在某個地理空間的區域範圍下，除了可得知當地居民是否罹患某種特殊疾病外，並同時紀錄病患的居住地點，可估計罹患該疾病的相對風險，並觀察其在空間上的變化情形。在此研究中，我們利用核估計法去估計相對風險，其中如何選擇頻寬成為我們有興趣探討的主題。若罹患該疾病的人數遠小於所有觀察對象的人數時，是否需要將對照組與病例組的頻寬設為一樣，亦是我們另一項研究重點。本研究在估計相對風險函數時，利用三種交叉驗證方法去選擇頻寬，並以誤差平方積分值來衡量估計結果好壞。藉此在對照組與病例組數量懸殊的情況下，達到更好的估計結果，以估計罹患疾病的相對風險。 To estimate some disease relative risk, we ask whether residents suffer from particular disease on the certain region and record the residence of patient. We estimate the relative risk and observe the changes in the space. In our study, we use kernel estimation method to estimate relative risk and interest in choosing the bandwidth of kernel estimation. Another focus of our study, we set the bandwidths of case group and control group whether to be same when the number of patients is much less than the observations. We propose three cross-validation methods to select the bandwidth and use the integrated square errors (ISE) to evaluate the estimation results. For the above purposes, we achieve better estimation result of disease relative risk when the number have wide gap between the case group and control group.
