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Predicting the demand of physician workforce: an international model based on "crowd behaviors"

BMC Health Services Research201212:79

DOI: 10.1186/1472-6963-12-79

Received: 3 August 2011

Accepted: 26 March 2012

Published: 26 March 2012

Abstract

Background

Appropriateness of physician workforce greatly influences the quality of healthcare. When facing the crisis of physician shortages, the correction of manpower always takes an extended time period, and both the public and health personnel suffer. To calculate an appropriate number of Physician Density (PD) for a specific country, this study was designed to create a PD prediction model, based on health-related data from many countries.

Methods

Twelve factors that could possibly impact physicians' demand were chosen, and data of these factors from 130 countries (by reviewing 195) were extracted. Multiple stepwise-linear regression was used to derive the PD prediction model, and a split-sample cross-validation procedure was performed to evaluate the generalizability of the results.

Results

Using data from 130 countries, with the consideration of the correlation between variables, and preventing multi-collinearity, seven out of the 12 predictor variables were selected for entry into the stepwise regression procedure. The final model was: PD = (5.014 - 0.128 × proportion under age 15 years + 0.034 × life expectancy)2, with R2 of 80.4%. Using the prediction equation, 70 countries had PDs with "negative discrepancy", while 58 had PDs with "positive discrepancy".

Conclusion

This study provided a regression-based PD model to calculate a "norm" number of PD for a specific country. A large PD discrepancy in a country indicates the needs to examine physician's workloads and their well-being, the effectiveness/efficiency of medical care, the promotion of population health and the team resource management.

Keywords

Physician manpower Medical education Healthcare quality Physician demand Prediction model

Background

Physicians are the key personnel who make medical decisions and deliver medical treatments to patients. The adequacy of a country's physician workforce greatly influences the quality of healthcare. The literature indicated growth in health worker density significantly reduced the burden of disease, especially the burden associated with communicable diseases [1]. On the contrary, physician shortages translated into inadequate care [2, 3] and greater costs for the treatment of disease [4, 5]. However, physician size has been reported not always positively related with healthcare quality. Physicians may induce demands, and physician surpluses may drive unnecessary utilization of healthcare [6]. As the rapid progression of globalization, physician migration across country borders has become more intense than ever [7]. During the past years, there have been 384 citations with the tag of "physician supply and/or demand" [8]. Appropriately matching physician supply and demand is now a critical worldwide concern.

Estimating the number of physicians a country requires is a complex task given the many contributing factors that have impacts on physicians' productivity, people's expectation of healthcare quality and the utilization of healthcare resources [9, 10]. These factors are theoretically divided into four domains: population, physician, healthcare system, and economics. Within the population domain, one needs to consider the age, birth rate, death rate, infant mortality, life expectancy, population growth rate, incidence and prevalence of diseases, health demands by age, literacy, and health expectations. Within the physician domain, it is necessary to take into account the practicing physician's age (as a measure of the number of physicians retiring), gender, specialty and subspecialty, number of work hours per week, and clinical competence. Within the healthcare system domain, there is a need to consider healthcare accessibility, number of hospital beds, availability of resources, structure of payment, availability of support personnel (i.e., nurses, midwives, and technicians) and overall treatment capacities. Final considerations need to be on the economics of a country, often expressed as GDP (gross domestic product), GNP (gross national product), GNPPC (GNP per person), or PPP (Purchasing Power Parity). The above factors may be correlated with the size of a country's physician workforce, but not necessarily have a causal relationship. As population size is known to be an essential factor that determines physician demand, physician density (PD, defined as the number of practicing physicians per 10,000 population) is often used to estimate physician needs.

Upon reviewing the literature, many factors have been reported to have significant relationships with physician density. Using a regression analysis of the World Bank data on 250 countries, physician density was reported to be influenced by GDP, female literacy, the percentage of female population aged over 60 years, and female life expectancy [10]. Similarly, a regression analysis for both LMICs (Low and Low-Middle Income Countries) and MHICs(middle and high income countries) showed that physician density was significantly associated with several health indicators of infant mortality rate, under 5 (year of age) mortality rate, maternal mortality rate, and life expectancy [1]. The number of hospital beds (per 1,000 inhabitants) had a positive impact on the growth rate of specialists [6], and the disability-adjusted life years (DALYs) had a significantly inverse relationship with the density of health workers [11]. As the above factors were observed to interact with one another, and with other hidden factors (e.g., economic factors underlying the child population factor), added by the difficulty in measurement (e.g., physician competency), the prediction of manpower for future needs became very difficult, especially in a rapidly changing health care environment. Currently, there has been no tool or formula that can accurately predict the optimal PD for a given country.

To predict reality, "the Wisdom of Crowd theory", suggested to aggregate information in "groups" rather than in "individual" [12]. In the book, entitled "The Wisdom of Crowds", Surowiecki argued that aggregating information in groups results in predicting reality better than by a single members of the groups. The opening anecdote in the book described "Francis Galton's surprise that the crowd at a country fair accurately guessed the weight of an ox; when the individual guesses were averaged; the average was closer to the true butchered weight of the ox than the estimates of individual crowd members."

With the rapid growth of information technology, abundant data on health indices and population demography has accumulated across country boundaries. Using aggregated international data of "crowd behaviors", the aim of the present study was to develop a PD prediction model for evaluating the needs of physician manpower that closely reflects the reality. When calculating the discrepancy between the observed and the predicted PD, the model may be used to screen the appropriateness of physician manpower in a nation, and provide warnings to prevent from the damage to healthcare in its early stage.

Methods

Twelve variables that were readily accessible on the world wide web, and having a possible impact on physicians' demands, were chosen. The variables consisted of health indicators, population demography, health care system, and socioeconomic status. The indicators were under age 5 year mortality rate, adult mortality rate, life expectancy, fertility rate, literacy, population density, proportion under age 15 years, proportion over age 60 years, gross domestic product, gross national income, purchasing power parities, and expenditure on health.

Data on PD and 12 variables were extracted from the World Health Organization (WHO), United Nations (UN), Organization for Economic Cooperation (OECD), and World Bank (WB) data banks for the years of 2004, 2005, and 2006. The study received ethical approval from IRB (Institutional Review Board) in Wanfang Hospital Taipei Medical University, with the reference number of 97044.

Statistical analyses

A six-step procedure was used to derive the international prediction model for PD, which consisted of: 1) reducing data by eliminating highly correlated variables, 2) selecting countries with complete data in the analysis, 3) dividing the countries randomly into two halves, 4) generating a prediction equation from the first half of the countries and using it to predict the observed PD for countries in the second half, 5) subsequent to the split-sample validation in step 4, the countries were combined into one dataset to derive an overall international PD model, and 6) the model was then used to predict PD and to calculate country-specific PD discrepancies.

Multiple stepwise-linear regression was used to derive the model that best predicted PD. A p-value of 0.15 was used for both the variable entry and variable removal criteria [13]. The sample squared multiple correlation (R2) was used to quantify the strength of the relationship in terms of the percentage of data variation explained by the regression model. Adequacy of model assumptions were assessed by a normal probability plot and by a plot of standardized residuals versus predicted values.

For the purpose of analyses, the mean PD across the 3 years (2004, 2005, and 2006) was calculated to be the outcome variable as the Pearson correlation (r) among the years was high (r > 0.97). Similarly, country-specific predictors were calculated as the mean of sex-specific and year-specific data because the correlations were also high (r > 0.96). Literacy was excluded from all the analyses because information was available only on half of the countries. Among the 11 remaining predictors, several were observed to be highly correlated with each other: under age 5 years mortality rate, adult mortality rate, and life expectancy (r > 0.93), proportion under age 15 years and fertility rate (r > 0.94), gross domestic product and gross national income (r > 0.94). As a result, the following 4 predictors were excluded from all analyses to prevent multi-collinearity: under age 5 years mortality rate, adult mortality rate, fertility rate, and gross national income. The remaining 7 predictor variables were considered for entry into the stepwise regression procedure: population density, proportion under age 15 years, proportion over age 60 years, life expectancy, gross domestic product, expenditure on health, and purchasing power parities.

A split-sample cross-validation was performed to assess the generalizability of the results [14]. The process consisted of splitting the original sample into a training set and validation set using random sampling. A regression equation was derived in the training set and the R2 between the observed and predicted response values was calculated. The regression coefficients from the training set were then used to calculate predicted values in the validation set. The cross-validation coefficient (R2*) between these predicted values and observed values in the validation set was calculated. The shrinkage coefficient was calculated as the difference between R2 and R2*of the training and validation sets. The smaller the shrinkage coefficient, the more confidence one can have in the generalizability of the results. Shrinkage coefficient values less than 5% indicate a generalizable model [14]. Given a satisfactory shrinkage coefficient, the data were combined from both sets and a final regression equation was derived based upon the entire sample. The final model was then applied to all the countries to calculate country-specific PD discrepancies (predicted PD minus observed PD) and the predicted number of required physicians using 2009 country populations.

The countries were then stratified by area and economic status. Analysis of covariance (ANCOVA), adjusting for observed PD, was used to examine whether the country-specific PD discrepancies differed by continent, membership in the OECD (Organization for Economic Cooperation and Development), and by economic status (low income, middle income, high income). Least squares means (with corresponding 95% confidence intervals) were calculated. Differences among categories were tested for statistical significance using Scheffé's adjustment for multiple comparisons.

Results

Among the 195 countries, 130 that had complete data on PD for the years 2004-2006 were included for analyses. The 130 countries were randomly and equally split into the training set and the validation set. Descriptive statistics of the variables are shown in Table 1 and Table 2. By ANOVA, the descriptive data in the training and validation sets were found not significantly different. As PD was positively-skewed and the plot of standardized residuals versus predicted values showed increasing error variance, a square root transformation was used to stabilize the regression variance of PD.
Table 1

The means (standard deviation) of physician manpower-related variables in 130 countries, in training and validation sets

Variables

Training Set(N = 65)

Validation Set(N = 65)

Entire Set(N = 130)

Physician density(per 10,000)

15.2 (14.0)

17.6 (14.8)

16.4 (14.4)

Population density(per square kilometre)

135.7 (222.4)

137.2 (214.7)

136.4 (217.8)

Proportion under age 15 years

29.6 (12.0)

29.3 (11.0)

29.4 (11.5)

Proportion over age 60 years

11.4 (7.4)

10.6 (6.7)

11.0 (7.1)

Life expectancy (years)

65.5 (12.4)

66.4 (11.8)

65.9 (12.1)

Gross domestic product (GDP, per capita)

10177 (15811)

10091 (14279)

10134 (15005)

Expenditure on health as percentage of GDP

6.6 (2.7)

6.6 (2.8)

6.6 (2.8)

Purchasing power parities

438 (1518)

299 (924)

370 (1258)

Notes. Data are partitioned into two subsets in a cross-validation analysis. The "training set" is the subset used for analysis, and the "validation set" is used for validating the analysis

Table 2

The distribution of area (continent) and economic status in 130 countries, in training and validation sets

 

Training Set

(N = 65)

Validation Set

(N = 65)

Entire Set

(N = 130)

Continent

   

   Africa

26 (40.0)

18 (27.7)

44 (33·8)

   Americas

3 (4.6)

1 (1.5)

4 (3.2)

   Asia

7 (10.8)

5 (7.7)

12 (9.2)

   Australia/Oceania

2 (3.1)

5 (7.7)

7 (5.4)

   Europe

20 (30.7)

24 (36.9)

44 (33.8)

   Middle East

7 (10.8)

12 (18.5)

19 (14.6)

Member of OECD

   

   No

50 (76.9)

50 (76.9)

100 (76.9)

   Yes

15 (23.1)

15 (23.1)

30 (23.1)

Economics

   

   Low income

17 (26.1)

20 (30.8)

37 (28.4)

   Middle income

28 (43.1)

25 (38.4)

53 (40.8)

   High income

20 (30.8)

20 (30.8)

40 (30.8)

OECD = Organization for Economic Cooperation and Development

The stepwise regression procedure retained the same two variables in both the training and validation sets: proportion under age 15 years and life expectancy. The univariate relationships between PD and each retained predictor variable are illustrated in Figures 1a and 1b. The regression coefficients from the multivariate analyses are shown in Table 3. The R2s were virtually identical in both sets and none of the regression coefficients were statistically different between the two sets. The shrinkage coefficient was 1.5%, indicating a high level of model generalizability. Given a low level of shrinkage, the data were combined from both sets and a final regression equation was derived based upon the entire sample of 130 countries: PD = (5.014 - 0.128 × proportion under age 15 years + 0.034 × life expectancy)2. The R2 of 80.4% from the final 2-variable model was virtually identical to the R2 of 80.3% from a full model consisting of all 7 variables. (Note: The 7 predictor variables were: population density, proportion under age 15 years, proportion over age 60 years, life expectancy, gross domestic product, expenditure on health, and purchasing power parities).
https://static-content.springer.com/image/art%3A10.1186%2F1472-6963-12-79/MediaObjects/12913_2011_Article_2015_Fig1_HTML.jpg
Figure 1

(a) Relationship between physician density (y axis) and proportion of population under age 15 years (x axis). The regression line equation is: PD = (8.179 - 0.159 × PropPop)2. (b) Relationship between physician density (y axis) and life expectancy (x axis). The regression line equation is: PD = (-5.577 + 0.138 × LifeExp)2.

Table 3

Regression coefficients (95% confidence intervals) from the Physician Density Prediction Model of two variables (proportion under age 15 years, life expectancy)

 

Training Set

(N = 65)

Validation Set

(N = 65)

Entire Set

(N = 130)

Intercept

4.841

(1.543, 8.139)

5.412

(2.056, 8.777)

5.014*

(2.676, 7.351)

Proportion under age 15 years

-0.125

(-0.162, -0.088)

-0.134

(-0.172, -0.096)

-0.128*

(-0.154, -0.102)

Life expectancy (years)

0.033

(-0.002, 0.068)

0.033

(-0.003, 0.069)

0.034

(0.009, 0.059)

R-squared

81.6%

80.1%

80.4%

Notes. * P-value < 0.001; P-value = 0.007

The present study used 2009 population data and the two model variables (the proportion under age 15 years and the life expectancy) to calculate a "predicted" (the norm) PD for a country. The "predicted" PD was then compared to the observed PD for each specific country, resulting in a calculated PD discrepancy. Table 4 ranks the countries from the highest to the lowest level of PD discrepancy. For a "negative discrepancy" (the observed PD less than the predicted PD), physician manpower can be considered as "under the norm", rather than "a deficit". In contrast, a "positive discrepancy" indicates the observed PD is greater than the predicted PD, and can be considered as "above the norm". There were 70 countries (70/130, 53.8%) with observed PDs that had "negative discrepancy", and 58 that had "positive discrepancy" (58/130, 44.6%). Figure 2 shows the relationship between PD discrepancy and observed PD in the 130 countries. It's interesting to note from Figure 2 that the breakpoint for "above the norm" in PD occurs at approximately 30 physicians per 10,000 population. The scatter-plot graph is divided into four quadrants by the vertical line of 30 PD and the horizontal line of "zero" discrepancy. Few countries with PD greater than 30 (per 10,000 population) were found to be "below the norm" in PD.
Table 4

The predicted and observed physician density (PD), continent, economic status, and analysis set in 130 countries, rank-ordered by the predicted-observed PD discrepancy

Rank

Country

Continent

OECD

Economic

Analysis Set

Predicted PD

Observed PD

Discrepancy (per 10,000)

Population

Physician number

1

Japan

AS

Yes

H

T

36.3

20.6

-15.7

126,804,433

-199,397

2

Bosnia/Herzegovina

EU

No

M

V

28.8

13.6

-15.2

4,621,598

-7,005

3

Sri Lanka

AS

No

M

T

19.3

5.5

-13.8

21,513,990

-29,629

4

Korea

AS

Yes

H

T

28.6

16.3

-12.3

48,636,068

-59,672

5

Romania

EU

No

M

T

30.8

19.3

-11.5

22,181,287

-25,600

6

Suriname

SA

No

M

T

13.0

1.6

-11.4

486,618

-555

7

Slovenia

EU

No

H

V

34.3

23.7

-10.7

2,003,136

-2,134

8

Canada

NA

Yes

H

T

31.1

21.4

-9.7

33,759,742

-32,794

9

Myanmar

AS

No

L

V

12.9

3.6

-9.3

48,137,741

-44,694

10

Bhutan

AS

No

M

T

9.6

0.5

-9.1

699,847

-635

11

Mauritius

AF

No

M

T

19.3

10.6

-8.7

1,294,104

-1,132

12

Poland

EU

Yes

M

T

30.5

22.0

-8.5

38,463,689

-32,643

13

Morocco

AF

No

M

T

13.0

5.1

-7.9

31,627,428

-24,973

14

Kiribati

AO

No

M

V

9.8

2.3

-7.5

115,401

-87

15

Croatia

EU

No

M

T

32.0

24.8

-7.2

4,486,881

-3,237

16

Serbia

EU

No

M

T

27.0

20.0

-7.0

7,344,847

-5,110

17

Montenegro

EU

No

M

V

26.0

20.0

-6.0

666,730

-399

18

Iran

ME

No

M

T

14.6

8.8

-5.8

67,037,517

-39,190

19

United Kingdom

EU

Yes

H

T

29.0

23.7

-5.3

61,284,806

-32,431

20

Albania

EU

No

M

V

16.9

11.8

-5.1

3,659,616

-1,859

21

Tunisia

AF

No

M

V

18.2

13.4

-4.8

10,589,025

-5,122

22

Seychelles

AF

No

M

T

19.4

15.1

-4.3

88,340

-38

23

Bangladesh

AS

No

L

V

7.1

2.8

-4.3

158,065,841

-68,214

24

Cyprus

EU

No

H

V

28.1

24.0

-4.1

1,102,677

-453

25

Vanuatu

AO

No

M

V

5.5

1.4

-4.1

221,552

-91

26

Luxembourg

EU

Yes

H

T

29.2

25.3

-3.9

497,538

-193

27

New Zealand

AO

Yes

H

V

25.4

22.0

-3.4

4,252,277

-1,436

28

Gabon

AF

No

M

V

6.2

2.9

-3.3

1,545,255

-509

29

Syria

ME

No

M

T

8.2

5.0

-3.2

22,198,110

-7,090

30

Nepal

AS

No

L

V

5.1

2.1

-3.0

28,951,852

-8,570

31

Kuwait

ME

No

H

V

20.9

18.0

-2.9

2,789,132

-822

32

India

AS

No

M

T

8.5

6.0

-2.5

1,180,512,215

-294,800

33

Djibouti

AF

No

M

T

4.1

1.8

-2.3

740,528

-174

34

Ghana

AF

No

L

V

3.8

1.5

-2.3

24,339,838

-5,699

35

Mauritania

AF

No

L

T

3.4

1.1

-2.3

3,205,060

-743

36

Eritrea

AF

No

L

T

2.6

0.5

-2.1

5,792,984

-1,195

37

Senegal

AF

No

L

T

2.5

0.6

-1.9

14,086,103

-2,691

38

Comoros

AF

No

L

V

3.4

1.5

-1.9

773,407

-143

39

Togo

AF

No

L

V

2.0

0.4

-1.6

6,199,841

-977

40

Macedonia

EU

No

M

V

25.6

24.1

-1.5

2,072,086

-320

41

Finland

EU

Yes

H

V

30.5

29.0

-1.5

5,255,068

-796

42

Namibia

AF

No

M

T

4.4

3.0

-1.4

2,128,471

-297

43

Nauru

AO

No

M

V

9.1

7.7

-1.4

14,264

-2

44

Timor-Leste

AS

No

M

T

2.1

1.0

-1.1

1,131,612

-129

45

Benin

AF

No

L

V

1.4

0.4

-1.0

9,056,010

-944

46

Sudan

AF

No

M

V

3.6

2.6

-1.0

41,980,182

-4,240

47

Australia

AO

Yes

H

T

28.5

27.5

-1.0

21,515,754

-2,165

48

Rwanda

AF

No

L

V

1.4

0.5

-0.9

11,055,976

-954

49

Germany

EU

Yes

H

V

35.0

34.2

-0.8

82,282,988

-6,898

50

Maldives

AS

No

M

V

10.0

9.2

-0.8

395,650

-31

51

Côte d'Ivoire

AF

No

L

T

2.0

1.2

-0.8

21,058,798

-1,639

52

Libya

AF

No

M

V

13.2

12.5

-0.7

6,461,454

-480

53

Cape Verde

AF

No

M

T

5.6

4.9

-0.7

431,822

-31

54

Mozambique

AF

No

L

T

1.0

0.3

-0.7

22,061,451

-1,531

55

Laos

AS

No

L

T

4.2

3.5

-0.7

6,993,767

-477

56

Hungary

EU

Yes

H

T

31.2

30.5

-0.7

9,880,059

-645

57

Guinea

AF

No

L

V

1.7

1.1

-0.6

10,324,025

-665

58

Central African Rep.

AF

No

L

T

1.3

0.8

-0.5

4,578,768

-231

59

United States

NA

Yes

H

T

24.6

24.1

-0.5

310,232,863

-14,835

60

Turkey

ME

Yes

M

V

15.0

14.6

-0.5

77,804,122

-3,674

61

Sierra Leone

AF

No

L

T

0.7

0.3

-0.4

5,245,695

-224

62

Burundi

AF

No

L

T

0.7

0.3

-0.4

9,863,117

-406

63

Botswana

AF

No

M

V

4.4

4.0

-0.4

2,029,307

-74

64

Latvia

EU

No

M

T

31.7

31.3

-0.3

2,217,969

-74

65

Cameroon

AF

No

M

T

2.2

1.9

-0.3

19,294,149

-626

66

Zimbabwe

AF

No

L

V

1.9

1.6

-0.3

11,651,858

-307

67

Congo (Brazzaville)

AF

No

M

V

2.2

2.0

-0.2

4,125,916

-71

68

Chad

AF

No

L

T

0.5

0.4

-0.1

10,543,464

-105

69

Malawi

AF

No

L

T

0.3

0.2

-0.1

15,447,500

-150

70

Burkina Faso

AF

No

L

T

0.5

0.5

0.0

16,241,811

-80

71

Ukraine

EU

No

M

T

30.3

30.3

0.0

45,415,596

-47

72

Liberia

AF

No

L

T

0.2

0.3

0.1

3,441,790

30

73

Niger

AF

No

L

V

0.1

0.2

0.1

15,306,252

170

74

Spain

EU

Yes

H

V

35.5

35.9

0.4

40,548,753

1,583

75

Angola

AF

No

M

V

0.3

0.8

0.5

13,068,161

704

76

Slovakia

EU

Yes

H

V

30.1

30.6

0.5

5,470,306

300

77

Mali

AF

No

L

T

0.2

0.8

0.6

13,796,354

844

78

Uganda

AF

No

L

V

0.2

0.8

0.6

33,398,682

2,044

79

Congo (Kinshasa)

AF

No

L

T

0.3

1.1

0.8

70,916,439

5,561

80

South Africa

AF

No

M

T

6.8

7.7

0.9

49,109,107

4,373

81

Zambia

AF

No

L

V

0.3

1.2

0.9

12,056,923

1,110

82

Guinea-Bissau

AF

No

L

T

0.2

1.2

1.0

1,565,126

151

83

Andorra

EU

No

H

V

35.6

36.6

1.0

84,525

8

84

Madagascar

AF

No

L

T

1.8

2.9

1.1

21,281,844

2,270

85

Pakistan

ME

No

L

V

6.4

7.7

1.3

177,276,594

22,940

86

Sao Tome & Principe

AF

No

L

V

3.3

4.9

1.6

219,334

36

87

Yemen

ME

No

L

V

1.7

3.3

1.6

23,495,361

3,871

88

Equatorial Guinea

AF

No

H

T

1.3

3.0

1.7

650,702

108

89

Czech Republic

EU

Yes

H

T

33.8

35.5

1.7

10,201,707

1,726

90

Afghanistan

ME

No

L

V

0.2

2.0

1.8

29,121,286

5,274

91

Estonia

EU

No

H

T

30.9

32.8

1.9

1,291,170

249

92

Portugal

EU

Yes

H

V

31.6

33.5

1.9

10,735,765

2,081

93

Cook Islands

AO

No

H

T

9.8

11.8

2.0

23,000

5

94

Qatar

ME

No

H

V

24.2

26.4

2.2

840,926

186

95

Moldova

EU

No

M

V

23.9

26.5

2.6

4,320,748

1,137

96

Ireland

EU

Yes

H

V

25.0

28.2

3.1

4,250,163

1,331

97

Italy

EU

Yes

H

T

35.7

39.0

3.3

58,090,681

19,097

98

Austria

EU

Yes

H

V

32.1

35.5

3.4

8,214,160

2,762

99

Bulgaria

EU

No

M

T

32.3

35.8

3.4

7,148,785

2,436

100

Denmark

EU

Yes

H

T

27.4

30.8

3.4

5,515,575

1,897

101

Iraq

ME

No

M

V

2.9

6.6

3.7

29,671,605

11,054

102

Sweden

EU

Yes

H

T

31.2

35.0

3.8

9,059,651

3,465

103

Oman

ME

No

H

T

11.0

15.0

4.0

3,525,875

1,398

104

Mexico

NA

Yes

M

V

13.7

17.9

4.2

112,468,855

47,141

105

Saudi Arabia

ME

No

H

V

9.4

13.7

4.3

29,207,277

12,531

106

France

EU

Yes

H

V

29.5

33.9

4.4

64,768,389

28,812

107

Malta

EU

No

H

T

30.4

35.6

5.2

406,771

212

108

Switzerland

EU

Yes

H

V

32.7

38.0

5.3

7,623,438

4,026

109

Netherlands

EU

Yes

H

V

29.3

37.1

7.8

16,783,092

13,090

110

Norway

EU

Yes

H

T

28.1

36.4

8.3

4,676,305

3,892

111

Lebanon

ME

No

M

T

14.5

23.6

9.1

4,060,766

3,689

112

Bahrain

ME

No

H

T

17.8

27.1

9.3

738,004

686

113

Belgium

EU

Yes

H

T

30.4

40.1

9.7

10,423,493

10,124

114

Lithuania

EU

No

M

T

29.1

39.6

10.5

3,545,319

3,725

115

Niue

AO

No

M

V

9.5

20.0

10.5

1,398

1

116

Iceland

EU

Yes

H

V

24.5

36.7

12.2

308,910

377

117

Kyrgyzstan

ME

No

L

V

11.4

24.4

13.0

5,508,626

7,183

118

Armenia

EU

No

M

V

22.9

36.1

13.3

2,966,802

3,933

119

Russia

EU

No

M

V

28.5

42.7

14.2

139,390,205

197,550

120

Jordan

ME

No

M

T

7.3

22.0

14.7

6,407,085

9,391

121

Egypt

AF

No

M

T

9.6

24.3

14.7

80,471,869

118,113

122

Tajikistan

ME

No

L

V

4.8

20.3

15.5

7,487,489

11,635

123

Greece

EU

Yes

H

V

35.1

50.8

15.7

10,749,943

16,836

124

Turkmenistan

ME

No

M

T

9.9

25.7

15.8

4,940,916

7,783

125

Uzbekistan

ME

No

L

V

10.2

26.7

16.5

27,865,738

45,950

126

Belarus

EU

No

M

V

29.5

46.9

17.4

9,612,632

16,757

127

Georgia

EU

No

M

T

26.5

44.9

18.3

4,600,825

8,442

128

Azerbaijan

EU

No

M

V

17.2

36.0

18.8

8,303,512

15,637

129

Israel

ME

No

H

V

17.3

37.4

20.1

7,353,985

14,787

130

Kazakhstan

AS

No

M

V

16.7

37.3

20.7

15,460,484

31,933

Notes. PD = physician density (per 10,000 population)

Discrepancy = Predicted PD minus Observed PD

Physician Number = Discrepancy × Population ÷ 10,000

T and V: T (Training set) or V (Validation set)

Continent: AF = Africa, AS = Asia, AO = Australia/Oceania, EU = Europe,ME = Middle East, NA = North America, SA = South America

OECD = Organization for Economic Cooperation and Development

Economics: L (Low income); M (Middle income); H (High income)

https://static-content.springer.com/image/art%3A10.1186%2F1472-6963-12-79/MediaObjects/12913_2011_Article_2015_Fig2_HTML.jpg
Figure 2

Relationship between discrepancy between the predicted and the observed PD (y axis) and observed physician density (x axis). The breakpoint for "above the norm" in physician density occurs at approximately 30 per 10,000.

Statistically significant differences in PD discrepancies were observed when more "broad stroke" comparisons were made among the countries' continents, membership in the OECD, and economic levels (Table 5). In general, countries grouped within continents which were more 'westernized' (Americas and Europe) had a greater mean "deficit" of physicians (-4.3 and -6.3 physicians per 10,000) than other continents. This result was congruent with being a member of the OECD and being considered a high income country.
Table 5

Comparison of physician density (per 10,000) discrepancies by continent, OECD status, and economics from analysis of covariance

 

Least Squares Mean Discrepancy

(95% Confidence Interval)

P-value

Continent

  

   Africa (AF)

6·7 (4·6, 8·8)

< 0·001*

   Americas (AM)

-4·3 (-9·3, 0·8)

 

   Asia (AS)

-1·2 (-4·1, 1·7)

 

   Australia/Oceania (OA)

1·1 (-2·7, 4·9)

 

   Europe (EU)

-6·3 (-8·6, -4·0)

 

   Middle East (ME)

5·8 (3·5, 8·2)

 

Member of OECD

  

   No

2·3 (1·1, 3·5)

< 0·001

   Yes

-4·1 (-6·6, -1·7)

 

Economics

  

   Low income (L)

6·7 (4·5, 8·9)

< 0·001

   Middle income (M)

0·8 (-0·7, 2·3)

 

   High income (M)

-4·5 (-6·5, -2·4)

 

OECD = Organization for Economic Cooperation and Development

* Statistically significant differences between AF & AM, AF & AS, AF & EU, AM & ME, AS & ME, EU & ME

Statistically significant differences between L & M, L & H, M & H

Discussion

Physician density itself is not the only factor determining health outcomes. Evaluating physician manpower for appropriateness is a complex task that should simultaneously consider many influencing factors on population, physician productivity, healthcare system, and the economics. This study developed an international PD regression model that applied "Crowd Theory", which incorporated many factors affecting observed PDs in 130 countries. The "predicted PDs", derived from the regression model was used as the "norm" for the PD that countries commonly used in maintaining their healthcare.

The final regression model retained two variables (proportion under age 15 years and life expectancy), which accounted for 80.4% of the total variance of PD. In predicting PD, "proportion under age 15 years" had an inverse relationship, while "life expectancy" had a positive relationship. However, correlational relationships do not imply that one factor causes the other. Children under age 15 years actually tend to utilize more medical services than the average age, thus it was assumed that the larger the child population a country had, the more physicians were needed. The inverse relationship may have been due to a hidden third variable, such as a country's economics. Kwame found quantitative evidence on the relationship between certain socioeconomic and demographic factors (e.g., birth rate, being reflective of population under 15 and per capita health care expenditure in Africa (Kwame 1992) [15]. An inverse relationship was also reported between birth rates and the economy that was known positively correlated with physician density [16, 17]. "Life expectancy", referring not only the length but also the quality of life, has been recognized as a standard measure in the world for measuring population health [18]. Therefore, it is of no surprise to have "life expectancy" retained in the regression model.

The relationship between physician density and healthcare quality has been a long time research focus. The shortage of physician manpower will increase physician workloads and hamper patient safety. The criterion for determining appropriate physician number is the level that physicians can provide acute healthcare and guarantee patient safety in a hospital setting. For example, in pediatrics, patient care with safety consideration is the care delivered to all children who visit, stay or are born in a hospital, day and night, attended by health care providers under reasonable workloads. Besides patient safety, when added to the requirements of timeliness, effectiveness, efficiency, equitableness and patient-centered care [19], physicians' workloads often increase and shortage of physician manpower emerges. It has been reported that heavy workloads and stress significantly impacts on patient care quality, physician performance, absenteeism, turnover and organizational performance [20]. Adequate physician manpower is one of the strategies to prevent physicians from burnout.

Early detection of physician shortage has been a great challenge. Soon after 2000 when physician supply was considered to exceed demand [21], physician shortages emerged in the United States and Canada [4]. Similar reports of physician shortages have also been reported in other developed countries, such as Japan [22, 23], Australia and Singapore [24]. These countries have increased student enrollment and established new medical schools to overcome the deficit. Unfortunately, the correction of physician shortage within a country has been taking an extended period of time, e.g., nearly 25 years in the United States.

The regression model in this study is derived from data of 130 countries around the world that reflects the PD most in a country. Thus, the predicted PD would be better used as a warning sign rather than an absolute number suggested for correction. A discrepancy between the predicted and the observed PD in a country indicates the physician manpower is either in surplus or in deficit, deviated from the norm of crowd behavior. A large negative discrepancy will highlight the needs to survey their physician's workloads and their well-being, and to improve quality of medical performance as well.

There seems to be a potential to increase physician number to improve health outcome, especially when physician shortages became a global concern. As early as 1986, Perrin reported simply increasing physician supply may not have much effect on healthcare quality [6]. To improve health status, benefits will also come from the focus on improving adherence to the standards of best medicine and from preventive efforts to diminish personal risk factors of disease (smoking, diet, and exercise). More focused efforts should also be put to improve physicians' competency, the services that they provide, and the team resource management, rather than just increasing physician supply [6, 25]. The above factors, being difficultly translated into "data" for analyses, may explain why some countries with negative discrepancy of PD had good health outcome.

Conclusion

An appropriate size of physician workforce is vital to maintain a nation in good health. When facing the crisis of physician shortage, the correction of manpower always takes an extended time period, and thus both the public and health personnel suffer. The regression PD model which provides information on how the observed PD deviates from the "norm" can be used to screen the appropriateness of physician manpower in a nation. To prevent damage to healthcare system when discrepancy appears between the observed and the predicted PD, we should examine not only the status of physician manpower, but also the physicians' workloads, the quality of medical performance, the physicians' well-being, the effectiveness of health promotional program and the team resource management.

Declarations

Acknowledgements

The research received the grant from the Health Department, Executive Yuan, Taiwan R.O.C. The author appreciated the contributions from Dr. Peter H. Harasym.

Authors’ Affiliations

(1)
Department of Pediatrics, E-Da Hospital
(2)
Department of Chinese Medicine, I-Shou University College of Medicine
(3)
Departments of Community Health Sciences, Clinical Neurosciences, Oncology, University of Calgary, 2500 University Dr. NW
(4)
Department of Surgery, Cathay General Hospital
(5)
Fu-Jen Catholic University College of Medicine

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Copyright

© Tsai et al; licensee BioMed Central Ltd. 2012

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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