非侵入性胎兒染色體檢測 (NIPT) 是一種對孕婦相對安全的檢驗胎兒有無先天遺傳疾病的方法。因為有一部分的胎兒小片段DNA會經由臍帶、胎盤，流到孕婦的血液裡，透過抽取孕婦血液取得胎兒游離DNA，以檢測胎兒是否有先天性的疾病。本研究目的是為了在第22對染色體找到可以偵測基因DNA有缺失的統計方法，作為醫學上在進行DNA有缺失之疾病的檢測方法之依據。
　　Olshen和Venkatraman (2004) 提出環狀分段法 (Circular Binary Segmentation, CBS)，將一有序的基因讀數 (reads count) 數據連接成環狀，找出平均數有顯著差異的改變點 (change point)。本研究擬考慮基因之間有相關的情況下，混合Hotelling’s T-squared test的想法，擴展CBS的方法至多維度的情形。此外，我們將使用統計模擬方法與實例比較兩種方法的型I錯誤發生率 (Type I error rate)、檢定力及型III錯誤發生率 (Type III error rate)。

Non-invasive Prenatal Testing (NIPT) is a relatively safe way for pregnant women to test whether fetuses have congenital disease, because small segments of fetuses’ DNA will enter into blood of pregnant women through by umbilical cord and placenta. Doctors extract the blood of pregnant women to obtain fetuses’ DNA, in order to detect whether fetuses have a congenital disease. The purpose of this study is to find a statistical method which can detect DNA gene deletion on chromosome 22, as the detection method of DNA deletion disease in medicine.
Olshen and Venkatraman (2004) proposed Circular Binary Segmentation (CBS) method connecting an ordered gene in a ring to find out the position with significant differences in average of reads count as change points. This study consider correlated data of reads count between genes, mixed ideas of Hotelling's T-squared test, extended CBS to multi-dimension cases. In addition, we will use statistical simulation methods and real examples to compare Type I error rate, power and Type III error rate of both methods.

1. Hotelling, H. (1931). The generalization of Student’s ratio. Annals of Mathematical Statistics 2 (3), 360–378.
2. Lai, W.R., Johnson, M.D. et al. (2005). Comparative analysis of algorithms for identifying amplifications and deletions in array CGH data. Bioinformatics, 21, 3763–3770.
3. Linn, S. C., West, R. B. et al., (2003). Gene expression patterns and gene copy number changes in dermatofibrosarcoma protuberans. American Journal of Pathology 163, 2383–2395.
4. Olshen, A. B. and Venkatraman, E. S. (2004). Circular binary segmentation for the analysis of array based DNA copy number data. Biostatistics, 5, 557–572.
5. Sen, A. and Srivastava, M. S. (1975). On tests for detecting a change in mean. Annals of Statistics 3, 98–108.
6. Venkatraman, E. S. and Olshen, A. B. (2007). A faster circular binary segmentation algorithm for the analysis of array CGH data. Bioinformatics, 23, 657-663.
7. Willenbrock, H. and Fridlyand, J. (2005). A comparison study: applying segmentation to array CGH data for downstream analyses. Bioinformatics, 21, 4084–4091.