957)definition. One of the main advantages of the DEA model is that it is capable ofidentifying any perceived slack in input used or output produced, and provides insighton possibilities for increasing output and/or conserving input in order for an inefficientDMU to be more efficient.

The details of the philosophy behind the DEA and its related features are given inCharnes et al (1978). Coelli (1996) has developed software (DEAP 2.1), a recentversion of which can be downloaded from the same public domain mentioned in

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Tab

le7:

Out

put-

wis

eef

ficie

ncie

san

dre

late

dra

nkin

gof

hosp

ital

s

Hos

pita

lT

YP

HO

MA

LN

BL

OO

DM

EN

TL

OR

AL

PR

EG

MA

LG

EN

MU

SCE

YE

EA

RF

ER

TT

OT

AL

DIS

NB

DIS

AL

IVP

AT

DA

Y

Mau

n0,

9638

(1)

0,98

47(5

)0,

9440

(4)

0,99

13(3

)0,

9889

(3)

0,97

55(7

)0,

9384

(7)

0,97

29(6

)0,

9949

(4)

0,47

49(1

0)0,

9802

(5)

0,98

75(3

)0,

9881

(5)

0,98

16(7

)0,

9769

(3)

S.D

.A.

Kan

ye0,

9459

(6)

0,98

61(3

)0,

7035

(10)

0,98

80(5

)0,

9886

(4)

0,98

99(2

)0,

9484

(6)

0,98

34(2

)0,

9951

(3)

0,94

00(6

)0,

9847

(4)

0,98

61(4

)0,

9905

(4)

0,98

96(3

)0,

9722

(5)

Gan

tsi

Prim

ary

0,92

81(7

)0,

9648

(9)

0,48

49(1

2)0,

9756

(10)

0,95

32(1

0)0,

9461

(11)

0,90

07(1

0)0,

9528

(9)

0,98

69(1

0)0,

3999

(13)

0,94

79(1

1)0,

9689

(9)

0,97

28(1

1)0,

9654

(10)

0,94

80(8

)

Deb

orah

0,91

23(1

0)0,

9744

(8)

0,99

99(1

)0,

9856

(7)

0,98

46(6

)0,

9757

(6)

0,92

51(9

)0,

9658

(7)

0,99

14(7

)0,

5753

(8)

0,97

59(7

)0,

9746

(7)

0,98

36(7

)0,

9830

(6)

0,96

84(7

)

Kas

ane

Prim

ary

0,91

46(9

)0,

9461

(13)

0,40

88(1

3)0,

9681

(12)

0,83

88(1

3)0,

8359

(13)

0,86

53(1

2)0,

9226

(12)

0,98

47(1

2)0,

8688

(7)

0,89

29(1

3)0,

9521

(13)

0,94

54(1

3)0,

9414

(13)

0,89

22(1

3)

Tsa

bong

Prim

ary

0,91

13(1

1)0,

9581

(11)

0,50

21(1

1)0,

9685

(11)

0,95

18(1

1)0,

9498

(10)

0,92

91(8

)0,

9512

(10)

0,98

59(1

1)0,

4049

(11)

0,94

76(1

2)0,

9612

(11)

0,96

73(1

2)0,

9622

(11)

0,92

85(1

0)

Tut

ume

Prim

ary

0,95

41(5

)0,

9861

(4)

0,82

21(8

)0,

9759

(9)

0,97

76(8

)0,

9832

(5)

0,95

79(4

)0,

9791

(3)

0,99

17(6

)0,

4026

(12)

0,98

61(3

)0,

9857

(5)

0,99

10(3

)0,

9862

(4)

0,94

11(9

)

Gom

are

Prim

ary

0,95

63(3

)0,

9745

(7)

0,85

62(7

)0,

9765

(8)

0,94

06(1

2)0,

9327

(12)

0,72

82(1

3)0,

9644

(8)

0,98

76(9

)0,

9763

(4)

0,95

91(9

)0,

9743

(8)

0,97

67(8

)0,

9716

(8)

0,92

25(1

1)

Prin

cess

Mar

ina

0,96

05(2

)0,

9926

(1)

0,97

61(3

)0,

9972

(1)

0,99

51(2

)0,

9927

(1)

0,96

96(3

)0,

9870

(1)

0,99

84(1

)0,

9853

(2)

0,99

17(1

)0,

9936

(1)

0,99

54(1

)0,

9942

(1)

0,99

36(1

)

Nya

ngab

gwe

0,95

48(4

)0,

9873

(2)

0,92

00(5

)0,

9960

(2)

0,99

58(1

)0,

9835

(4)

0,95

26(5

)0,

9788

(4)

0,99

67(2

)0,

9472

(5)

0,98

66(2

)0,

9880

(2)

0,99

13(2

)0,

9897

(2)

0,99

32(2

)

Bam

alet

e0,

8998

(12)

0,97

93(6

)0,

9819

(2)

0,98

67(6

)0,

9810

(7)

0,98

39(3

)0,

9812

(2)

0,97

60(5

)0,

9941

(5)

0,99

32(1

)0,

9762

(6)

0,97

76(6

)0,

9858

(6)

0,98

56(5

)0,

9707

(6)

Ath

lone

0,10

00(1

3)0,

9560

(12)

0,78

70(9

)0,

9882

(4)

0,98

53(5

)0,

9717

(8)

0,89

35(1

1)0,

9131

(13)

0,99

04(8

)0,

5676

(9)

0,94

90(1

0)0,

9609

(12)

0,97

52(9

)0,

9619

(12)

0,97

46(4

)

Goo

dhop

e0,

9252

(8)

0,96

35(1

0)0,

8711

(6)

0,96

40(1

3)0,

9660

(9)

0,96

86(9

)1,

0000

(1)

0,95

10(1

1)0,

9781

(13)

0,98

17(3

)0,

9601

(8)

0,96

43(1

0)0,

9746

(10)

0,96

61(9

)0,

9205

(12)

Not

e:R

anki

ngap

pear

sin

brac

kets

.

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Table 6: Individual hospitals considered for thestudy

No. District Hospital

1 North West Maun Hospital

2 Southern S.D.A. Kanye hospital

3 Gantsi Gantsi Primary Hospital

4 Kgatleng Deborah Relief Memorial Hospital

5 Chobe Kasane Primary Hospital

6 Kgalagadi Tsabong Primary Hospital

7 Tutume Tutume Primary Hospital

8 Okavango Gomare Primary Hospital

9 Gaborone Princess Marina Hospital

10 Francistown Nyangabgwe Hospital

11 South East Bamalete Lutheran Hospital

12 Lobatse Athlone Hospital

13 Goodhope Goodhope Primary Hospital

Section 2. It provides the estimates of relative efficiencies, together with the slack andsurplus variables associated with the above linear programming problem. It may benoted that, since all the outputs are simultaneously considered in this approach,TOTAL was excluded from the list of outputs, thus there will be only 14 outputs forthe application of DEA.

Table 9 summarises the relative efficiency scores of the 22 health districts under DEA.It can be seen that most of the health districts have performed with optimal (relative)efficiency except three: Kweneng East, Kgalagadi and Boteti. This is an expectedfinding when all the outputs are taken into consideration. As mentioned earlier, theefficiency scores in Table 9 cannot be directly compared with the rankings found in

Table 8: Ranking of hospitals

Rank District Hospital

1 Gaborone Princess Marina Hospital

2 Francistown Nyangabgwe Hospital

3 Southern S.D.A. Kanye hospital

4 North West Maun Hospital

5 Tutume Tutume Primary Hospital

6 South East Bamalete Lutheran Hospital

7 Kgatleng Deborah Relief Memorial Hospital

8 Okavango Gomare Primary Hospital

9 Lobatse Athlone Hospital

10 Gantsi Gantsi Primary Hospital

11 Goodhope Goodhope Primary Hospital

12 Kgalagadi Tsabong Primary Hospital

13 Chobe Kasane Primary Hospital

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Table 9: Efficiency scores of 22 health districts in Botswana,using DEA

Health districts Efficiency score Health districts Efficiency score

North West 1 Tutume 1

North East 1 Boteti 0,959

Serowe/Palapye 1 Okavango 1

Bobirwa 1 Gaborone 1

Kweneng East 0,995 Francistown 1

Southern 1 South East 1

Gantsi 1 Lobatse 1

Mahalapye 1 Selebi Phikwe 1

Kgatleng 1 Kweneng West 1

Chobe 1 Goodhope 1

Kgalagadi 0,821 Hukuntsi 1

Table 10: Results of Kwaneng East District, technicalefficiency � 0,995

Output Original value Projected value Output slack

TYPHO 20 104 29 985,493 9 789,339

MALN 415 2 099,263 1 682,361

BLOOD 21 599 22 510,366 812,359

MENTL 56 748 57 469,780 461,654

ORAL 15 058 15 127,024 0

PREG 3 909 5 159,896 1 232,978

MALGEN 23 740 24 008,069 159,247

MUSC 76 571 83 995,617 7 073,625

EYE 7 908 8 457,134 512,884

EAR 4 785 9 175,133 4 368,199

FERT 3 270 4 242,438 957,449

DISNB 2 796 2 808,817 0

DISALIV 8 084 10 231,892 2 110,836

PATDAY 40 590 62 861,278 22 085,219

Input Input surplus

HOSP 2 2,000 0

CLIN 15 15,000 0

HPOST 23 23,000 0

BEDS 263 219,231 43,769

DOCS 25 25,000 0

NURS 278 265,695 12,305

OTHERS 165 142,375 22,625

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Table 11: Results of Kgalagadi District, technicalefficiency � 0,821


TYPHO 5 428 13 989,807 7 378,506

MALN 258 336,367 22,123

BLOOD 4 001 4 873,216 0

MENTL 11 450 17 646,776 3 700,683

ORAL 2 119 3 044,628 463,688

PREG 931 1 262,318 128,360

MALGEN 3 637 6 939,337 2 509,473

MUSC 18 054 25 914,454 3 924,692

EYE 1 460 2 018,191 239,912

EAR 1 211 2 106,867 631,870

FERT 1 041 1 267,937 0

DISNB 324 493,938 99,306

DISALIV 1 312 1 986,183 388,168

PATDAY 8 807 10 726,921 0

Inputs Input surplus

HOSP 1 0,525 0,475

CLIN 5 5,000 0

HPOST 12 7,935 4,065

BEDS 41 41,000 0

DOCS 3 3,000 0

NURS 68 58,252 9,748

OTHERS 26 23,363 2,637

Sections 3 and 4. This study reveals that a closer scrutiny is warranted with respect tothe three health districts whose efficiency scores are less than unity.

As mentioned earlier, an interesting feature of DEA is that it provides informationregarding output slackness and input surplus for those DMUs whose efficiency scoresare less than unity. In other words, it is possible to project how much more their outputtargets ought to be for the given inputs they have, and also to project how much lessof each input was necessary for the current output levels. Tables 10–12 provide suchinformation for the three districts, which have efficiency scores of less than unity. Itmay be noted that the original value and output slack need not add up to the projectedvalue. This is because it is also possible that there is a radial movement of the DMUtowards the efficient frontier.

The corresponding efficiency scores for the 13 individual hospitals considered inSection 4 are presented in Table 13. It can be seen from this table that all hospitals havean efficiency score of one, except for Tsabong Primary Hospital in Kgalagadi District,which has a score of 0,885. The lack of optimality for this hospital was also revealedin Table 9. The corresponding projected output slacks or input surpluses are indicatedin Table 14. Here, too, the original value and slack need not add to the projected valuedue for the same reason mentioned earlier.

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Table 12: Results of Boteti District, technicalefficiency � 0,959

Output Original value Projected value Output slacks

TYPHO 15 724 28 877,227 12 483,621

MALN 810 849,901 5,407

BLOOD 8 514 9 269,365 392,797

MENTL 24 885 30 457,699 4 512,973

ORAL 3 667 6 219,457 2 396,298

PREG 2 530 3 229,403 591,664

MALGEN 8 146 10 998,700 2 505,804

MUSC 43 958 45 829,948 0

EYE 4 430 4 618,651 0

EAR 2 383 6 000,076 3 515,596

FERT 1 961 2 462,217 417,708

DISNB 1 011 1 072,639 18,586

DISALIV 5 349 5 640,971 64,184

PATDAY 30 706 32 813,230 799,617

Input Input surplus

HOSP 3 0,946 2,054

CLIN 7 7,000 0

HPOST 11 11,000 0

BEDS 166 115,303 50,697

DOCS 16 14,951 1,049

NURS 160 146,590 13,410

OTHERS 84 84,000 0

Table 13: Efficiency scores of 13 hospitals in Botswana, using DEA

No. Health district Name of the hospital Efficiency score

1 North West Maun Hospital 1

2 Southern S.D.A. Kanye hospital 1

3 Gantsi Gantsi Primary Hospital 1

4 Kgatleng Deborah Relief Memorial Hospital 1

5 Chobe Kasane Primary Hospital 1

6 Kgalagadi Tsabong Primary Hospital 0.885

7 Tutume Tutume Primary Hospital 1

8 Okavango Gomare Primary Hospital 1

9 Gaborone Princess Marina Hospital 1

10 Francistown Nyangabgwe Hospital 1

11 South East Bamalete Lutheran Hospital 1

12 Lobatse Athlone Hospital 1

13 Goodhope Goodhope Primary Hospital 1

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Table 14: Results of Tsabong Primary Hospital, technicalefficiency � 0,885


TYPHO 5 428 17 581,632 11 448,931

MALN 258 291,495 0

BLOOD 4 001 5 124,201 603,763

MENTL 11 450 18 016,285 5 079,767

ORAL 2 119 3 337,939 943,835

PREG 931 1 201,812 149,943

MALGEN 3 637 7 292,613 3 183,433

MUSC 18 054 28 135,576 7 737,681

EYE 1 460 2 123,356 473,809

EAR 1 211 1 921,094 552,873

FERT 1 041 1 176,150 0

DISNB 324 478,448 112,384

DISALIV 1 312 2 133,160 650,827

PATDAY 8 807 9 950,386 0

Inputs Input surplus

HOSP 1 0,680 0,320

CLIN 5 5,000 0

HPOST 12 10,663 1,337

BEDS 41 41,000 0

DOCS 3 2,978 0,022

NURS 68 65,784 2,216

OTHERS 26 26,000 0

6. CONCLUDING REMARKS

Using the Stochastic Frontier Regression analysis, it was found that health districtssuch as Gaborone, Serowe/Palapye and Francistown performed relatively better intreating patients of most of the ailment groups. On the other hand, Hukuntsi, Chobe andKgalagadi were found to have the lowest ranks. This may be attributed to the fact thatdistricts such as Gaborone, Serowe/Palapye and Francistown are urban (or semi-urban),whereas Hukuntsi, Chobe and Kgalagadi are rural districts.

When we considered patients from all ailment groups together, using the DEA it wasfound that three health districts — Kweneng East, Kgalagadi and Boteti — have atechnical efficiency score of less than one, while all other districts scored one. Thisindicates that most of the health districts are (relatively) efficient in using their inputsto produce the outputs. When 13 hospitals were compared, Tsabong Hospital in theKgalagadi District was found to be the only one with a technical efficiency score of lessthan one.

Health being one of the major concerns in Botswana, the authors feel that this studywill be useful to policy makers and health planners in terms of reallocating surplusinput to nearby or needy DMUs. Similar analyses may be made across different timepoints to get an idea of changes in the efficiency scores of DMUs over the years.

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This study has been carried out using the data published by the Central StatisticsOffice, Republic of Botswana for the year 1997. As it is based on published data, it issubject to all limitations associated with the use of secondary data.

REFERENCES

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a comparison of the technical efficiencies of health districts and hospitals in botswana

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