生存分析-隨機(jī)森林試驗(yàn)與代碼

1、隨機(jī)森林模型在生存分析中的應(yīng)用【摘要】目的：本文探討隨機(jī)森林方法用于高維度、強(qiáng)相關(guān)、小樣本的生存資料分析時，可以起到變量篩選的作用。方法：以乳腺癌數(shù)據(jù)集構(gòu)建乳腺癌轉(zhuǎn)移風(fēng)險評估模型為實(shí)例進(jìn)行實(shí)證分析，使用隨機(jī)森林模型進(jìn)行變量選擇，然后擬合cox回歸模型。結(jié)果：隨機(jī)森林模型通過對變量的選擇，有效的解決數(shù)據(jù)維度高且強(qiáng)相關(guān)的情況，得到了較高的AUC值。一、數(shù)據(jù)說明該乳腺癌數(shù)據(jù)集來自于NCBI,有77個觀測值以及22286個基因變量。通過篩選選取454個基因變量。將數(shù)據(jù)隨機(jī)分為訓(xùn)練集合測試集，其中2/3為訓(xùn)練集,1/3為測試集。繪制K-M曲線圖：UEUUnJ*士AJM二、隨機(jī)森林模型隨機(jī)森林由許多的決策

2、樹組成，因?yàn)檫@些決策樹的形成采用了隨機(jī)的方法，因此也叫做隨機(jī)決策樹。隨機(jī)森林中的樹之間是沒有關(guān)聯(lián)的。當(dāng)測試數(shù)據(jù)進(jìn)入隨機(jī)森林時，其實(shí)就是讓每一顆決策樹進(jìn)行分類，最后取所有決策樹中分類結(jié)果最多的那類為最終的結(jié)果。因此隨機(jī)森林是一個包含多個決策樹的分類器，并且其輸出的類別是由個別樹輸出的類別的眾數(shù)而定。使用randomForestSRC包得到的隨機(jī)森林模型具有以下性質(zhì)：Numberofdeaths:27Numberoftrees:800Minimumterminalnodesize:3Averageno.ofterminalnodes:14.4275No.ofvariablestriedateach

3、split:3Totalno.ofvariables:452Analysis:RSFFamily:survSplittingrule:logrankErrorrate:19.87%發(fā)現(xiàn)直接使用隨機(jī)森林得到的模型，預(yù)測誤差很大，達(dá)到了19.8%,進(jìn)一步考慮使用隨機(jī)森林模型進(jìn)行變量選擇，結(jié)果如下：>our.rf$rfsrc.refit.objSamplesize:52Numberofdeaths:19Numberoftrees:500Minimumterminalnodesize:2Averageno.ofterminalnodes:11.554No.ofvariablestriedatea

4、chsplit:3Totalno.ofvariables:9Analysis:RSFFamily:survSplittingrule:logrank*random*Numberofrandomsplitpoints:10Errorrate:11.4%>our.rf$topvars1 "213821_s_at""219778_at""204690_at""220788_s_at""202202_s_at”6"211603_s_at""213055_at"&quo

5、t;219336_s_at""37892_at"一共選取了9個變量，同時誤差只有11.4%接下來，使用這些變量做cox回歸，剔除模型中不顯著(>0.01)的變量，最終參與模型建立的變量共有4個。模型結(jié)果如下：exp(coef)exp(-coef)lower.95upper.95'218150_at'1.65410.60460.1108624.6800'200914_x_at'0.99151.00860.340942.8833'220788_s_at'0.26493.77500.059441.1805'2

6、01398_s_at'1.74570.57290.331099.2038'201719_s_at'2.47080.40470.938086.5081'202945_at'0.41182.42840.039904.2499'203261_at'3.15020.31740.3364129.4983'203757_s_at'0.78611.27200.616561.0024'205068sat'0.10739.31800.022230.5181最后選取六個變量擬合生存模型，繪制生存曲線如下:CoxModel026

7、810丁12Time下面繪制訓(xùn)練集：ROCffl線，分別在訓(xùn)練集和測試集上繪制ROC®線,結(jié)果如下:gHqoQotrETSCd8ZJ1000.20.406081.0Time-dependentROCcurveFalsePositiveRate測試集:Time-dependentROCcurve80o1.FalsePositiveRate由于測試集上的樣本過少，所以得到的AUC值波動大，考慮使用bootstrap多次計(jì)算訓(xùn)練集上的AUC值并求平均來測試模型的效果：AUCat1year0.8039456AUCat3year:0.6956907AUCat5year:0.7024846由此可

8、以看到，隨機(jī)森林通過刪除貢獻(xiàn)較低的變量，完成變量選擇的工作，在測試集上具有較高的AUC值，但是比lasso-cox模型得到的AUC略低。附錄：10ad("/R/brea.rda")library(survival)set.seed(10)i<-sample(1:77,52)train<-dati,test<-dat-i,library(randomForestSRC)disease.rf<-rfsrc(Surv(time,status).,data=train,ntree=800,mtry=3,nodesize=3,splitrule="l

9、ogrank")disease.rfour.rf<-var.select(object=disease.rf,vdv,method="vh.vimp",nrep=50)our.rf$rfsrc.refit.objour.rf$topvarsindex<-numeric(var.rf$modelsize)for(iin1:var.rf$modelsize)indexi<-which(names(dat)=var.rf$topvarsi)data<-dat,c(1,2,index)i<-sample(1:77,52)train<-d

10、atai,test<-data-i,mod.brea<-coxph(Surv(time,status).,data=train)train_data<-train,c(1,2,which(summary(mod.brea)$coefficients,5<=0.1)+2)tset_data<-test,c(1,2,which(summary(mod.brea)$coefficients,5<=0.1)+2)mod.brea1<-coxph(Surv(time,status).,data=train_data)summary(mod.brea1)names

11、(coef(mod.brea1)plot(survfit(mod.brea1),xlab="Time",ylab="Proportion",main="CoxModel",=TRUE,col=c("black","red","red"),ylim=c(0.6,1)index0<-numeric(length(coef(mod.brea1)coefficients<-coef(mod.brea1)name<-gsub("",

12、"",names(coefficients)for(jin1:length(index0)index0j<-which(names(dat)=namej)library(survivalROC)riskscore<-as.matrix(dati,index0)%*%as.matrix(coefficients)y1<-survivalROC(Stime=train$time,status=train$status,marker=riskscore,predict.time=1,span=0.25*(nrow(train)A(-0.20)y3<-sur

13、vivalROC(Stime=train$time,status=train$status,marker=riskscore,predict.time=3,span=0.25*(nrow(train)A(-0.20)y5<-survivalROC(Stime=train$time,status=train$status,marker=riskscore,predict.time=5,span=0.25*(nrow(train)A(-0.20)a<-matrix(data=c("y1","y3","y5",y1$AUC,y3

14、$AUC,y5$AUC),nrow=3,ncol=2);aplot(y1$FP,y1$TPype="l",xlab="FalsePositiveRate",ylab="TruePositiveRate",main="Time-dependentROCcurve",col="green")lines(y3$FP,y3$TP,col="red",lty=2)lines(y5$FP,y5$TP,col="blue",lty=3)legend("bott

15、omright",bty="n",legend=c("AUCat1year:0.9271","AUCat3years:0.8621","AUCat5years:0.8263"),col=c("green","red","blue"),lty=c(1,2,3),cex=0.9)abline(0,1)riskscore<-as.matrix(dat-i,index0)%*%as.matrix(coefficients)y1<-surviv

16、alROC(Stime=test$time,status=test$status,marker=riskscore,predict.time=1,span=0.25*(nrow(train)A(-0.20)y3<-survivalROC(Stime=test$time,status=test$status,marker=riskscore,predict.time=3,span=0.25*(nrow(train)A(-0.20)y5<-survivalROC(Stime=test$time,status=test$status,marker=riskscore,predict.ti

17、me=5,span=0.25*(nrow(train)A(-0.20)a<-matrix(data=c("y1","y3","y5",y1$AUC,y3$AUC,y5$AUC),nrow=3,ncol=2);aplot(y1$FP,y1$T|Pype=T,xlab="FalsePositiveRate",ylab="TruePositiveRate”,main="Time-dependentROCcurve",col="green")lines(y3$FP,y

18、3$TP,col="red",lty=2)lines(y5$FP,y5$TP,col="blue",lty=3)legend("bottomright",bty="n",legend=c("AUCat1year:0.8761","AUCat3years:0.7611","AUCat5years:0.7611"),col=c("green","red","blue"),lty=c(1,2,3),ce

19、x=0.9)abline(0,1)a<-matrix(0,30,3)for(cin1:30)i<-sample(1:77,52)train<-datai,test<-data-i,mod.brea<-coxph(Surv(time,status).,data=train)train_data<-train,c(1,2,which(summary(mod.brea)$coefficients,5<=0.1)+2)tset_data<-test,c(1,2,which(summary(mod.brea)$coefficients,5<=0.1)+2)mod.brea1<-coxph(Surv(time,status).,data=train_data)names(coef(mod.br