International Vaccine Institute, SNU Research Park, San 4–8 Bongcheon-7 dong, Kwanak-gu, Seoul, Korea

National Institute of Health and Epidemiology, No. 1 Yersin Street, Hanoi, Vietnam

Robert Wood Johnson Foundation Health & Society Scholar, Columbia University, USA

Abstract

Background

Spatial filtering using a geographic information system (GIS) is often used to smooth health and ecological data. Smoothing disease data can help us understand local (neighborhood) geographic variation and ecological risk of diseases. Analyses that use small neighborhood sizes yield individualistic patterns and large sizes reveal the global structure of data where local variation is obscured. Therefore, choosing an optimal neighborhood size is important for understanding ecological associations with diseases. This paper uses Hartley's test of homogeneity of variance (F_{max}) as a methodological solution for selecting optimal neighborhood sizes. The data from a study area in Vietnam are used to test the suitability of this method.

Results

The Hartley's F_{max }test was applied to spatial variables for two enteric diseases and two socioeconomic determinants. Various neighbourhood sizes were tested by using a two step process to implement the F_{max}test. First the variance of each neighborhood was compared to the highest neighborhood variance (upper, F_{max1}) and then they were compared with the lowest neighborhood variance (lower, F_{max2}). A significant value of F_{max1 }indicates that the neighborhood does not reveal the global structure of data, and in contrast, a significant value in F_{max2 }implies that the neighborhood data are not individualistic. The neighborhoods that are between the lower and the upper limits are the optimal neighbourhood sizes.

Conclusion

The results of tests provide different neighbourhood sizes for different variables suggesting that optimal neighbourhood size is data dependent. In ecology, it is well known that observation scales may influence ecological inference. Therefore, selecting optimal neigborhood size is essential for understanding disease ecologies. The optimal neighbourhood selection method that is tested in this paper can be useful in health and ecological studies.

Introduction

Spatial filtering can be used to create smoothed maps of health and ecological patterns

People do not live in isolation; they live in groups (neighborhood) that may influence their life style, health, and health seeking behavior. Thus, a neighborhood level study is sometimes essential to identify important public health problems and to generate hypotheses about their potential causes

Ecological variables can be measured at different geographic scales from local to global. In ecology, it is well known that observation scales influence ecological inference

Methodology

The Study area

Health and socioeconomic data of a study area in Khanh Hoa Province, on the coast of central Vietnam, were used to test the proposed method. The size of the study area is 740 square kilometers consisting of 33 communes in two districts: Nha Trang (151 square kilometres) and Ninh Hoa (589 square kilometres). A dynamic population database is maintained for the study area which is updated on yearly basis. In 2002, the population of the study area was 329,596, of which 54% of the population is from Nha Trang. We created a household-level geographic information system (GIS) database that includes a point for each active household (described below) in 2002. The household settlements are clustered, leaving a large portion non-inhabited land within the administrative boundaries, which led us to define household-based working study area by creating 500 meters radius buffer around each household point and dissolving boundaries between buffers (Figure

The geographic features of the study area in Vietnam

**The geographic features of the study area in Vietnam**. Map showing the geographic characteristics of the study area along with the geographic positing of the study area in Vietnam

The GIS data

In 2003, we conducted a global positioning system (GPS) survey using handheld receivers to identify the geographic locations of every household in the study area. A base map of commune boundaries and other geographic features (e.g., rivers, roads, railways, lakes) was first acquired in digital format. The household GPS survey data were projected in the same geographic referencing system (i.e., Transverse Mercator) so that the household points could be accurately integrated with the study area base map. When several households shared a single structure or closely connected structures a single point was plotted. We received a list of 72,152 households from the census 2002. A total of 3,587 households could not be included in the GIS for a variety of reasons (e.g., migration out, living on a military base with no access, and household confirmation was not possible due to the absence of household members). Thus, the GIS was created for the 68,565 households, which were referenced spatially by 32,542 points. Several checks were made for missing households, misallocations, and wrong identification numbers, and the erroneous data were corrected. Finally, the household data were mapped in groups (the smallest geographic entity), and their positions were verified by ground-truthing.

The attribute data

We used two social variables, religion and literacy (i.e., years of schooling), and two enteric disease incidence variables (i.e., shigellosis and

The

Data categorization and manipulation

We categorized the two variables, literacy and religion, to define the social status of the study population. A person having six years of schooling or above was considered to be literate, and the religion was classified by Buddhist and non-Buddhist. Since the data were obtained at the individual level, the data were aggregated by spatially referenced household points. Neighborhood level data were then obtained for each of the spatially referenced points of household (32,542 points for the 329,596 individuals in 68,565 households) by aggregating household level data of surrounding neighbors using circular windows of various sizes. The neighborhood level social variables were estimated by the percentage of people living within neighborhoods, and the disease incidence variables were expressed in rates per 10,000 people. Our aim was to create a local-level neighborhood variable for these phenomena. Therefore, based on the working size of the study area and the spatial distribution of the population we set the minimum size to a 100-meter radius neighborhood and increased the size stepwise by 100 meters until a 2000 meter size was reached. This resulted in 20 different neighborhood sizes from which to select an optimal neighborhood size.

Statistical analysis

Since the data from smaller neighborhoods are individualistic in nature, a high variance value is expected. In contrast, a low variance value is expected for larger neighborhoods. A high variance value means that data are local and low variance means that they are global. To select an optimal size of neighborhood that can ensure that the ecological data are neither local nor global, we used Hartley's test of homogeneity of variance _{MAX}, is calculated by

where

Under the null hypothesis, the test assumes that the variances are equal. The critical value (CV) was calculated under the F-distribution with (k, _{MAX }- 1) degrees of freedom at α = 0.05. Here, k is the number of groups and _{MAX }is the maximum sample size among groups.

The F_{max }test involved two steps. First the variance of each neighborhood was compared to the highest neighborhood variance (upper, F_{max1}) and then they were compared with the lowest neighborhood variance (lower, F_{max2}). A significant value (means the value does not fall within the CV) of F_{max1 }indicates that the neighborhood does not have a global structure of data, and in contrast, a significant value in F_{max2 }implies that the neighborhood data are not individualistic. The neighborhoods that are between the lower and the upper limits are the optimal neighbourhood sizes.

Results

There were 131 cases of

The data variances for the

The data variance by neighborhood size

**The data variance by neighborhood size**. Graphical presentation of the data variances for the

The test results for homogeneity variance of _{max1 }test statistic at the level α = 0.05 shows a neighborhood size above 900 meters would reveal the global structure of the data, and the F_{max2 }statistic shows that any neighborhoods below 200 meters would make the data too individualistic. Thus, the choice of optimal neighborhood lies between 200 and 900 meters. Considering the values of several parameters such as minimum population size, skewness and kurtosis of the incidence rate, we argue that a 500-meter neighborhood is optimal size for modeling the local variation of the disease incidence.

Descriptive statistics and results of variance ratio (F_{max}) test for the

r ^{†}

Population size

Incidence Rate/10000 Population

Upper F_{max }Test

Lower F_{max }Test

Min

Max

Mean

Min

Max

Mean

Variance

F_{max1}

DF_{1 }*

CV_{1 }**

F_{max2}

DF_{2 }*

CV_{2 }**

100

1

1779

158

.00

1429.00

4.612

646.023

49.116

20

1.571

1.000

1

3.842

200

1

5143

492

.00

370.40

4.451

195.453

14.860

19

1.587

**3.305**

2

2.996

300

1

7372

914

.00

208.30

4.538

108.599

8.257

18

1.604

5.949

3

2.605

400

1

9252

1416

.00

161.30

4.533

73.509

5.589

17

1.623

8.788

4

2.372

**500**

3

12265

1971

.00

144.90

4.494

52.889

4.021

16

1.644

12.215

5

2.214

600

4

15784

2571

.00

227.30

4.486

42.481

3.230

15

1.667

15.207

6

2.099

700

4

19178

3236

.00

92.59

4.441

33.666

2.560

14

1.692

19.189

7

2.010

800

4

21949

3953

.00

52.91

4.434

28.671

2.180

13

1.720

22.532

8

1.939

900

4

24982

4711

.00

38.46

4.446

25.298

**1.923**

12

1.753

25.537

9

1.880

1000

4

26772

5508

.00

35.71

4.463

22.733

1.728

11

1.789

28.418

10

1.831

1100

6

28821

6324

.00

36.50

4.4939

20.647

1.570

10

1.831

31.289

11

1.789

1200

25

31691

7160

.00

36.50

4.5101

18.831

1.432

9

1.880

34.306

12

1.753

1300

50

34877

8029

.00

46.51

4.5099

17.453

1.327

8

1.939

37.015

13

1.720

1400

63

36311

8921

.00

37.17

4.5184

16.444

1.250

7

2.010

39.286

14

1.692

1500

63

37334

9832

.00

31.65

4.5266

15.655

1.190

6

2.099

41.266

15

1.667

1600

63

38471

10760

.00

28.33

4.5429

15.116

1.149

5

2.214

42.738

16

1.644

1700

63

39259

11693

.00

28.17

4.5510

14.593

1.109

4

2.372

44.269

17

1.623

1800

63

40278

12651

.00

27.70

4.5727

14.114

1.073

3

2.605

45.772

18

1.604

1900

63

41457

13657

.00

26.32

4.5990

13.639

1.037

2

2.996

47.366

19

1.587

2000

63

42492

14703

.00

26.32

4.6152

13.153

1.000

1

3.842

49.116

20

1.571

^{† }r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV_{1 }and CV_{2 }= critical values at 95% confidence level for Upper F_{max }and Lower F_{max }respectively Bold figures in F_{max1 }and F_{max2 }are the upper and lower limit of optimal neighborhoods, and the bold figure in "r" column is the choice of optimal neighborhood size.

When looking at literacy, the F_{max1 }test statistic shows a neighborhood above 600 meters would reveal the global pattern, and the F_{max2 }test statistic demonstrates any neighborhoods below 700 meters would make the data individualist (Table _{max1 }and CV_{1 }is smaller than the difference between F_{max2 }and CV_{2 }of a 600-meter neighborhood. The summary statistics and test results of religious status under various neighborhood sizes are shown in Table

Descriptive statistics and results of variance ratio (F_{max}) test for the literacy status under various neighborhoods, Khanh Hoa Province, Vietnam, 2002. (n = 32,542)

r ^{†}

Population size

Incidence Rate/10000 Population

Upper F_{max }Test

Lower F_{max }Test

Min

Max

Mean

Min

Max

Mean

Variance

F_{max1}

DF_{1 }*

CV_{1 }**

F_{max2}

DF_{2 }*

CV_{2 }**

100

1

1859

195

.00

100.00

50.226

221.986

3.262

20

1.571

1.000

1

3.842

200

1

5681

611

.00

100.00

50.191

167.826

2.466

19

1.587

1.323

2

2.996

300

1

8362

1143

.00

88.89

50.215

146.722

2.156

18

1.604

1.513

3

2.605

400

2

11276

1785

.00

83.33

50.229

134.220

1.972

17

1.623

1.654

4

2.372

500

2

15425

2504

.00

83.33

50.250

124.628

1.831

16

1.644

1.781

5

2.214

600

2

20047

3282

.00

80.50

50.241

117.075

**1.720**

15

1.667

1.896

6

2.099

**700**

2

23875

4146

.00

80.52

50.270

110.223

1.620

14

1.692

**2.014**

7

2.010

800

2

28601

5075

.00

80.46

50.296

104.018

1.528

13

1.720

2.134

8

1.939

900

2

33159

6055

.00

80.14

50.318

98.808

1.452

12

1.752

2.247

9

1.880

1000

4

36182

7081

15.70

75.96

50.333

94.737

1.392

11

1.789

2.343

10

1.831

1100

9

39576

8129

11.11

74.55

50.344

91.235

1.341

10

1.831

2.433

11

1.789

1200

25

43628

9194

15.97

73.14

50.355

88.216

1.296

9

1.880

2.516

12

1.752

1300

25

47769

10297

16.07

72.95

50.373

85.460

1.256

8

1.939

2.598

13

1.720

1400

25

49747

11427

16.52

72.44

50.386

82.739

1.216

7

2.010

2.683

14

1.692

1500

25

51108

12580

16.54

71.57

50.390

80.180

1.178

6

2.099

2.769

15

1.667

1600

66

52454

13750

16.54

70.89

50.394

77.521

1.139

5

2.214

2.864

16

1.644

1700

128

53725

14925

16.61

70.67

50.392

74.995

1.102

4

2.372

2.960

17

1.623

1800

138

55422

16133

16.61

69.93

50.393

72.569

1.066

3

2.605

3.059

18

1.604

1900

138

57913

17398

17.36

69.52

50.394

70.210

1.032

2

2.996

3.162

19

1.587

2000

148

59428

18708

17.75

68.81

50.412

68.054

1.000

1

3.842

3.262

20

1.571

^{† }r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV_{1 }and CV_{2 }= critical values at 95% confidence level for Upper F_{max }and Lower F_{max }respectively Bold figures in F_{max1 }and F_{max2 }are the upper and lower limit of optimal neighborhoods, and the bold figure in "r" column is the choice of optimal neighborhood size.

Descriptive statistics and results of variance ratio (F_{max}) test for the ethnicity status under various neighborhoods, Khanh Hoa Province, Vietnam, 2002. (n = 32,542)

r ^{†}

Population size

Incidence Rate/10000 Population

Upper F_{max }Test

Lower F_{max }Test

Min

Max

Mean

Min

Max

Mean

Variance

F_{max1}

DF_{1 }*

CV_{1 }**

F_{max2}

DF_{2 }*

CV_{2 }**

100

1

1859

195

.00

100.00

7.283

243.304

4.026

20

1.571

1.000

1

3.842

200

1

5681

611

.00

100.00

7.344

183.209

3.032

19

1.587

1.328

2

2.996

300

1

8362

1143

.00

100.00

7.383

153.024

2.532

18

1.604

1.590

3

2.605

400

2

11276

1785

.00

100.00

7.402

133.603

2.211

17

1.623

1.821

4

2.372

500

2

15425

2504

.00

100.00

7.467

121.327

2.008

16

1.644

2.005

5

2.214

600

2

20047

3282

.00

88.57

7.534

112.520

1.862

15

1.667

**2.162**

6

2.099

**700**

2

23875

4146

.00

88.57

7.609

105.353

**1.744**

14

1.692

2.309

7

2.010

800

2

28601

5075

.00

82.50

7.682

99.320

1.644

13

1.720

2.450

8

1.939

900

2

33159

6055

.00

75.00

7.719

93.729

1.551

12

1.752

2.596

9

1.880

1000

4

36182

7081

.00

69.49

7.745

88.828

1.470

11

1.789

2.739

10

1.831

1100

9

39576

8129

.00

63.73

7.761

84.867

1.404

10

1.831

2.867

11

1.789

1200

25

43628

9194

.00

62.40

7.776

81.459

1.348

9

1.880

2.987

12

1.752

1300

25

47769

10297

.00

62.40

7.793

78.140

1.293

8

1.939

3.114

13

1.720

1400

25

49747

11427

.00

61.91

7.801

74.610

1.235

7

2.010

3.261

14

1.692

1500

25

51108

12580

.00

60.84

7.820

71.456

1.183

6

2.099

3.405

15

1.667

1600

66

52454

13750

.00

58.06

7.851

69.027

1.142

5

2.214

3.525

16

1.644

1700

128

53725

14925

.00

50.55

7.873

66.823

1.106

4

2.372

3.641

17

1.623

1800

138

55422

16133

.00

46.79

7.891

64.531

1.068

3

2.605

3.770

18

1.604

1900

138

57913

17398

.00

44.54

7.907

62.339

1.032

2

2.996

3.903

19

1.587

2000

148

59428

18708

.00

39.71

7.915

60.426

1.000

1

3.842

4.026

20

1.571

^{† }r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV_{1 }and CV_{2 }= critical values at 95% confidence level for Upper F_{max }and Lower F_{max }respectively Bold figures in F_{max1 }and F_{max2 }are the upper and lower limit of optimal neighborhoods, and the bold figure in "r" column is the choice of optimal neighborhood size.

The test results for the choice of optimal neighborhood size for shigellosis obtained from the Nha Trang subpopulation are shown in Table _{max1}test statistic reveals that a neighborhood size over 800 meters would produce a global pattern. On the other hand, the F_{max2 }test statistic illustrates that a neighborhood below 300 meter would yield an individualistic pattern. Out of the choices between 400 and 800 meters, we suggest a 400 meter neighborhood size based on the criteria mentioned above for

Descriptive statistics and results of variance ratio (F_{max}) test for shigella incidence under various neighborhoods, Nha Trang, Vietnam, 1999–2001. (n = 13565)

r ^{†}

Population size

Incidence Rate/10000 Population

Upper F_{max }Test

Lower F_{max }Test

Min

Max

Mean

Min

Max

Mean

Variance

F_{max1}

DF_{1 }*

CV_{1 }**

F_{max2}

DF_{2 }*

CV_{2 }**

100

3

5692

1015

.00

333.30

6.041

197.436

25.397

20

1.571

1.000

1

3.842

200

3

17440

3223

.00

333.30

6.155

74.927

9.638

19

1.587

2.635

2

2.996

300

3

25689

6026

.00

57.14

6.112

38.808

4.992

18

1.605

**5.088**

3

2.606

**400**

10

34531

9388

.00

41.67

6.116

28.304

3.641

17

1.624

6.976

4

2.373

500

30

47539

13112

.00

57.47

6.102

22.808

2.934

16

1.644

8.656

5

2.215

600

33

61692

17105

.00

34.36

6.121

18.871

2.427

15

1.667

10.462

6

2.099

700

33

73490

21480

.00

35.46

6.129

16.566

2.131

14

1.692

11.918

7

2.010

800

87

88015

26126

.00

27.47

6.140

14.514

**1.867**

13

1.721

13.603

8

1.939

900

87

102106

30938

.00

22.87

6.148

13.374

1.720

12

1.753

14.763

9

1.881

1000

87

111244

35834

.00

31.15

6.158

12.651

1.627

11

1.789

15.606

10

1.831

1100

87

121667

40711

.00

19.67

6.137

11.774

1.515

10

1.831

16.769

11

1.789

1200

150

134222

45547

.00

18.28

6.116

11.057

1.422

9

1.881

17.856

12

1.753

1300

425

146883

50410

.00

17.64

6.119

10.536

1.355

8

1.939

18.739

13

1.721

1400

628

152901

55270

.00

16.40

6.135

10.079

1.297

7

2.010

19.589

14

1.692

1500

628

156963

60090

1.21

15.92

6.135

9.588

1.233

6

2.099

20.592

15

1.667

1600

628

161121

64829

1.77

15.92

6.123

9.104

1.171

5

2.215

21.687

16

1.644

1700

628

165020

69457

1.21

15.92

6.129

8.751

1.126

4

2.373

22.562

17

1.624

1800

628

170190

74078

2.73

15.92

6.135

8.411

1.082

3

2.606

23.474

18

1.605

1900

628

177965

78890

2.68

15.92

6.153

8.099

1.042

2

2.996

24.378

19

1.587

2000

628

182551

83821

2.98

15.92

6.171

7.774

1.000

1

3.842

25.397

20

1.571

^{† }r = size of neighborhood in meter radius

* DF = degrees of freedom

_{1 }and CV_{2 }= critical values at 95% confidence level for Upper F_{max }and Lower F_{max }respectively Bold figures in F_{max1 }and F_{max2 }are the upper and lower limit of optimal neighborhoods, and the bold figure in "r" column is the choice of optimal neighborhood size.

To get an understanding of local geographic variation of the disease and social variables, we created isopleth maps with the spatially smoothed data by using the optimal neighborhood sizes. Spatially smoothed data are more appropriate for disease and ecological mapping than the raw data

Local geographic pattern of

**Local geographic pattern of Vibro parahaemolyticus incidence rate in Khanh Hoa province, Vietnam**. The map was created based on the household point locations, thus the upper part of the study where no households are located have been omitted during the creation of the surface map. The lighter tones indicate lower

Local geographic pattern of literacy status in Khanh Hoa province, Vietnam

**Local geographic pattern of literacy status in Khanh Hoa province, Vietnam**. The map was created based on the household point locations, thus the upper part of the study where no households are located have been omitted during the creation of the surface map. The lighter tones indicate lower literacy status and the darker tones indicate higher literacy status.

Local geographic pattern of ethnicity status in Khanh Hoa province, Vietnam

**Local geographic pattern of ethnicity status in Khanh Hoa province, Vietnam**. The map was created based on the household point locations, thus the upper part of the study where no households are located have been omitted during the creation of the surface map. The lighter tones indicate lower proportion of ethnically minority group and the darker tones indicate higher proportion of the ethnically minority group.

Local geographic pattern of shigella incidence rate in Nha Trang, Vietnam

**Local geographic pattern of shigella incidence rate in Nha Trang, Vietnam**. The map was created based on the household point locations, thus the upper part of the study where no households are located have been omitted during the creation of the surface map. The lighter tones indicate lower shigella incidence rate and the darker tones indicate higher shigella incidence rate.

Discussion and conclusion

The Hartley's F_{max }test of homogeneity provides a solution for determining the optimal neighborhood size for modeling the local variation of health and social determinants. The methodological approach illustrates that the choice of optimal neighborhood is data dependent.

Measuring ecological data at a neighborhood scale to understand the spatial variability requires considerable knowledge of the phenomenon being measured

Since spatial filtering smoothes data, average errors may be inherent in the data

One of the biggest problems in spatial epidemiology and ecological exposure assessment is in identifying geographic patterns

A scientifically validated method is required to assist geographic research

Acknowledgements

This work was supported by the Diseases of the Most Impoverished Program, funded by the Bill and Melinda Gates Foundation and coordinated by the International Vaccine Institute.