基于統(tǒng)計(jì)學(xué)習(xí)的影像遺傳學(xué)方法綜述

郝小可 李蟬秀 嚴(yán)景文 沈 理 張道強(qiáng)

近年來(lái),神經(jīng)影像學(xué)伴隨著認(rèn)知神經(jīng)科學(xué)的發(fā)展為人腦工作機(jī)制的研究帶來(lái)了新的活力.同時(shí)隨著無(wú)創(chuàng)式腦成像技術(shù)的發(fā)展,研究者們希望能夠從腦結(jié)構(gòu)和腦功能的層次來(lái)研究與情緒加工相關(guān)的腦活動(dòng)影響,從而探索神經(jīng)系統(tǒng)疾病易感性個(gè)體差異的神經(jīng)基礎(chǔ).其中,常用的相關(guān)腦成像包括結(jié)構(gòu)磁共振成像(Structural magnetic resonance imaging, sMRI)、功能磁共振成像(Functional magnetic resonance imaging,fMRI)、彌散張量成像(Diあusion tensor imaging,DTI)、正電子發(fā)射斷層掃描成像(Positron emission tomography,PET).與此同時(shí),隨著遺傳學(xué)技術(shù)的發(fā)展,研究者們可以從更精細(xì)的分子水平(例如單核苷酸多態(tài)性(Single nucleotide polymorphism,SNP))來(lái)尋找神經(jīng)系統(tǒng)疾病和精神疾病相關(guān)的遺傳標(biāo)記.

在神經(jīng)影像學(xué)和分子遺傳學(xué)的基礎(chǔ)之上,Hariri等提出了影像遺傳學(xué)(Imaging genetics或Imaging genomics)這一概念,即結(jié)合多模態(tài)神經(jīng)影像學(xué)和遺傳學(xué)方法,檢測(cè)腦結(jié)構(gòu)及與神經(jīng)疾病、認(rèn)知和情緒調(diào)節(jié)等行為相關(guān)腦功能的遺傳變異[1?3].

其運(yùn)用腦影像技術(shù)將腦的結(jié)構(gòu)與功能作為表型來(lái)評(píng)價(jià)基因?qū)€(gè)體的影響,探討基因是如何影響大腦的神經(jīng)結(jié)構(gòu)和功能,以及由此導(dǎo)致的神經(jīng)系統(tǒng)病理.研究遺傳與大腦結(jié)構(gòu)和功能的相關(guān)性,在“基因與腦”之間架起一座看得見(jiàn)的橋梁[4?6],可以更好地揭示神經(jīng)精神疾病的發(fā)病機(jī)制.影像遺傳學(xué)這種工具同時(shí)還可以識(shí)別出某種腦疾病的生物學(xué)指標(biāo)或其內(nèi)表型,為預(yù)測(cè)和診斷疾病提供了更精確的方法.具體來(lái)說(shuō),由于SNP是在基因組水平上單個(gè)核苷酸變異引起的DNA序列多態(tài)性,在一定程度上反映了個(gè)體的遺傳特性,因此,研究者大多考慮將SNP作為關(guān)聯(lián)分析的基因型數(shù)據(jù).在內(nèi)表型數(shù)據(jù)獲取中,研究者大多采用臨床上廣泛使用的MRI腦影像數(shù)據(jù)進(jìn)行分析:sMRI作為度量大腦結(jié)構(gòu)組織的成像技術(shù),能夠量化分析形態(tài)學(xué)(如灰質(zhì)體積)的異常; fMRI作為血氧水平依賴(lài)功能成像技術(shù),無(wú)論靜息態(tài)還是任務(wù)態(tài),都能夠反映不同腦區(qū)的激活程度,從而產(chǎn)生明顯的信號(hào)差異.基于不同模態(tài)腦成像技術(shù),目前影像遺傳學(xué)主要關(guān)注基因SNP與腦結(jié)構(gòu)、功能、連接關(guān)聯(lián)分析的相關(guān)研究[7?10].

早期的影像遺傳學(xué)是單變量成對(duì)的統(tǒng)計(jì)分析方法,即通過(guò)多次檢驗(yàn),發(fā)現(xiàn)SNP或者基因與復(fù)雜疾病或可測(cè)的數(shù)量性狀(Quantitative trait,QT)的關(guān)聯(lián)性研究方法.而全基因組關(guān)聯(lián)研究(Genomewide association study,GWAS)正是利用全基因組高通量測(cè)序技術(shù),對(duì)研究對(duì)象的基因組中序列變異進(jìn)行分型,并利用生物統(tǒng)計(jì)學(xué)和生物信息學(xué)的方法,最終篩選出具有顯著性的SNP[11].自從2005年Science上發(fā)表的第一篇有關(guān)年齡相關(guān)性視網(wǎng)膜黃斑變性(Age-related macular degeneration) GWAS研究論文[12]以來(lái),該方法也被用在精神疾病的分析上[13].GWAS在影像遺傳學(xué)的研究中發(fā)揮了極大的作用,但是也存在一些問(wèn)題,比如,嚴(yán)格的多重校正,使得許多微小效應(yīng)的變異無(wú)法通過(guò)校正水平.其次,GWAS僅僅能得到遺傳變異跟性狀之間的單個(gè)關(guān)聯(lián)程度,并不能很好地解釋其中的復(fù)雜機(jī)制.

近年來(lái),隨著統(tǒng)計(jì)學(xué)習(xí)在學(xué)術(shù)界和工業(yè)界迅速發(fā)展,許多領(lǐng)域已經(jīng)嘗試?yán)眠@些數(shù)據(jù)分析工具來(lái)解決本領(lǐng)域的一些問(wèn)題.而在影像遺傳學(xué)的關(guān)聯(lián)分析中,相對(duì)于單變量統(tǒng)計(jì)分析,基于多變量的統(tǒng)計(jì)學(xué)習(xí)技術(shù)的應(yīng)用最為廣泛,同時(shí)也取得了非常理想的效果.國(guó)際上,一些學(xué)者也撰寫(xiě)了影像遺傳學(xué)的相關(guān)方法綜述文獻(xiàn):1)Medland等針對(duì)使用傳統(tǒng)的單變量統(tǒng)計(jì)模型處理大規(guī)模全基因組—全腦影像關(guān)聯(lián)分析提出了所面臨的問(wèn)題和挑戰(zhàn),回顧了研究者在不同中心數(shù)據(jù)庫(kù)(其中包括ENIGMA1http://enigma.ini.usc.edu/、IMAGEN2http://www.imagen-europe.com/、IMAGENMEND3http://www.imagemend.eu/以及ADNI4等)的研究成果[14];2)Liu等主要對(duì)獨(dú)立成分分析(ICA)等其他多變量方法在影像遺傳學(xué)中的應(yīng)用進(jìn)行了歸納和總結(jié)[15];3)Thompson等在綜述中重點(diǎn)回顧了基因與大腦結(jié)構(gòu)連接(DTI)與功能網(wǎng)絡(luò)(靜息態(tài)fMRI)之間的相關(guān)分析工作[16].本文在以上綜述工作的基礎(chǔ)上,首先對(duì)基于統(tǒng)計(jì)學(xué)習(xí)的遺傳—影像關(guān)聯(lián)研究進(jìn)展進(jìn)行回顧,如圖1所示,其中包括單變量和多變量統(tǒng)計(jì)學(xué)習(xí)方法;本文重點(diǎn)關(guān)注基于結(jié)構(gòu)化的多變量分析建模思路和算法框架,即通過(guò)生物學(xué)過(guò)程以及醫(yī)學(xué)領(lǐng)域知識(shí)(如代謝通路/網(wǎng)絡(luò)、多模態(tài)融合、診斷信息等)誘導(dǎo)的方法獲得更好的關(guān)聯(lián)性能和生物解釋;最后,對(duì)遺傳影像學(xué)中一些待解決的問(wèn)題以及未來(lái)研究發(fā)展方向進(jìn)行了展望.

1 單變量分析方法

單基因變量統(tǒng)計(jì)分析中最常見(jiàn)的方法是設(shè)立實(shí)驗(yàn)組和對(duì)照組進(jìn)行皮爾森卡方檢驗(yàn)(Pearson′s chisquared test)作為等位基因檢測(cè)方法,即通過(guò)分析各種病癥的一組病人和一組正常對(duì)照者的相應(yīng)基因組位點(diǎn)之間是否有統(tǒng)計(jì)差異來(lái)確認(rèn)該位點(diǎn)是否是致病基因的.基于單變量統(tǒng)計(jì)方法的基因—影像關(guān)聯(lián)分析可以使用線(xiàn)性回歸(Linear regression)和方差分析(Analysis of variance)模型作為等位基因的關(guān)聯(lián)分析方法[17].多次單變量模型,假設(shè)基因特征維數(shù)為p,影像特征維數(shù)為q,則需要擬合p×q個(gè)線(xiàn)性回歸模型(yj=βjkxk),檢測(cè)所有p×q個(gè)零假設(shè)(null hypothesesH0:βjk=0),最后對(duì)p值(p-value)進(jìn)行排序.例如,一個(gè)較早的經(jīng)典工作是來(lái)自2009年P(guān)otkin等在病例與對(duì)照組和影像表現(xiàn)型上進(jìn)行全基因組GWAS關(guān)聯(lián)分析,SNP對(duì)腦區(qū)定量表現(xiàn)型的影響可以通過(guò)廣義的線(xiàn)性模型來(lái)計(jì)算,該模型由影像表現(xiàn)型、疾病診斷和基因數(shù)據(jù)共同構(gòu)建,表達(dá)式如下:

其中,Y表示神經(jīng)影像某一腦區(qū)的QT,bi表示各個(gè)變量系數(shù),SNP×diagnosis表示相互作用的關(guān)系.模型分析得到的顯著p值即為SNP與QT相關(guān)的檢測(cè)結(jié)果[18].

在單變量基因—腦影像關(guān)聯(lián)檢測(cè)中,我們根據(jù)研究問(wèn)題的規(guī)模,將其歸納成不同的尺度[19]:在基因?qū)用姘?)候選基因/SNP[20?23],2)相關(guān)生物功能特性通路/網(wǎng)絡(luò)[24?26],3)全基因組[18,27?30];相應(yīng)的在腦影像層面包括 1)個(gè)別感興趣區(qū)域[18,20,24,27],2)包含多個(gè)感興趣區(qū)的回路[21,25,28], 3)全腦[22?23,26,29?30].無(wú)論是候選基因位點(diǎn)SNP與神經(jīng)影像[31]、腦脊液[32]、認(rèn)知量表得分[33]等其他任何QT關(guān)聯(lián)分析,還是全基因組與神經(jīng)影像關(guān)聯(lián)分析[29],甚至可以考慮全基因組與更小粒度的體素級(jí)別的腦影像之間進(jìn)行關(guān)聯(lián)分析[30],線(xiàn)性回歸與方差分析的方法都可以解決不同尺度的影像遺傳學(xué)研究問(wèn)題.在單變量基因影像關(guān)聯(lián)分析研究中,有些研究者已經(jīng)發(fā)布了相關(guān)的統(tǒng)計(jì)分析軟件,如Plink5http://pngu.mgh.harvard.edu/～purcell/plink/download.shtml[34].

圖1 基于統(tǒng)計(jì)學(xué)習(xí)的影像遺傳學(xué)關(guān)聯(lián)分析研究方法Fig.1 Association analysis in imaging genetics based on statistical learning

GWAS遺傳統(tǒng)計(jì)分析要從上百萬(wàn)甚至上千萬(wàn)個(gè)SNP中發(fā)現(xiàn)與疾病表型的關(guān)聯(lián).盡管可以利用Bonferroni校正來(lái)嚴(yán)格地控制顯著性[35?36],但是這種策略會(huì)導(dǎo)致許多微小效應(yīng)的變異無(wú)法通過(guò)校正水平,而多個(gè)這樣的微小效應(yīng)變異有可能會(huì)共同作用從而對(duì)性狀產(chǎn)生較大的影響.單變量分析方法在影像遺傳學(xué)中的應(yīng)用具有較為直觀的解釋性,能夠簡(jiǎn)單快速地檢測(cè)出單個(gè)SNP與單個(gè)QT之間的關(guān)聯(lián)程度,但由于數(shù)據(jù)變量的高維特性而導(dǎo)致的很大數(shù)量的多重比較最終使得統(tǒng)計(jì)測(cè)試結(jié)果不具有顯著性,而且上述檢驗(yàn)方法基于一個(gè)嚴(yán)格的假設(shè),即基因位點(diǎn)或者影像特征變量之間是統(tǒng)計(jì)獨(dú)立的,而忽略了變量之間相關(guān)性這一重要信息.因此,面對(duì)單變量方法存在的不足,在高維特征的基因—影像關(guān)聯(lián)分析這一研究問(wèn)題中仍然需要在方法學(xué)上進(jìn)行改進(jìn)和創(chuàng)新.

2 多變量分析方法

繼2010年Stein等提出基于單變量體素級(jí)別的全基因組關(guān)聯(lián)分析(vGWAS)[30]之后,Hibar等提出了一種基于多變量的體素級(jí)別全基因組關(guān)聯(lián)分析(Voxel-wise gene-wide association study,vGeneWAS)[37?38].該方法將一個(gè)基因內(nèi)的所有SNP通過(guò)主成分回歸(Principal components regression, PCReg)的方法來(lái)解決變量共線(xiàn)性的問(wèn)題,首先在SNP回歸變量集上使用主成分分析(Principle component analysis,PCA)獲得最大化方差的相互正交因子,然后對(duì)這些正交因子使用標(biāo)準(zhǔn)的偏F測(cè)試(Partial F-test).Hibar等使用與Stein等在2010年工作中相同的基因和腦影像數(shù)據(jù)集,通過(guò)SNP形成的若干個(gè)基因的分組,然后聯(lián)合這些分組后的SNP與體素級(jí)別的影像進(jìn)行關(guān)聯(lián)測(cè)試.實(shí)驗(yàn)結(jié)果表明,該方法獲得了更好的關(guān)聯(lián)性能,并且減少了統(tǒng)計(jì)測(cè)試的次數(shù).因此,為了增強(qiáng)基因與性狀的關(guān)聯(lián)檢測(cè)能力,一些學(xué)者和研究人員通過(guò)使用多變量方法來(lái)解決影像遺傳學(xué)中多基因或多位點(diǎn)聯(lián)合效應(yīng)的關(guān)聯(lián)問(wèn)題[15,39].近年來(lái),基于統(tǒng)計(jì)學(xué)習(xí)的影像遺傳學(xué)研究備受關(guān)注,很多工作是通過(guò)求解目標(biāo)函數(shù)的優(yōu)化問(wèn)題來(lái)實(shí)現(xiàn)檢測(cè)和識(shí)別具有高度關(guān)聯(lián)的基因和影像特征.而基因—影像關(guān)聯(lián)問(wèn)題可以通過(guò)多變量基因特征輸入X、單變量影像表型QT輸出Y的廣義線(xiàn)性回歸函數(shù)進(jìn)行描述,模型表達(dá)式如下:

Kohannim等使用改進(jìn)的嶺回歸(Ridge regression)模型增強(qiáng)了基因與影像關(guān)聯(lián)的檢測(cè)能力[46?47],即使用基于Lasso的回歸模型評(píng)估了全基因組與候選腦區(qū)體積的關(guān)聯(lián)效應(yīng),發(fā)現(xiàn)了多個(gè)敏感基因,且這些基因通過(guò)了全基因組顯著性測(cè)試.

2.1 多變量基因回歸單變量影像

基于L1范數(shù)懲罰約束的回歸模型[48?49]已經(jīng)被成功地應(yīng)用到多變量基因數(shù)據(jù)分析中,即識(shí)別出與特定腦區(qū)高度關(guān)聯(lián)的稀疏SNP位點(diǎn),從而為處理檢測(cè)和識(shí)別高維基因SNP特征選擇的小樣本回歸問(wèn)題提供了一種普適的技術(shù)框架.然而,基于L1范數(shù)的約束并沒(méi)有充分考慮特征變量之間的結(jié)構(gòu)關(guān)系,因此,在理論上并不能達(dá)到最佳的回歸結(jié)果.在考慮了融合SNP特征之間的空間結(jié)構(gòu)關(guān)系之后,Silver等提出了使用成組稀疏[50?52]的模型來(lái)解決影像遺傳學(xué)問(wèn)題.這些關(guān)聯(lián)模型傾向于選擇處于同一個(gè)組中的SNP位點(diǎn)或者傾向于選擇相鄰的特征變量,其正則化形式表達(dá)如下:

圖2 樹(shù)型結(jié)構(gòu)引導(dǎo)稀疏回歸模型[54]Fig.2 Tree-guided sparse regression model[54]

2.2 多變量影像回歸單變量基因

在基于統(tǒng)計(jì)學(xué)習(xí)的影像遺傳學(xué)研究中,大部分的工作集中在發(fā)現(xiàn)和檢測(cè)與影像相關(guān)聯(lián)的多變量基因位點(diǎn),而很少有研究探索當(dāng)表型測(cè)量變量變化時(shí)SNP值的變化情況,即利用表型QT特征回歸基因型SNP的值.Wang等提出了任務(wù)相關(guān)的縱向稀疏回歸模型來(lái)實(shí)現(xiàn)縱向影像表型與基因型的關(guān)聯(lián)分析[56].該回歸模型損失函數(shù)的表達(dá)形式如下:

其中,X為影像數(shù)據(jù),Y為基因數(shù)據(jù),該模型需要學(xué)習(xí)優(yōu)化的關(guān)聯(lián)系數(shù)是一個(gè)張量形式W={W1,···,WT}∈Rq×p×T,d為影像表型變量特征數(shù),p為回歸任務(wù)SNP的個(gè)數(shù),T為縱向時(shí)間點(diǎn)數(shù)(T=4,分別為基線(xiàn)、6個(gè)月、12個(gè)月和24個(gè)月).正則化約束表示形式如下:

實(shí)際上,?longitudinal(W)是L21范數(shù)的一種推廣形式,如圖3所示,通過(guò)在多個(gè)回歸任務(wù)以及多個(gè)時(shí)間點(diǎn)上特征權(quán)重的聯(lián)合約束,能夠選擇出與任務(wù)相關(guān)的縱向影像表型特征標(biāo)志.當(dāng)p=1時(shí),Y表示風(fēng)險(xiǎn)基因SNP位點(diǎn),該模型可以從表型到基因型分析的新視角來(lái)研究單個(gè)基因?qū)Υ竽X結(jié)構(gòu)和功能變化的影響.

在單變量基因多變量影像關(guān)聯(lián)分析中,絕大多數(shù)的研究都是針對(duì)單模態(tài)表型QT.而為研究基因與多模態(tài)腦影像之間的關(guān)聯(lián),Hao等通過(guò)構(gòu)建從腦影像X到基因Y的回歸模型并引入L21范數(shù)作為正則化約束的方法實(shí)現(xiàn)了多模態(tài)影像與候選風(fēng)險(xiǎn)基因位點(diǎn)的關(guān)聯(lián)分析[57],其正則化表達(dá)形式如下:

圖3 任務(wù)相關(guān)的縱向稀疏回歸模型[56]Fig.3 Task-correlated longitudinal sparseregression model[56]

2.3 多變量基因回歸多變量影像

上述的基因位點(diǎn)多變量分析只是針對(duì)于單個(gè)影像QT的回歸,并不能充分利用影像多變量特征之間的相關(guān)關(guān)系.近年來(lái),也有一些方法是專(zhuān)門(mén)解決多變量基因輸入多變量影像輸出的問(wèn)題,如組稀疏多任務(wù)回歸和特征選擇模型[58],如圖5所示.多任務(wù)回歸使用了本文第2.2節(jié)中多模態(tài)特征選擇相同的表達(dá)形式作為一種可以用來(lái)約束多個(gè)聯(lián)合相關(guān)表型與基因變量產(chǎn)生關(guān)聯(lián)的正則化項(xiàng),表達(dá)形式如下:

圖4 多模態(tài)關(guān)聯(lián)模型[57]Fig.4 Multi-modality association model[57]

圖5 組稀疏多任務(wù)回歸和特征選擇模型[58]Fig.5 Group-sparse multi-task regression and feature selection model[58]

此外,Wang等還考慮到SNP位點(diǎn)之間的連鎖不平衡LD結(jié)構(gòu)關(guān)系,利用||W||G2,1正則化項(xiàng)在模型中嵌入SNP的成組關(guān)系這一先驗(yàn)信息,使得在同一個(gè)LD組中的SNP被同時(shí)檢測(cè)到,表達(dá)形式如下:

實(shí)驗(yàn)結(jié)果表明這些嵌入多變量基因結(jié)構(gòu)的稀疏學(xué)習(xí)模型所篩選出的位點(diǎn)對(duì)于回歸任務(wù)具有較小的誤差,從而在關(guān)聯(lián)分析中具有更好的性能.該模型能夠檢測(cè)到多個(gè)相關(guān)的基因位點(diǎn)與多個(gè)相關(guān)腦區(qū)的聯(lián)合關(guān)聯(lián).

另外一種低秩回歸(Reduced rank regression, RRR)的模型作為廣義線(xiàn)性回歸模型的擴(kuò)展,也可以解決多變量基因輸入和多變量影像標(biāo)記輸出的關(guān)聯(lián)分析問(wèn)題.其模型的表達(dá)形式如下:

其中,權(quán)重矩陣W∈Rp×q滿(mǎn)足 rank(W)≤min(p,q),即權(quán)重矩陣可以分解成兩個(gè)秩為r的滿(mǎn)秩矩陣W=BAT,其中B∈Rp×r,A∈Rq×r.權(quán)重矩陣W的分解不但可以減少關(guān)聯(lián)分析中需要估計(jì)的參數(shù),而且可以分別對(duì)基因和影像變量進(jìn)行稀疏化約束.稀疏的低秩回歸模型(Sparse reduced rank regression,SRRR)6http://wwwf.imperial.ac.uk/～gmontana/psrrr.htm,如圖6所示,通過(guò)使用L1范數(shù)分別對(duì)A和B進(jìn)行約束實(shí)現(xiàn)對(duì)相關(guān)SNP和影像QT的特征選擇[59?60].為方便求解,可以假設(shè)XTX=I以及Γ=I,SRRR的目標(biāo)函數(shù)形式如下:

圖6 稀疏低秩回歸模型[59?60]Fig.6 Sparse reduced rank regression model[59?60]

在實(shí)際應(yīng)用中常取r=1,即A和B分別為影像和基因特征的權(quán)重向量.實(shí)驗(yàn)結(jié)果表明,相對(duì)多次單變量線(xiàn)性模型,SRRR模型能夠進(jìn)行多變量基因型輸入多變量表現(xiàn)型輸出的關(guān)聯(lián)分析,在檢測(cè)和識(shí)別相關(guān)變量問(wèn)題中具有更好的性能.該模型還可以通過(guò)引入更加豐富的生物學(xué)過(guò)程等先驗(yàn)信息進(jìn)行擴(kuò)展.

2.4 多變量基因多變量影像雙變量關(guān)聯(lián)分析

在影像遺傳學(xué)研究中,多變量回歸模型已經(jīng)能夠很好地解決基因或者影像預(yù)測(cè)因子特征選擇的問(wèn)題;而對(duì)于多輸出的變量特征,多任務(wù)回歸模型[58http://www.iu.edu/～hdbig/SCCA/,61]可以在一定程度上考慮多個(gè)回歸輸出變量之間的協(xié)方差結(jié)構(gòu)關(guān)系.但是高維的回歸輸出會(huì)產(chǎn)生較高的計(jì)算時(shí)間代價(jià),而且多變量輸出結(jié)構(gòu)復(fù)雜,僅簡(jiǎn)單地考慮對(duì)多個(gè)回歸任務(wù)進(jìn)行成組約束進(jìn)行關(guān)聯(lián)分析的模型往往過(guò)于嚴(yán)格和理想化.為了充分考慮雙多變量之間的協(xié)方差結(jié)構(gòu),Liu等提出了使用并行獨(dú)立成分分析(Parallel independent component analysis,PICA)7http://mialab.mrn.org/software/ fi t/index.html[62?63]方法來(lái)分析具有關(guān)聯(lián)機(jī)制的基因與影像數(shù)據(jù),從而發(fā)現(xiàn)這兩種模態(tài)數(shù)據(jù)的最大相關(guān)獨(dú)立成分.但是該方法并不能恢復(fù)產(chǎn)生貢獻(xiàn)的SNP和影像中的重要腦區(qū),從而導(dǎo)致這些成分喪失了合理的生物標(biāo)記解釋性.另外一種類(lèi)型的雙多變量模型,如典型相關(guān)分析(Canonical correlation analysis,CCA)[64?65]或者偏最小二乘回歸(Partial least squares regression,PLS)[66?67]可以分別尋找兩組變量中的線(xiàn)性組合使得基因和影像兩塊數(shù)據(jù)之間的相關(guān)性或者協(xié)方差最大,相對(duì)回歸模型,可以更好地解決多變量基因多變量影像關(guān)聯(lián)分析這一問(wèn)題.在此以經(jīng)典的CCA模型為例闡述雙多變量關(guān)聯(lián)方法,該類(lèi)模型能夠找到兩組模態(tài)數(shù)據(jù)特征變量之間的相關(guān)性,其表達(dá)形式如下:

其中c1和c2分別為控制特征向量稀疏性的參數(shù).將稀疏學(xué)習(xí)引入多基因多影像關(guān)聯(lián)分析中,模型可以自動(dòng)地從高維的雙變量中選擇具有相關(guān)性的稀疏SNP和QT特征變量.然而,SCCA的一個(gè)主要問(wèn)題是該模型仍然沒(méi)有充分考慮特征變量之間的結(jié)構(gòu)關(guān)系,即很多先驗(yàn)信息并沒(méi)有被用到模型的建立中,例如同一個(gè)LD塊中基因位點(diǎn)SNP之間可能具有某些共同的特性,以及大腦在完成某種功能時(shí)需要多個(gè)腦區(qū)協(xié)同工作.因此,在多基因多影像關(guān)聯(lián)的研究中,為了彌補(bǔ)傳統(tǒng)SCCA的不足,很多學(xué)者利用各種先驗(yàn)信息對(duì)SCCA模型進(jìn)行了擴(kuò)展和改進(jìn)[73?76].例如,Yan等提出了嵌入淀粉樣蛋白轉(zhuǎn)錄先驗(yàn)信息的結(jié)構(gòu)化SCCA模型8http://www.iu.edu/～hdbig/SCCA/,如圖7所示.該模型利用組稀疏正則化約束將SNP位點(diǎn)的LD塊成組的先驗(yàn)信息嵌入SCCA優(yōu)化模型中[73],表達(dá)形式如下:

其中,L2范數(shù)約束組內(nèi)的特征變量盡可能具有相同的權(quán)重貢獻(xiàn),即在關(guān)聯(lián)分析中更傾向于選擇同一個(gè)LD塊中的SNP位點(diǎn);L1范數(shù)通過(guò)約束組間的稀疏性來(lái)選擇少數(shù)具有強(qiáng)關(guān)聯(lián)的LD塊.此外,該模型還引入了大腦功能網(wǎng)絡(luò)信息作為腦區(qū)變量特征相似性的先驗(yàn)知識(shí),即當(dāng)大腦網(wǎng)絡(luò)中的連接權(quán)重較高時(shí)則兩個(gè)腦區(qū)結(jié)點(diǎn)具有相似的特性(基因表達(dá)高度相關(guān)),其正則化約束表達(dá)形式如下:

圖7 稀結(jié)構(gòu)化稀疏的雙多變量關(guān)聯(lián)模型[73]Fig.7 Structured sparse bi-multivariate correlation model[73]

3 總結(jié)和展望

影像遺傳學(xué)作為新興的前沿交叉學(xué)科,涉及到了神經(jīng)科學(xué)、影像學(xué)、遺傳學(xué)、醫(yī)學(xué)、生物統(tǒng)計(jì)學(xué)、數(shù)據(jù)挖掘、統(tǒng)計(jì)學(xué)習(xí)等多種科學(xué)和研究技術(shù).而基因組、多模態(tài)影像組數(shù)據(jù)(包括不同時(shí)間點(diǎn)的縱向腦影像)也為影像遺傳學(xué)研究提供了豐富的數(shù)據(jù)實(shí)驗(yàn)平臺(tái),使得基因與腦結(jié)構(gòu)或者功能之間產(chǎn)生關(guān)聯(lián)的致病機(jī)制能夠通過(guò)具有遺傳特性的影像內(nèi)表型呈現(xiàn)出來(lái).統(tǒng)計(jì)學(xué)習(xí)技術(shù)作為基于數(shù)據(jù)驅(qū)動(dòng)的關(guān)聯(lián)分析強(qiáng)有力工具,通過(guò)充分發(fā)掘和利用基因與影像等生物標(biāo)記數(shù)據(jù)內(nèi)在的結(jié)構(gòu)信息,能夠分析易感基因與大腦結(jié)構(gòu)或者功能的相關(guān)性,更好地揭示腦認(rèn)知行為或者相關(guān)疾病的產(chǎn)生機(jī)制.本文回顧了近年來(lái)基于稀疏學(xué)習(xí)的關(guān)聯(lián)分析算法在影像遺傳學(xué)研究領(lǐng)域的應(yīng)用,大量的實(shí)驗(yàn)和報(bào)告顯示模型所檢測(cè)到的部分關(guān)聯(lián)結(jié)果也在生物和醫(yī)學(xué)界得到了驗(yàn)證.

本文所回顧的基于結(jié)構(gòu)化方法的多變量影像遺傳學(xué)研究之所以可以取得很好的效果,是因?yàn)閿?shù)據(jù)分析的模型中嵌入了大量的先驗(yàn)知識(shí)(例如LD能夠刻畫(huà)SNP之間的簡(jiǎn)單結(jié)構(gòu)關(guān)系).而本文所歸納總結(jié)的結(jié)構(gòu)化多變量方法正是通過(guò)生物學(xué)過(guò)程以及醫(yī)學(xué)領(lǐng)域知識(shí)(如代謝通路/網(wǎng)絡(luò)、多模態(tài)融合、診斷信息等)誘導(dǎo)的一般性方法.在此基礎(chǔ)上,研究者可以對(duì)先驗(yàn)信息進(jìn)行補(bǔ)充、對(duì)模型進(jìn)行拓展.目前有一些工作已經(jīng)考慮了利用更具有遺傳功能生物特性的先驗(yàn)知識(shí)應(yīng)用在模型的建立和學(xué)習(xí)訓(xùn)練中,其中包括基因本體(Gene ontology,GO)、功能標(biāo)注、通路分析系統(tǒng)(如KEGG(Kyoto encyclopedia of genes and genomes)通路數(shù)據(jù)庫(kù)或者OMIM (Online mendelian inheritance in man)疾病數(shù)據(jù)庫(kù)等)[52,77].那么如何根據(jù)這些先驗(yàn)知識(shí)設(shè)計(jì)更加適合實(shí)際應(yīng)用問(wèn)題的模型進(jìn)行數(shù)據(jù)分析,即實(shí)現(xiàn)假設(shè)驅(qū)動(dòng)與數(shù)據(jù)驅(qū)動(dòng)相結(jié)合[78],以期待得到更好的關(guān)聯(lián)結(jié)果依然是當(dāng)前的研究熱點(diǎn).

盡管結(jié)構(gòu)化多基因多影像性狀的關(guān)聯(lián)結(jié)果可以在一定程度上解釋遺傳效應(yīng),但是對(duì)于影響同一性狀表現(xiàn)的多個(gè)非等位基因之間可能存在交互關(guān)系即異位顯性(Epistasis)的機(jī)制并不是十分清楚.目前已經(jīng)有一些工作是針對(duì)SNP之間的交互作用對(duì)影像QT的研究[79].這些方法主要是基于遍歷成對(duì)搜索的方法.例如,Hibar等利用迭代確定獨(dú)立篩選(Sure independence screening,SIS)算法實(shí)現(xiàn)并檢測(cè)出與某個(gè)腦區(qū)性狀顯著關(guān)聯(lián)的SNP-SNP之間的交互作用[80].這些遍歷搜索帶來(lái)相當(dāng)高的計(jì)算時(shí)間代價(jià),而一些高效的稀疏模型[49]對(duì)于多次交互關(guān)系的異位顯性研究有望提供高效的學(xué)習(xí)算法.對(duì)于高維特征變量基因位點(diǎn)檢測(cè)的效率問(wèn)題,除了提高算法本身的效率以外,還可以通過(guò)引入分布式并行計(jì)算方法完成大數(shù)據(jù)的計(jì)算[81].因此,還需要進(jìn)一步發(fā)展和構(gòu)建更加高效的算法模型或者工作框架來(lái)進(jìn)行全基因組和全腦特征變量交互的影像遺傳學(xué)研究.

在以往的影像遺傳學(xué)研究中,大多數(shù)工作采用無(wú)監(jiān)督的關(guān)聯(lián)分析,即僅僅關(guān)注基因與腦結(jié)構(gòu)或者功能之間的關(guān)系,忽略了診斷類(lèi)別或相關(guān)的量表得分信息.而目前有一些研究工作已經(jīng)通過(guò)引入診斷信息來(lái)指導(dǎo)模型進(jìn)行基因—影像關(guān)聯(lián)分析.例如, Vounou等采用“兩步”策略,首先選擇具有判別性的腦影像區(qū)域,然后再進(jìn)行其與基因的關(guān)聯(lián)分析[60].隨后,Batmanghelich為了避免“兩步”策略的關(guān)聯(lián)信息損失,基于貝葉斯框架設(shè)計(jì)了融合基因、影像、診斷三者邏輯聯(lián)系的模型,將腦影像特征作為一個(gè)中間表型來(lái)檢測(cè)與疾病相關(guān)的遺傳變異,同時(shí)地進(jìn)行基因和影像特征的選擇[82];這種產(chǎn)生式建模方法,帶來(lái)了良好的關(guān)聯(lián)解釋性,但是在具體實(shí)現(xiàn)中計(jì)算復(fù)雜程度較高.Hao等通過(guò)構(gòu)建基于多類(lèi)別診斷標(biāo)記信息引導(dǎo)的多模態(tài)結(jié)構(gòu)和功能影像的模型來(lái)檢測(cè)與候選風(fēng)險(xiǎn)基因位點(diǎn)相關(guān)聯(lián)的一致性腦區(qū)[83];但是對(duì)于這樣的單輸出回歸模型,并不能用于發(fā)現(xiàn)和檢測(cè)與影像相關(guān)的多變量基因位點(diǎn).上述基于引入監(jiān)督信息的基因與影像關(guān)聯(lián)的研究目的是為了獲得腦認(rèn)知行為或者疾病產(chǎn)生的機(jī)制,為疾病的診斷和預(yù)測(cè)提供依據(jù),但是最終并沒(méi)有顯式地應(yīng)用在疾病的診斷預(yù)測(cè)中;另一方面,也有一些研究只關(guān)注疾病診斷分類(lèi)問(wèn)題,即直接將基因與影像等多模態(tài)數(shù)據(jù)進(jìn)行簡(jiǎn)單的特征融合作為預(yù)測(cè)因子以提高分類(lèi)精度[42,61,84],但其中并沒(méi)有涉及多模態(tài)數(shù)據(jù)之間的相關(guān)性分析而缺乏復(fù)雜致病機(jī)制的解釋性.因此,如何對(duì)基因、腦影像、量表得分、診斷信息數(shù)據(jù)構(gòu)建聯(lián)合關(guān)聯(lián)、回歸和分類(lèi)的多任務(wù)統(tǒng)一模型[85],既能揭示基因與腦影像之間的關(guān)聯(lián)性同時(shí)又實(shí)現(xiàn)基于生物標(biāo)志特征的疾病診斷和預(yù)測(cè),也將成為影像遺傳學(xué)未來(lái)研究的發(fā)展方向.

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