隨著次世代基因定序(Next Generation Sequencing, NGS)與人工受孕(In Vitro Fertilization, IVF)的成熟發展，到目前為止，已經有許多生物研究針對女性生殖道系統中的菌相做分析，證實女性生殖道系統中的微生物群落分佈會影響妊娠相關的結果。例如，女性在懷孕期間的生殖道菌相若是由乳酸桿菌主導的，則卵子能有較高的著床率並提高懷孕的機率。除此之外，也有許多研究從統計的角度進行分析，並利用狄利克雷多項式分配(Dirichlet-Multinomial Distribution)來描述獨立樣本中的微生物群落分佈。但臨床試驗多為重複測量的成對資料，因此本研究主要是考慮成對資料的微生物群落分佈，建立成對卜瓦松模型(Model of Paired-Poisson, MPP)，並對微生物群落做多元尺度分析(Metric Multi-Dimensional Scaling, MMDS)或主成分分析(Principal Component Analysis, PCA)進行降維。之後，引入貝式理論，利用多元常態分佈模型對成對樣本資料進行分群。最後，透過統計模擬成對資料，並利用本研究所提出的分群模型進行分群，與K組平均演算法(K-means algorithm)及階層式分群演算法(Hierarchical clustering algorithm)的分群結果做比較。若成對資料的各群分佈差異足夠大，則兩者的分群結果一致；若成對資料的各群分佈有重疊，則本研究所提出的分群模型結果會比較好。而實例資料中，因為不容易符合理論假設，無論是K組平均演算法或是本研究所提出的分群模型，分群結果皆與實際有落差。

With the development of Next Generation Sequencing (NGS) and In vitro fertilization, so far, many biological studies have analyzed the microflora in the female reproductive tract system and confirmed that the microbial community will affect related outcomes of pregnancy. For example, if the reproductive tract of a woman is dominated by Lactobacillus during pregnancy, the ovum will have a higher implantation rate and increase the probability of pregnancy. In addition, many studies analyzed the microflora from the statistical point of view, and used Dirichlet multinomial distribution to describe the microbial community in independent samples. However, the data of most clinical trials are repeated measurements. Therefore, our research mainly considers the microbial community of paired data and establishes a Model of Paired Poisson (MPP). After dimension reduction by metric multi-dimensional scaling method (MMDS) or principal component analysis (PCA) of microbial community, Bayesian theory is introduced and multivariate normal distribution model is used to cluster paired sample data. Finally, this study simulates paired data, and uses the clustering model proposed in this study to grouping subjects. Compared with the clustering results of K-means algorithm and Hierarchical clustering algorithm, if the distribution of each group of paired data is separated enough, the clustering results of the three algorithms are consistent. If the distribution of each group of paired data overlaps, the results of the clustering model proposed in this study will be better. However, in the real data, because it is not easy to conform the theoretical hypothesis, the clustering results of either the K-means algorithm or the clustering model proposed in this study are different from the actual results.

1. Chun, J. and F.A. Rainey, Integrating genomics into the taxonomy and systematics of the Bacteria and Archaea. International Journal of Systematic and Evolutionary Microbiology, 2014. 64(2): p. 316-324.
2. Schloss, P.D. and J. Handelsman, Toward a census of bacteria in soil. PLoS Comput Biol, 2006. 2(7): p. e92.
3. Ohshima, C., H. Takahashi, S. Insang, C. Phraephaisarn, P. Techaruvichit, R. Khumthong, H. Haraguchi, K. Lopetcharat and S. Keeratipibul, Next-generation sequencing reveals predominant bacterial communities during fermentation of Thai fish sauce in large manufacturing plants. LWT, 2019. 114: p. 108375.
4. Shin, J., S. Lee, M.-J. Go, S.Y. Lee, S.C. Kim, C.-H. Lee and B.-K. Cho, Analysis of the mouse gut microbiome using full-length 16S rRNA amplicon sequencing. Scientific Reports, 2016. 6(1): p. 1-10.
5. Ott, S., M. Musfeldt, D. Wenderoth, J. Hampe, O. Brant, U. Fölsch, K. Timmis and S. Schreiber, Reduction in diversity of the colonic mucosa associated bacterial microflora in patients with active inflammatory bowel disease. Gut, 2004. 53(5): p. 685-693.
6. Luan, C., L. Xie, X. Yang, H. Miao, N. Lv, R. Zhang, X. Xiao, Y. Hu, Y. Liu and N. Wu, Dysbiosis of fungal microbiota in the intestinal mucosa of patients with colorectal adenomas. Scientific Reports, 2015. 5(1): p. 1-9.
7. Peters, B.A., J.A. Shapiro, T.R. Church, G. Miller, C. Trinh-Shevrin, E. Yuen, C. Friedlander, R.B. Hayes and J. Ahn, A taxonomic signature of obesity in a large study of American adults. Scientific Reports, 2018. 8(1): p. 1-13.
8. Gagliardi, A., V. Totino, F. Cacciotti, V. Iebba, B. Neroni, G. Bonfiglio, M. Trancassini, C. Passariello, F. Pantanella and S. Schippa, Rebuilding the gut microbiota ecosystem. International Journal of Environmental Research and Public Health, 2018. 15(8): p. 1679.
9. Weaver, C.M., Diet, gut microbiome, and bone health. Current Osteoporosis Reports, 2015. 13(2): p. 125-130.
10. Kupcinskas, J. and G.L. Hold, Other Helicobacters and the gastric microbiome. Helicobacter, 2018. 23: p. e12521.
11. Mailhe, M., D. Ricaboni, V. Vitton, J.-M. Gonzalez, D. Bachar, G. Dubourg, F. Cadoret, C. Robert, J. Delerce and A. Levasseur, Repertoire of the gut microbiota from stomach to colon using culturomics and next-generation sequencing. BMC Microbiology, 2018. 18(1): p. 1-11.
12. Chen, C., X. Song, W. Wei, H. Zhong, J. Dai, Z. Lan, F. Li, X. Yu, Q. Feng and Z. Wang, The microbiota continuum along the female reproductive tract and its relation to uterine-related diseases. Nature Communications, 2017. 8(1): p. 1-11.
13. Van Oostrum, N., P. De Sutter, J. Meys and H. Verstraelen, Risks associated with bacterial vaginosis in infertility patients: a systematic review and meta-analysis. Human Reproduction, 2013. 28(7): p. 1809-1815.
14. Romero, R., S.K. Dey and S.J. Fisher, Preterm labor: one syndrome, many causes. Science, 2014. 345(6198): p. 760-765.
15. Nelson, D.B., A.L. Hanlon, G. Wu, C. Liu and D.N. Fredricks, First trimester levels of BV-associated bacteria and risk of miscarriage among women early in pregnancy. Maternal and Child Health Journal, 2015. 19(12): p. 2682-2687.
16. Holmes, I., K. Harris and C. Quince, Dirichlet multinomial mixtures: generative models for microbial metagenomics. PloS One, 2012. 7(2): p. e30126.
17. Tvedebrink, T., Overdispersion in allelic counts and θ-correction in forensic genetics. Theoretical population biology, 2010. 78(3): p. 200-210.
18. La Rosa, P.S., J.P. Brooks, E. Deych, E.L. Boone, D.J. Edwards, Q. Wang, E. Sodergren, G. Weinstock and W.D. Shannon, Hypothesis testing and power calculations for taxonomic-based human microbiome data. PloS One, 2012. 7(12): p. e52078.
19. Shi, P. and H. Li, A model for paired‐multinomial data and its application to analysis of data on a taxonomic tree. Biometrics, 2017. 73(4): p. 1266-1278.
20. Ding, T. and P.D. Schloss, Dynamics and associations of microbial community types across the human body. Nature, 2014. 509(7500): p. 357-360.
21. Turnbaugh, P.J., M. Hamady, T. Yatsunenko, B.L. Cantarel, A. Duncan, R.E. Ley, M.L. Sogin, W.J. Jones, B.A. Roe and J.P. Affourtit, A core gut microbiome in obese and lean twins. Nature, 2009. 457(7228): p. 480-484.
22. Mardia, K.V., Kent, J.T. and Bibby, J.M., Multivariate Analysis,1979. Academic Press, London.
23. 線代啟示錄(2013)。跡數與行列式的導數。檢字https://ccjou.wordpress.com/2013/06/03/%E8%B7%A1%E6%95%B8%E8%88%87%E8%A1%8C%E5%88%97%E5%BC%8F%E7%9A%84%E5%B0%8E%E6%95%B8/(2021年5月21)
24. Mehta, C.R., The exact analysis of contingency tables in medical research. Statistical Methods in Medical Research, 1994. 3(2): p. 135-156.
25. Lewis, C.D., Industrial and Business Forecasting Methods,1982. Butterworths Publishing, London.
26. 線代啟示錄(2013)。古典多維標度法(MDS)。檢字https://ccjou.wordpress.com/2013/05/29/%E5%8F%A4%E5%85%B8%E5%A4%9A%E7%B6%AD%E6%A8%99%E5%BA%A6%E6%B3%95-mds/(2021年5月21)
27. Manco, M., L. Putignani and G.F. Bottazzo, Gut microbiota, lipopolysaccharides, and innate immunity in the pathogenesis of obesity and cardiovascular risk. Endocrine Reviews, 2010. 31(6): p. 817-844.
28. Stanislawski, M.A., D. Dabelea, L.A. Lange, B.D. Wagner and C.A. Lozupone, Gut microbiota phenotypes of obesity. NPJ Biofilms and Microbiomes, 2019. 5(1): p. 1-9.
29. Ding, C., Y. Yu and Q. Zhou, Bacterial Vaginosis: Effects on Reproduction and Its Therapeutics. Journal of Gynecology Obstetrics and Human Reproduction, 2021: p. 102174.