隨著醫療科技的進步，數據的訊息量呈指數增長，為了減輕醫療人力的負擔，因此期盼透過人工智慧與醫療技術的結合來協助醫師判斷病人疾病有無，常見的解決方法為運用線性判別分析來進行判別，但傳統的判別分析無法運用到高維度的張量資料上，例如：磁力共振成像(Magnetic Resonance Imaging, MRI) 影像資料與電腦斷層掃描(Computed Tomography, CT) 影像資料，除了上述問題外，許多研究都只用到單一平台資料，尚未有研究結合不同平台的資料來進行疾病的判斷，若能結合跨平台數據，可能有助於提升疾病判斷的準確率。對此，Pan et al. (2019) 提出CATCH模型，可結合張量資料與共變量資料來判別類別反應變數，並且提出矯正張量與共變量之間的線性關係的重要性，最後結合病人生理資訊資料與三維度磁振造影資料，來判斷病人屬於何種類型的注意力不足過動症，但該模型假設共變量在不同類別下需有相同的共變異數，然而此假設在實務上可能無法滿足。故本研究將該方法進行延伸，建立一個新模型(命名為CATCH+ 模型)，並透過模擬研究的方式，來比較現存模型與新模型的判別能力。最後，本研究運用上述方法，來判別大腸直腸癌是否復發與乳癌病患是否有骨質疏鬆症。

With the rapid development of technology, the information we can collect is becoming more and more various. In order to help alleviate the workload of physicians, it is expected that the combination of artificial intelligence and medical technology can assist physicians in improving the accuracy and efficiency of diagnosis. A relatively simple solution is to use linear discriminant analysis to make the discrimination, but traditional model cannot be applied to high-dimensional tensor data, such as Magnetic Resonance Imaging (MRI) data and Computed Tomography (CT) data. In addition to the abovementioned problems, many studies only use single platform data, and no studies have combined data from different platforms. Pan et al. (2019) proposed a CATCH model that integrates the covariates and the tensor to predict the categorical outcome and suggests the importance of a linear relationship between tensor and covariates. However, the model assumes the same covariance matrix of covariates in different categories, but this assumption may not be satisfied in practice. Therefore, we propose a new model called the CATCH+ model. At the end of the thesis, the proposed method is demonstrated based on the recurrence of the colon cancer and osteoporosis in breast cancer patient.

[1] 乳癌病患之骨質疏鬆問與答。取自. https://wwwv.tsgh.ndmctsgh.edu.tw/unit/10021/20013.
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