Spatial Point Pattern Analysis Of Larynx Cancer Biology Essay

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Does the pattern of larynx cancer appear to cluster, or is it completely random. Based on this very simple map, can you see any evidence to suggest that cases of larynx cancer cluster around the incinerator?

"The first - order properties of a spatial point process describe how the mean number of points per unit area (the intensity) varies through space" (Kaluzny S. P. et al 1998). Though, it may be difficult to say if the pattern of larynx is completely random, the simple map (Figure 1) above indicates that the pattern of larynx cancer has some clusters around the incinerator, to the South-East and the North of the map (indicated by red circles). This implies that it is not completely random. However, the pattern around the incineration may not be attributed to it (incinerator) as clusters also exist further away from it. The quadrat (Table 1) also shows clearly that we have high intensity/density cases of up to 3 and 4 in some cells. This further confirms that the pattern of larynx cancer is not completely random.

2. Do the maps display any areas of particularly high intensity? What is the intensity of cancer cases around the site of the incinerator?

Figure 2a: Map of Kernel Intensity. Figure 2b: 3D Image of Map of Kernel Intensity.

Figure 2c: Kernel Intensity of Larynx/Position of Incinerator.

"The second - order properties of a spatial point process describe how the interaction of spatial dependence between points through space" (Kaluzny S. P. et al 1998). It can be observed from the map of kernel intensity (Figure 2a) that the areas with cluster cases of larynx depict contours with higher values while the image in Figure 2b represents the 3D image of the contours peaks which depicts points of high intensity. The highest peak of the 3D image represents the highest density of the larynx cancer. This is also shown as the white patch in Figure 2c. The spatial point pattern distribution is further elaborated in Figure 2c where particular areas to the North and North-East of the map have high intensity. The intensity of larynx cancer around the incinerator is high as there is a cluster around it. However, it is not as high as that to the North and North - East of the incinerator. The areas of high intensity are shown by the red circles.

3. Examine the form of the function G (w). What does it tell you about the pattern of Larynx cancer?

Figure 3: Map of G (w) Function for Larynx Cancer.

In the second - order effect, if there is a need to model the interdependency of points, the nearest neighbours can be examined (Brunsdon C. 2010). "The nearest neighbour provides an objective method for looking at small scale interaction between points" (Kaluzny S. P. et al 199). The G (w) function indicates that the line in the G (w) function graph (Figure 3) climbs gradually at the base; hence, there is a tendency for point repulsion (regularity). By implication, the pattern of larynx cancer shows that there is a tendency for more regularity than interaction (clustering).

4. Look at the graph, it shows the value of K for various distances (plotted along the x - axis) compared against the value of K for CSR model - is there any evidence of clustering and if so, at what distance?

Figure 4: Plot of Larynx Cancer K - function/CSR process.

The K - function plot shows data that is very close to an expected CSR process. The plot shows an evidence of clustering in Figure 4. The farther away the K-function plot is from the CSR process the higher the tendency of clustering. The clustering is observed to have occurred from the distance 200 to 3400 units because at this point, the K (d) plot is observed to be higher than the CSR model.

5. Look at the results - how do they compare with those obtained from a graph of K (d) you constructed above?

Figure 5a: Confidence Envelope L(d) Function. Figure 5b: Plot of Larynx Cancer K - function/CSR process.

The peaks in the positive values indicate clustering and on the other hand, troughs of negative values indicate regularity in the point (Bailey T. And Gatrell A. 1995). In the K (d) plot, clustering appeared where the plot is observed to be higher than the CSR model. It can be observed from the confidence envelope that those areas with higher clusters in the CSR Model are in the positive values while those areas in the negative values indicate regularity. The points on the peaks shows that there is higher intensity clustering in lung cancer than the larynx cancer.

6. What assumption have you made about the distribution of population and what conclusion might we wrongly reach, regarding the role of the incinerator causing cancer, if we do not account for this factor?

The assumption made is that the distribution of population is not uniform and not static. This implies that the population around the incinerator may be lower than those away from it. Hence, the ratio of occurrence of larynx cancer would be in relation to the population density. It is also necessary to determine whether there is evidence of spatio-temporal clustering where data such as disease incidence has associated temporal information such as date of birth, date of death and date of diagnoses (J de Smith M et al. 2009). The conclusion that might be wrongly reach is that the incinerator may not have anything to do with the larynx cancer without considering the fact that the people would move from one point to another thereby infecting population of other areas.

7. From the results of the statistical analyses, how does the pattern of lung cancers compare to that of larynx cancer?

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LUNG CANCER LARYNX CANCER

Table 2a: Intensity/Density of Cancer Cases. Table 2b: Intensity/Density of Larynx Cases.

The data depicted in the quadrats (Tables 2a and 2b) clearly indicate that the events in each cell of lung cancer are relatively higher than larynx cancer. The intensity of lung cancer is so significant that there is a maximum of 99 units in one of the cells compared to larynx cancer which has a maximum of 4 units in its cell. Consequently, the occurrence of lung cancer is more intense lung cancer than larynx cancer per unit cell.

LUNG CANCER LARYNX CANCER

The point-pattern of lungs cancer depicts higher clusters than larynx cancer implying that lung cancer cases are significantly higher than the larynx cancer cases. Though there are clusters in both cancer cases, the clusters of lungs cancer is of higher intensity than the larynx cancer. However, the intensity around the incinerator is not as high as other places farther North - East and North of the graph (circled in red).

Highest Concentration

LUNG CANCER LARYNX CANCER

The pattern of lung cancer is observed to be more concentrated than the larynx cancer in the Kernel Intensity map (areas marked in black circles). It is noticed that the concentration is highest at the white and yellow tints of the Kernel Intensity Map. The highest concentration of lung cancer is observed to be close to the incinerator.

LUNG CANCER LARYNX CANCER

Figure 2b: 3D Kernel Intensity for Larynx.

A vital point was noted; that is, the highest intensity of lung and larynx cancer did not occur around the incinerator. However, the highest incident of lung cancer has a closer range to the incinerator than the highest incident of larynx cancer. Consequently, the highest peak of the lung cancer is closer to the incinerator than the highest peak of the larynx cancer though it may not be inferred that cancer is caused by the incinerator.

LUNG CANCER LARYNX CANCER

Figure 3: Map of G (w) Function for Lung Cancer. Figure 3: Map of G (w) Function for Larynx Cancer.

The map of G (w) Function for lung cancer and larynx cancer depicts the second order effect (degree of dependency). In the case of lung cancer, the G (w) funtion increases rapidly at the initial stage while that of larynx cancer increases gradually. This implies that the lung cancer depicts an appreciable high point interaction (cluster) compared to larynx cancer which is regular. Because the lung cancer has more cases than larynx cancer, the G(w) function of lung cancer is smoother than the larynx cancer. That means the points are closer together unlike that of larynx cancer that are spaced out. This could be observed in the graph where the curve is smooth while that of the larynx cancer is rough at the curve.

LUNG CANCER LARYNX CANCER

The pattern of the lung cancer indicates that it is generally higher than the expected CSR model. This means that the lung cancer pattern depicts higher clusters than larynx cancer. As it can be seen,there is a wider gap between the CSR model and the observed pattern of cancer in the lung cancer than the larynx cancer.

LUNG CANCER LARYNX CANCER

Figure 5a: L(d) Function.

The values of K (d), G (w) and L (d) make it more glaring that the pattern of lung cancer shows significant cluster. Furthermore, lung cancer is higher than the CSR model as against larynx cancer. There is no negative value in the graph of lung cancer indicating high intensity of cluster while larynx cancer has values below zero indicating regularity. On the whole, the level of point interaction is not as expected in lung cancer in relation to larynx cancer.

8. Assuming that the lung cancer is a good measure of the underlying population distribution, are there any parts of the study area which seem to have an excess of larynx cancers?

Bivariate K-function.

The distribution of larynx cancer is seen to be random in the area as there are no clusters seen lest close to the incinerator. If we assume that the lung cancer is a good measure of the underlying population distribution, then the area close to the incinerator has an excess of larynx cancer. This is in relation the number of cases in line with the population density at the incinerator.

9. In not more than 500 words, describe the application of point-pattern analysis in a GIS application context other than medical/health/epidemiology.

"Everything is related to everything else, but near things are more related than distant things" (Tobler, 1979).

Introduction

"Point Pattern Analysis involves the ability to describe patterns of locations of point events and test whether there is a significant occurrence of clustering of points in a particular area" (Burden F.F. 2003). Haggett et al. (1977) highlighted that spatial point patterns analysis came to prominence in geography in the late 1950s/early 1960s, when a paradigm of spatial analysis became reliable. Furthermore, he observed that researchers adopted techniques that had been used in plant ecology literature in the description of spatial patterns and applying them in other contexts such as studies of distribution of settlements, spatial arrangement of stores within cities/towns and drumlins distribution in glaciated areas. This write-up will dwell on the application of point pattern analysis in a GIS application context in relation to ecology - forestry.

Application of Point Pattern Analysis in Ecology - Forestry

"Forestry statistics is an important field of applied statistics with long tradition" (Stoyan D and Pentinen A 2000). Furthermore, Stoyan D. and Pentinen A. (2000) stated that point processes or marked point processes can be used to solve many forestry problems. In this case, "points" are location of trees and "marks" are characteristics which include diameter at breast height or level of damage by factors within the environment. Point pattern analysis can also be employed in quantifying the spatial pattern of plant communities (Criessie N.A.C 1993). However, Legedre P. and Fortin M. (1989) stated that "information on the spatial pattern of individual plants in the forests may refine our understanding of ecological process such as forest establishment, growth, competition, reproduction and mortality". Investigation of stand disturbance history can also be carried out using point pattern analysis (Moer M. 1997).

Ripley's K (t) is a second order descriptive statistics in 2 D point pattern which is widely used in point pattern analysis in forestry (Hasse P. 1995). The Ripley's is basically used to analyse spatial pattern of individual trees. To test whether an observed pattern is regularly spaced, random and aggregated, individual analysis compares the distribution of tree- to-tree distances. "Ripley's K(t) estimates are evaluated with respect to step-size distance values (t). Larger Ripley's K(t) values at a certain (t) may indicate attractive properties (clustering) among individual trees, while smaller Ripley's K(t) values at the same (t) may indicate dispersive spatial properties (regularity) among individual trees" (Woodall C.W. and Graham J.M. 2004).

Figure 1: Image showing clustered pine trees in a 10m x 10m square plot. Adopted from (Stoyan D. and Pentinen A. 2000).

Clustering and regularity may co-exist on different scales in a forest. That is, trees may be regularly distributed on a small scale especially for older trees as a result of competition among neighbours and for young trees as a result of planting in rows. However, they could be clustered on a larger scale due to ecological heterogeneity (Stoyan D. and Pentinen A. 2000). Figure 1 is an example of a clustered forest.

Conclusion

Point Pattern Analysis is a class of techniques that seeks to identify patterns in spatial data and has become prominent over the years in solving several problems. Studies showed that point pattern analysis has been applied in the study of health/epidemiology, settlement distributions, and the spatial arrangement of stores amongst others. Forestry..................................

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