6 Spatial Point Pattern Analysis
6.6 Summary
This chapter has provided the spatial point pattern analysis for cancers recorded in the Perth metropolitan region in 2005. We have shown that cancer incidence and mortality data in 2005 for five types of cancer are inhomogeneous Poisson processes using the inhomogeneous K-function. Based on the Poisson nature of the data, the Berman-Turner algorithm was used for the model fitting. All the covariates available have been investigated for modelling. However, no covariates have been found to account for 2005 prostate cancer incidence point pattern appropriately.
Two treatments of missing values have been applied to lung cancer mortality for model fitting and it has been illustrated that point patterns have influence on the spatial point pattern analysis. The fitting is slightly better when the data are treated using method 2 than method 1.
Perth CBD is selected as the key reference point as spatial trends for modelling. For lung cancer incidence, Kwinana industrial area is also used as reference point for modelling. It has been found that the distance from Kwinana is a better spatial trend for lung cancer incidence than the distance from Perth CBD. Kriging analysis has shown that melanoma cancer incidence is high in the western Perth metropolitan area. As a result, coastline is used as the reference line as well for modelling and we have found that the coastline accounts for melanoma incidence. Two models indicate that both of them are adequate to
account for the lung cancer and melanoma cancer incidence data respectively from different perspectives.
Quantile-quantile plots have been used to check whether the fitted model is acceptable and lurking variable plots have been applied to show whether the fitted function captures the dependence of intensity on the covariates. For lung cancer incidence analysis, it has been found that the point patterns in 1993 and 2005 are quite similar. A good fit is obtained when popdens is considered for the modelling. For mortality analysis, only one covariate is enough to get an adequate fit: the susceptible population density based on year 2003.
Although the fitted intensity function captures the dependence of intensity both on the percentage of population above age 50 (aged) and the population density overall, it seems that aged contributes to lung cancer death more than population density.
For year 2005 melanoma incidence modelling, population density (popdens) accounts for more than the proportion of the people aged 30 or above (aged30+). This is probably due to the fact that melanoma cancer incidence affects any age group of people except children under the age of 10. The incidence point pattern in 2005 is quite similar to the point pattern in 2001 when population density and spatial trends are considered. For melanoma mortality model fitting, lurking variable plots indicate that the fitted intensity function captures dependence on susceptible population intensity. This covariate is enough to obtain a good fit for mortality data when spatial trend is considered.
For colorectal cancer analysis, we have shown that there are less covariates involved in fitting mortality data than fitting incidence data. For year 2005 colorectal incidence modelling, population density (popdens) accounts for data more than aged. This is probably due to the fact that colorectal cancer incidence affects any people aged 10 or over.
Spatially susceptible population density and spatial trends are not enough to obtain a good fitting for incidence point pattern in 2005. For colorectal cancer mortality model fitting, susceptible population and spatial trends are enough to get a good fitting. The adequacy of the fit is confirmed by the least variability in the image of the smoothed residual field.
For breast cancer incidence analysis, it has been found that the point pattern in 2005 is quite similar to the point pattern in 1992. A good fit is obtained when popdens is considered for the modelling. For mortality analysis, female population density (popdensf) and spatially susceptible population intensity (1999) are able to acount for the point pattern in order to get an adequate fit. Although the fitted intensity function captures the dependence of intensity on popdensf and agedf, it seems that popdensf contributes to breast cancer death more than agedf(proportion of females aged 40 above).
For prostate cancer mortality, it has been indicated that the proportion of people aged 40+
(agedm) is a better covariate than male population density (popdensm) in most cases. These two covariates only improve the fitting when working with susceptible population intensity.
The spatial trends (transformations of coordinates) and susceptible population intensity are enough to make an appropriate fitting. The estimated mortality number of prostate cancer is about 43 per 100 square kilometres in Perth 2005. Nearly all prostate cancer death is linked to prostate cancer incidence because the fitted model has been verified by the perfect capture of dependence on susceptible population intensity through lurking variable plots.
In conclusion, incidence modelling is more complex than mortality modelling. For mortality, it is often sufficient to use the susceptible population intensity in addition to the spatial trends. In contrast, for incidence modelling, the population density (or the proportion of selected age groups) is also required. Moreover, the agreement between fitted model and mortality data is usually better than that between fitted model and incidence data.
This chapter has provided the spatial point pattern analysis for cancer incidence and mortality data in Perth and the correlation between each type of cancer and covariates has been investigated. These findings will be informative to health service on the spatial distribution of cancer risks for each individual cancer incidence and mortality.