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International Journal of Health Geographics logoLink to International Journal of Health Geographics
. 2005 Jun 1;4:12. doi: 10.1186/1476-072X-4-12

Neighborhood size and local geographic variation of health and social determinants

Mohammad Ali 1,✉, Jin-Kyung Park 1, Vu Dinh Thiem 2, Do Gia Canh 2, Michael Emch 3, John D Clemens 1
PMCID: PMC1156930  PMID: 15927082

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 (Fmax) 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 Fmax 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 Fmaxtest. First the variance of each neighborhood was compared to the highest neighborhood variance (upper, Fmax1) and then they were compared with the lowest neighborhood variance (lower, Fmax2). A significant value of Fmax1 indicates that the neighborhood does not reveal the global structure of data, and in contrast, a significant value in Fmax2 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 [1-4]. Since population distributions are highly heterogeneous in space, an ordinary point plot of all cases is not useful. Smoothing data by adjusting for the population at risk is necessary to identify areas with higher disease rates [5]. Smoothing disease data can provide the true relative risk of a disease across a study area [6]. There are other reasons to filter health and ecological data. Field survey data gathering systems usually generate errors. Filtering removes random noise caused by inaccurate records or mislocated cases [1,7,8]. There are many intervening factors at the individual level that may influence spatial processes of disease phenomena. For instance, an individual's biological or socioeconomic status may influence their health status. Neighbors usually have similar risk, particularly for environmentally related diseases, unless the spatial process of the disease is exclusively affected by individual-level characteristics. Also, some risk factors of diseases genuinely operate at the population level [9].

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 [9]. Twigg et al. showed that the behavioral practices of an individual are influenced by neighbors [10]. Some variables do not make sense at the individual scale and should be modeled as ecological variables. For instance, a household with a good sanitation system can be exposed to bad sanitation from neighbors. Ecological factors are more meaningful if the data are measured by neighborhood. Spatial filtering can be used to model such neighborhood level phenomena.

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 [11-13]. Determining the neighborhood size (or the area) over which densities of the phenomena are estimated is important. A large neighborhood makes the data flat over the entire study area whereby important local level variation is obscured that could point to ecological associations. In contrast, a small neighborhood may reveal individualistic patterns [1], and that may not be useful for identifying ecological relationships with health outcomes. Defining an optimal neighborhood size is difficult [14,15]. Bailey and Gatrell [16] suggested exploring different sizes and looking at the variation at those scales to come up with an optimal neighborhood size. However, literature that describes methodologies for selecting the optimal size of neighborhood is scarce. Thus, one often chooses the scale arbitrarily, and the use of an arbitrary scale may yield spurious outcomes. This paper introduces a methodological approach for selecting the optimal neighborhood size that can be used to measure ecological variables and to investigate ecological links with local variation of diseases.

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 1). This resulted in a 394 square kilometres working study area for the entire population and 79 square kilometres for Nha Trang specifically.

Figure 1.

Figure 1

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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 Vibrio parahaemolyticus). The disease incidence data were obtained from a population-based passive surveillance system that was begun in January 1997 [17]. The socioeconomic data were obtained from a 2002 population survey. The survey data shows approximately 85% of the population is secular, 10% Buddhist, and 5% Christian. Only 11% had not attended school, 37% had received a primary education, and the rest (52%) completed secondary or higher education.

The Vibrio parahaemolyticus data were derived from the disease surveillance of the study area from 1997 to 1999. V. parahaemolyticus, a gram-negative, halophilic bacterium, inhabits marine and estuarine environments. The microorganism was first identified as a cause of food borne illness in Japan in 1950 [18]. A polymerase chain reaction (PCR) based method to detect the toxR sequence specific to Vibro parahaemolyticus was used to identify cases as reported elsewhere [19]. The shigellosis study was carried out for three years (2001–2003) in Nha Trang in collaboration with the Diseases of the Most Impoverished Program [20]. All shigellosis cases were detected through microbiological test of stool samples.

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 [21] that evaluates variation in variances across neighborhoods. The Hartley's test statistic, FMAX, is calculated by

graphic file with name 1476-072X-4-12-i1.gif

where

Inline graphic = maximum value of the variances among groups

Inline graphic = minimum value of the variances among groups

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

The Fmax test involved two steps. First the variance of each neighborhood was compared to the highest neighborhood variance (upper, Fmax1) and then they were compared with the lowest neighborhood variance (lower, Fmax2). A significant value (means the value does not fall within the CV) of Fmax1 indicates that the neighborhood does not have a global structure of data, and in contrast, a significant value in Fmax2 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 Vibro parahaemolyticus in 127 household points in the entire study area for the three years of study (1997–1999), and 308 cases of shigellosis were observed in 295 household points for the year 2001 through 2003 in Nha Trang. Out of the total 329,596 population, 31,924 (9.7%) were Buddhists who were identified in 3,681 household points of the total study area. And, a total of 168,699 (51.2%) literate persons were observed in 30,069 household points.

The data variances for the Vibro parahaemolyticus incidence rates under various neighborhood sizes show a declining trend with an increase in neigborhood size (Figure 2). The rapid decline observed at smaller scales virtually disappears with larger neighborhood sizes. The pattern is similar for shigellosis as well as for both socioeconomic variables (figures not shown).

Figure 2.

Figure 2

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The data variance by neighborhood size. Graphical presentation of the data variances for the Vibro parahaemolyticus incidence in Khanh Hoa, Vietnam under various sizes of neighborhood.

The test results for homogeneity variance of Vibro parahaemolyticus incidence rates under various neighborhood sizes are listed in Table 1. The Fmax1 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 Fmax2 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.

Table 1.

Descriptive statistics and results of variance ratio (Fmax) test for the Vibrio parahaemolyticus incidence under various neighborhoods, Khanh Hoa Province, Vietnam, 1997–99. (n = 29,211)

r † Population size Incidence Rate/10000 Population Upper Fmax Test Lower Fmax Test
Min Max Mean Min Max Mean Variance Fmax1 DF1 * CV1 ** Fmax2 DF2 * CV2 **
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
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† r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV1 and CV2 = critical values at 95% confidence level for Upper Fmax and Lower Fmax respectively Bold figures in Fmax1 and Fmax2 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 Fmax1 test statistic shows a neighborhood above 600 meters would reveal the global pattern, and the Fmax2 test statistic demonstrates any neighborhoods below 700 meters would make the data individualist (Table 2). In this case, we believe that 700 meters is the optimal size because the difference between Fmax1 and CV1 is smaller than the difference between Fmax2 and CV2 of a 600-meter neighborhood. The summary statistics and test results of religious status under various neighborhood sizes are shown in Table 3. For religion, a 700-meter size neighborhood is also appropriate.

Table 2.

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

r † Population size Incidence Rate/10000 Population Upper Fmax Test Lower Fmax Test
Min Max Mean Min Max Mean Variance Fmax1 DF1 * CV1 ** Fmax2 DF2 * CV2 **
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
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† r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV1 and CV2 = critical values at 95% confidence level for Upper Fmax and Lower Fmax respectively Bold figures in Fmax1 and Fmax2 are the upper and lower limit of optimal neighborhoods, and the bold figure in "r" column is the choice of optimal neighborhood size.

Table 3.

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

r † Population size Incidence Rate/10000 Population Upper Fmax Test Lower Fmax Test
Min Max Mean Min Max Mean Variance Fmax1 DF1 * CV1 ** Fmax2 DF2 * CV2 **
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
Open in a new tab

† r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV1 and CV2 = critical values at 95% confidence level for Upper Fmax and Lower Fmax respectively Bold figures in Fmax1 and Fmax2 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 4. The Fmax1test statistic reveals that a neighborhood size over 800 meters would produce a global pattern. On the other hand, the Fmax2 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 Vibro parahaemolyticus.

Table 4.

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

r † Population size Incidence Rate/10000 Population Upper Fmax Test Lower Fmax Test
Min Max Mean Min Max Mean Variance Fmax1 DF1 * CV1 ** Fmax2 DF2 * CV2 **
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
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† r = size of neighborhood in meter radius

* DF = degrees of freedom

**CV1 and CV2 = critical values at 95% confidence level for Upper Fmax and Lower Fmax respectively Bold figures in Fmax1 and Fmax2 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 [22]. A widely used geostatistical interpolation method called kriging [23,24] was used to create those maps. The maps ware produced as a quintile distribution for the respective phenomenon. Figure 3 shows the local geographic pattern of the Vibro parahaemolyticus incidence rate in Khanh Hoa province, Figure 4 shows the geographic pattern of literacy status in Khanh Hoa province, Figure 5 shows the pattern of religion in Khanh Hoa province, and Figure 6 shows the pattern of shigellosis incidence in Nha Trang. All of the maps show clear local geographic variation of the phenomena.

Figure 3.

Figure 3

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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 Vibro parahaemolyticus incidence rate and the darker tones indicate higher Vibro parahaemolyticus incidence rate.

Figure 4.

Figure 4

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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.

Figure 5.

Figure 5

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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.

Figure 6.

Figure 6

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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 Fmax 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. Vibrio parahaemolyticus incidence requires a scale from 200 and 900 meters, and we argued that a 500 meter neighborhood is most appropriate based on the values of other parameters. The choice of neighborhood size for social variables (i.e., literacy and religion) ranged from 600 to 700 meters, and we suggested 700 meters for both. Similarly, out of the options between 300 and 800 meters for shigellosis incidence in Nha Trang, we suggest a 400 meter neighborhood. The maps produced using optimal neighborhood sizes show clear local geographic variation of the respective phenomenon suggesting the suitability of the approach. Since the ecological process may differ from one variable to another [25], different optimal neighborhood sizes are expected. The results of our analyses confirm this notion.

Measuring ecological data at a neighborhood scale to understand the spatial variability requires considerable knowledge of the phenomenon being measured [26]. For example, dissemination of an innovation may diffuse to close neighbors through literate persons. However, the media through which it diffuses is assumed spatially heterogeneous. For instance, a friendly neighborhood may accelerate the innovation, but disputes among neighbors may impede diffusion of the innovation. It would be ideal to assign weight for these social factors while measuring ecological variables, but that requires considerable knowledge about the spatial process of the phenomenon. For sanitation status, a poorly constructed latrine can be an important source of pollution by spreading fecal matter to nearby areas. Therefore, a distance decay weight can be applied here considering there is an inverse relationship from the source of pollution [27].

Since spatial filtering smoothes data, average errors may be inherent in the data [28]. Such ecological bias [29] can be more apparent in a predefined geographic area than within the natural boundary created through spatially smoothed data using optimal neighborhood modeling. Ecological bias may also be present when modeling variables with large neighborhood sizes.

One of the biggest problems in spatial epidemiology and ecological exposure assessment is in identifying geographic patterns [29] through spatial interpolation. Selection of an interpolation method has strong implications on the representation of spatial patterns as well as on the accuracy of interpolated data [30]. Interpolating the data based on spatially smoothed data obtained by an optimal neighborhood size could provide more accuracy in the local variation of the phenomena being measured. The optimal neighborhood may help ecological analysis in two ways: aggregating the data (both dependent and independent variables) using optimal neighbourhood scales and performing the analysis at the ecological level, or by limiting the dependent variable at the individual level, but attaching ecological covariates (obtained through optimal neighbourhood size) to each individual [31].

A scientifically validated method is required to assist geographic research [32], and to properly use GIS technology in health and ecological studies [33]. In our paper, we have outlined a method to choose optimal neighbourhood sizes for addressing local spatial variation of disease and social determinants. The method can be useful in health and ecological studies.

Acknowledgments

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.

Contributor Information

Mohammad Ali, Email: mali@ivi.int.

Jin-Kyung Park, Email: jkpark@ivi.int.

Vu Dinh Thiem, Email: vudinhthiem@hn.vnn.vn.

Do Gia Canh, Email: vncddp2@hn.vnn.vn.

Michael Emch, Email: me2159@columbia.edu.

John D Clemens, Email: jclemens@ivi.int.

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