3.5 Temporal analysis
4.1.2 Global Moran‟s I
Being a composite index, the global Moran‟s index is the measure of overall clustering of the data, used to evaluate the overall spatial association of the total research area. The Global Moran‟s uses the “z” statistic to evaluate the existence of clusters in the spatial arrangement of the given data and shows the level of significance with the rule that if the “z” statistic value is greater than the value 1.96 then there is statistical significance. Also, while positive sign represents positive spatial autocorrelation, the converse is true for negative. The next three Tables (Tables 4.1, 4.2 and 4.3) give a summary output of the results for the global Moran‟s index for the years 2009, 2010 and 2011.
Table 4.1: Summary Table of the Global Moran’s Index output results for year 2009
Global Moran's Index Summary
Moran's Index: -0.023716
Expected Index: -0.021739
Variance: 0.003136
z-score: -0.035293
The results in Table 4.1 above gave the summary output for the global Moran‟s index for the year 2009. We observed Global Moran‟s index to be -0.023716 with an expected value of - 0.021739, a z-score of -0.035293 and a p-value of 0.971846. The Moran‟s index evaluated whether the pattern expressed is clustered, dispersed, or random. The index found to be
-0.023716 indicated a weak negative spatial autocorrelation in our data. Although our calculated index was close to zero, it is suggested tendency towards dispersion in pediatric TB cases for the year 2009. This indicated a map pattern in which the geographic units (which are counties in our research) of similar values scattered throughout the map. The z-score of -0.035293 and a p-value of 0.971846 indicates statistical insignificance. This stated that feature values of the year 2009 were randomly distributed across the study area.
Table 4.2: Summary Table of the Global Moran’s I output results for year 2010
Global Moran's I Summary
Moran's Index: 0.045062
Expected Index: -0.021739
Variance: 0.005432
z-score: 0.96359
p-value: 0.364746
The results in Table 4.2 above gave the summary output for the global Moran‟s I for the year 2010. Global Moran‟s statistic was observed to be 0.045062 with an expected value of -
0.045062 indicated a weak positive spatial autocorrelation in the data. The positive Moran's I index value indicated tendency toward clustering in the pediatric cases for the year 2010. This
pointed out a map pattern in which the geographic units of similar values tend to cluster on the map. Also, the z-value found to be 0.96359 and p-value of 0.364746 like in 2009 depicted that there is statistical insignificance. This stated that feature values again like in 2009 were also randomly distributed across the study area. Of importance to note was the magnitude for both the Moran‟s index and also the p-value as they were in the increasing and decreasing trend respectively.
Table 4.3: Summary Table of the Global Moran’s I output results for year 2011
Global Moran's I Summary
Moran's Index: 0.096283
Expected Index: -0.021739
Variance: 0.005225
z-score: 1.632828
p-value: 0.102505
The results in Table 4.3 above presented summary output for the global Moran‟s index for year 2011. Moran‟s statistic was 0.096283 with an expected value of -0.021739, a z-score of 1.632828 and a p-value of 0.102505. The Moran‟s index found to be 0.096283 indicated a weak positive spatial autocorrelation in our data. Although our calculated index was close to zero, it
there was an increase in the Moran‟s index to 0.096283 and the positive spatial autocorrelation indicated a map pattern in which the geographic units of similar values tend to cluster on the map.
Our findings for the global Moran‟s index were similar to the results by Peng et al. (2007) which had a Moran‟s index of 0.1667 as both showed a pattern of spatial clustering. The z-score of 1.632828 and a p-value of 0.102505 still indicated that there was statistical insignificance in our data for the year 2011. Of importance was that although there was statistical insignificance in our data, there was a drift towards statistical significance as indicated by the trend over the three years of the study.
(a) (b)
(c)
Figure 4.6 Choropleth maps (a), (b) and (c) showing the distribution of incidence of pediatric TB cases over the study region for the years 2009, 2010 and 2011 respectively
Figure 4.6 above showed the incidence per 100,000 population. Figure 4.6 (a) showed the distribution for the year 2009, Figure 4.6 (b) shows the distribution for the year 2010 while Figure 4.6 (c) shows the distribution of the cases for the year 2011. We observe generally that cases of pediatric tuberculosis are in all the counties rather, all counties have been affected and that only the magnitude varies. For the year 2009, the incidence is high in the Rift valley south region and part of Nyanza and also some parts of Eastern and North Eastern as compared to other regions in the country. Particularly, Nyamira, Kisii and Bomet recorded the highest incidence in the same year. This is shown in the Figure Figure 4.7 below. In the year 2010, the counties with high incidence of cases were Marsabit, Kitui, Westpokot, Embu and Siaya. In the year 2011, the counties that were mostly affected were Kakamega, Vihiga, Kirinyaga and Meru. The other counties with high incidence were Marsabit, Isiolo, Samburu, Kilifi, Bomet, Mombasa and Nairobi.
4.1.3 Local indicators of Spatial Association (LISA)
Local spatial statistics look for specific areas in an image that have clusters of similar or dissimilar values. The Local Moran‟s index identified counties clustering. Positive values for Local Moran‟s index indicates that a feature has neighbouring features with similarly high or low attribute values; this feature is part of a cluster while negative values for Local Moran‟s index indicates that a feature has neighbouring features with dissimilar values; this feature is an outlier.
Figure 4.8 showed that some counties in the year 2009 had high-low relationship with its neighbours. These were Samburu, Nyamira, part of Kisii and Bomet. It also showed the type of relationship that existed between the counties and its neighbours as high – low and not significant.
Although showing that there was no statistical significant relationship for almost all the counties, Samburu and Nyamira both had a high – low type of relationship which indicated that the there was a high reported incidence of pediatric TB cases in these two counties and surrounded by counties with low incidence of pediatric cases. This is an indication of clustering in these counties.
Figure 4.9 below identified counties which had a statistically significant relationship with its neighbours. These included Kitui, Embu, Kirinyaga, Baringo, Uasingishu, Nandi, Kericho, Siaya and Westpokot. It also showed the type of relationships where counties shaded red indicated a high – high relationship while counties shaded yellow indicated a high – low type of relationship and that counties shaded blue indicated a low – low relationship.
For the findings of the three types of relationship, Baringo, Uasin-gishu, Nandi and Kericho counties all had a low – low type of relationship indicating that the counties had a low incidence of pediatric cases and surrounded by counties with low incidence of pediatric cases which implied clustering. Westpokot and Siaya counties had a high – low type of relationship indicating that the two counties had a high incidence of pediatric TB cases while the surrounding
counties which had a high – high type of relationship meaning that these counties had a high incidence of pediatric TB cases and the surrounding cases also had high incidence and hence implying clustering.
Figure 4.10: A map showing statistical significant relationship between counties and their neighbours in the year 2011
These were high –high and high – low. The counties observed to have a high- high relationship with its neighbours were Isiolo, Meru and some part of Samburu. This type of relationship indicated that the respective counties had a high incidence of pediatric TB and surrounded by counties with high incidence. The other type of relationship which was of high – low indicated that Kakamega and Vihiga had a high incidence and surrounded by counties with low incidence of pediatric tuberculosis. It was also observed that the type of relationship for a bigger part of our study area was classified as insignificant.
4.1.4 Hot spot detection (Getis and Ord’s local statistic)
The Getis-Ord Gi index identifies hot spots. This is useful for determining clusters of similar values, where concentrations of high values result in a high Gi value and concentrations of low values result in a low Gi value. The z-score values in Figures 4.11, 4.12 and 4.13 were used to identify the statistically significant counties. Specifically, a z-score value at 0.05 significance level would have to be less than -1.96 or greater than 1.96 to be statistically significant. Statistical significance in the negative direction implies a cold spot while in the positive direction
implies hot spots. These Figures showed the behaviour of Getis and Ord‟s local statistic for the three years.
Figure 4.11: A map showing the hot spot areas in the year 2009
Figure 4.11 above showed varying z-scores for the different counties. We observed that majority of the counties had z-score ranging between -1.65 to 1.65. Kiambu County had z-score value within the range of -1.96 and -1.65 while Migori County has z-score value within the range of 1.65 and 1.96. This could explain the distribution of pediatric cases in the year 2009 as random
(statistically insignificant) while Kiambu and Migori depicted some tendency of dispersion and clustering respectively.
Figure 4.12 above illustrated different z-score values for the year 2010. Majority of the counties had z-scores ranging within -1.65 to 1.65. Counties like Mandera, Bungoma, Kakamega, Vihiga and Siaya had a z-score ranging from -1.96 to -1.65 while Baringo, Marakwet, Uasin-gishu, Nandi, Kisumu and Kericho had z-score within the range of -2.58 to -1.96. Kitui, Makueni, Kajiado, Nairobi, Kiambu, Muranga, Embu, Meru and Kirinyaga had z-score values ranging within 1.96 to 2.58 and that Tharaka-Nithi and Machakos had z-score values greater than 2.58. hence Machakos and Tharaka-Nithi were the hot spot counties while counties surrounding them indicated tendency towards being hot spots. Baringo, Marakwet, Uasin-gishu, Nandi, Kisumu and Kericho showed tendency towards being cold spots.
The below map (Figure 4.13) showed different z-scores for the different counties in the year 2011. We observed that while majority of the counties had z-score values ranging from -1.65 to 1.65, Baringo county had a z-score within the range of -2.58 to -1.96. Marsabit had a z-score within the range of 1.65 to 1.96 while counties like Isiolo, Meru and part of Samburu had z- scores within the range of 1.96 to 2.58. There were no hot spots in the year 2011 but Isiolo and Meru showed some tendency towards being hot spot counties while Baringo showed tendency towards being a cold spot.
Figure 4.13: A map showing the hot spot areas in the year 2011
4.1.5 Temporal analysis
Spatial autocorrelation can be a valuable tool to study how spatial patterns change over time. Results of this type of analysis lead to further understanding of how spatial patterns change from
the past to the present, or estimations of how spatial patterns will change from the present to the future.
Table 4.4: A summary Table of the computed global Moran’s I for the years 2009, 2010 and 2011
Year Moran‟s I Expected (I) Variance (I) Z-Value P-Value 2009 -0.023716 -0.021739 0.003136 -0.035293 > -1.96 0.971846 2010 0.045062 -0.021739 0.005432 0.96359 < 1.96 0.364746 2011 0.096283 -0.021739 0.005225 1.632828 <1.96 0.102505
From the Table 4.4, we observed that the global Moran‟s I changed from -0.023716 for the year 2009 to 0.045062 for the year 2010 and then to 0.096283 for the year 2011 depicting an upward trend in the global statistic. The expected value (-0.021739) gave us the value of the Moran‟s I when the pattern is random. When compared with the Moran‟s I, it was observed that there was an increasing trend in clustering of pediatric TB over the years of study.
Although using the three global maps produced for the years 2009, 2010 and 2011, we could not exactly visually discern whether or not spatial patterns were becoming concentrated or more dispersed, the computed Moran‟s I statistic for the three years depicted an increasing trend in the value for Moran‟s I. It was evident therefore that there has been an overall clustering of the pediatric cases for the three years of study.
In summary, the population of children under the age of 15 years (16571877) as indicated in our methodology means that the number of children is 41430/100,000 population which forms 41.43% of the total population in Kenya. This is indeed a huge population and considering the age size, it can be classified as a vulnerable group in the sense that if infected, they are likely to develop the disease. Also, if not treated they are likely to be the agents of future epidemic.
Although an exact picture of the incidence of childhood TB is difficult because of the difficulties in the diagnosis of childhood TB, the incidence of 53/100,000 population for the year 2009, 42/100,000 population for the year 2010 and 56/100,000 population for the year 2011 from our results are a useful approximation of incidence. It is important to note that the cases could be underestimated as some children would die undiagnosed.
Figure 4.6 hinted to us that the non-uniformity in the distribution of the pediatric cases in both space and time for the different years of study allowing for further investigation. It was also observed that despite statistical non-significance in major parts of the country, the entire country has been reporting an increasing incidence of childhood TB and this if not prevented may result in the disease being a future epidemic. Other than identifying counties with significant TB clusters for high rates of pediatric TB, we were also able to identify areas with suspected elevation in risk. Spatial analysis showed hot spots of the disease.
While several studies have used GIS and spatial analysis to describe the pattern of various infectious diseases, only a handful has focused on TB. Moran's I and Getis's G statistics results
different spatial distribution. Like the findings by Tong et al., (2009), Local Moran's I statistical analysis could point out the high incidence region of childhood. Also, the findings of our study like that for Huang et al., (2010), showed that distribution of the incidence cases were not stochastic at space and time, and that clusters did exist. In consideration to LISA which is the localized version of the global Moran‟s index, the findings portrayed that the incidence of pediatric TB varied for different counties. This gave some indication that the distribution of the cases was not really random but rather, there was high concentration of cases in some parts while others had low concentration. This has been supported by the findings of Dirk et al. (2008) which indicated that the transmission of infectious diseases is closely linked to the concepts of spatial and temporal proximity and hence transmission is more likely to occur if the at-risk individuals are close in a spatial and a temporal sense.
Lastly, it was evident that there has been an overall clustering of the pediatric cases for the three years of study.