SVM Applied to Cancer Epidemiology

Although the exact mechanism of carcinogenesis and the exact relationships between the environmental factors and the cancer mortality are not clearly understood yet, it is already widely recognized that many trace elements are involved in the metabolism of carcinogenesis, because there are plenty of evidences to support this point of view In clinical study it has been confirmed that the contents of trace elements (especially the contents of Se, Zn, Cu, Co, Mo) of cancer tissue and that of normal tissue around are always different [51 66 128]. The content of Se and Zn/Cu ratio in the serum of cancer patients are also abnormal compared with that of normal persons. And there are data that the intake quantity of trace elements and the breast cancer mortality in different regions indeed exhibit obvious correlation [141], as illustrated by Table 12.1. 

Based on the data listed in Table 12.1, the relationship between trace element intake and breast cancer mortality found by support vector regression can be expressed as follows  

2 SVR applied to find multiple correlation coefficients between the cancer mortality and trace element content in soil of different provinces and regions of China 

The detailed metabolism of leucocythemia is not very clear yet, but it has been known that LiiCOj or AS2O3 can be used to treat the acute leucocythemia. And it is also found that the trace element contents in the hair or blood of leucocythemia patients are abnormal compared with that of the ordinary persons. So it is interesting to investigate if there are some correlations between the amount of trace elements in soil and the mortality of leucocythemia of different local regions. 

If we define the regions with mortality lower than 2x10 as the samples of class 1 , and that higher than 2x10 as samples of class 2 , and make classification by SVM. The criterion of class 1 obtained can be expressed as follows  

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