R/meta.RateR.R

In exactmeta: Exact fixed effect meta analysis

meta.RateR <-
function(data.mi, BB.grdnum=5000, B.sim=10000, cov.prob=0.95, print=T, studyCI=T, midp=T, ratio.upper=1000)
  {
    data.orginal=data.mi

   if(sum(data.mi[,1])+sum(data.mi[,2])>0){ 
    data.mi=data.mi[data.mi[,1]+data.mi[,2]>0,,drop=F]
    n=length(data.mi[,1])
    n1=data.mi[,1];             n2=data.mi[,2]
    e1=data.mi[,3];             e2=data.mi[,4]
    lambda1=n1/e1;              lambda2=n2/e2
     
    id=(1:n)[n1*n2==0]
    lambda1[id]=(n1[id]+0.5)/e1[id];  
    lambda2[id]=(n2[id]+0.5)/e2[id]
    
    weight=(e1*e2/(e1+e2))/sum(e1*e2/(e1+e2))
    lambda1.pool=sum(lambda1*weight)
    lambda2.pool=sum(lambda2*weight)
    varlambda1=1/n1
    varlambda2=1/n2
   
  
    mu.MH=log(lambda2.pool)-log(lambda1.pool);  
    sd.MH=sqrt(sum(varlambda2*weight^2)/lambda2.pool^2+sum(varlambda1*weight^2)/lambda1.pool)

    ci.MH=c(mu.MH-qnorm((1+cov.prob)/2)*sd.MH, mu.MH+qnorm((1+cov.prob)/2)*sd.MH)
    p.MH=1-pchisq(mu.MH^2/sd.MH^2,1)
 
    d0=min(log(ratio.upper)/4, max(abs(ci.MH)))
    BB.grdnum=2*(round(BB.grdnum/2))+1
    delta.grd=exp(seq(-d0*4, d0*4,length=BB.grdnum)); 
    
    pv1.pool=pv2.pool=numeric(0)
    for(kk in 1:n)
      { xx1=data.mi[kk,1]
        xx2=data.mi[kk,2] 
        ee1=data.mi[kk,3] 
        ee2=data.mi[kk,4]
        fit=prateR.exact(xx1, xx2, ee1, ee2, delta.grd, midp=midp)
        pv1.pool=rbind(pv1.pool, fit$pv1); pv2.pool=rbind(pv2.pool, fit$pv2)
        if(print==T)
          cat("study=", kk, "\n")
      }
        

    sigma0=1/e1+1/e2
    
    set.seed(100)
    tnull=matrix(0,B.sim,3)
    y=matrix(runif(B.sim*n), n, B.sim)
    y=y/(1+1e-2)
    tnull[,1]=apply(-log(1-y)/sigma0, 2, sum)
    tnull[,2]=apply(y/sigma0, 2, sum)
    tnull[,3]=apply(asin(y)/sigma0, 2, sum)


    alpha0=(1+cov.prob)/2; 
    cut=rep(0,3)
    for(b in 1:3)
       cut[b]=quantile(tnull[,b], 1-alpha0)
        

    t1=t2=matrix(0,BB.grdnum,3)
    pv1.pool=pv1.pool/(1+1e-2)
    pv2.pool=pv2.pool/(1+1e-2)
    t1[,1]=apply(-log(1-pv1.pool)/sigma0, 2, sum);  t2[,1]=apply(-log(1-pv2.pool)/sigma0, 2, sum)
    t1[,2]=apply(pv1.pool/sigma0, 2, sum);          t2[,2]=apply(pv2.pool/sigma0, 2, sum)
    t1[,3]=apply(asin(pv1.pool)/sigma0, 2, sum);    t2[,3]=apply(asin(pv2.pool)/sigma0, 2, sum)
    

    ci.fisher=  c(min(delta.grd[t1[,1]>=cut[1]]),max(delta.grd[t2[,1]>=cut[1]]))
    ci.cons=    c(min(delta.grd[t1[,2]>=cut[2]]),max(delta.grd[t2[,2]>=cut[2]]))
    ci.iv=c(min(delta.grd[t1[,3]>=cut[3]]),max(delta.grd[t2[,3]>=cut[3]]))    
    ci.MH=exp(ci.MH)
    ci.range=c(min(delta.grd), max(delta.grd))

    est.fisher=delta.grd[abs(t2[,1]-t1[,1])==min(abs(t2[,1]-t1[,1]))][1]    
    est.cons=delta.grd[abs(t2[,2]-t1[,2])==min(abs(t2[,2]-t1[,2]))][1]    
    est.iv=delta.grd[abs(t2[,3]-t1[,3])==min(abs(t2[,3]-t1[,3]))][1]    
    est.MH=exp(mu.MH)
    est.range=NA

    if(sum(n1)==0)
      {ci.fisher[2]=ci.cons[2]=ci.iv[2]=Inf;
       est.fisher=est.cons=est.iv=Inf}

    if(sum(n2)==0)
      {ci.fisher[1]=ci.cons[1]=ci.iv[1]=0
       est.fisher=est.cons=est.iv=0}

    n0=(BB.grdnum+1)/2
    c1=t1[n0,]; c2=t2[n0,]

    p.fisher=  min(1, 2*min(c(1-mean(tnull[,1]>=c1[1]), 1-mean(tnull[,1]>=c2[1]))))
    p.cons=    min(1, 2*min(c(1-mean(tnull[,2]>=c1[2]), 1-mean(tnull[,2]>=c2[2]))))
    p.iv=min(1, 2*min(c(1-mean(tnull[,3]>=c1[3]), 1-mean(tnull[,3]>=c2[3]))))


    pvalue=c(p.cons, p.iv, p.fisher, p.MH, NA)
    ci=cbind(ci.cons, ci.iv, ci.fisher,ci.MH, ci.range)
    ci=rbind(c(est.cons, est.iv, est.fisher, est.MH,  est.range), ci, pvalue)
    ci=round(ci, 5)
    rownames(ci)=c("est", "lower CI", "upper CI", "p")
    colnames(ci)=c("constant", "inverse-variance", "fisher", "asymptotical-MH", " range")
    }else 
    {ci=rbind(rep(NA, 4), rep(0, 4), rep(Inf, 4), rep(1, 4))
     rownames(ci)=c("est", "lower CI", "upper CI", "p")
     colnames(ci)=c("constant", "inverse-variance", "fisher", "asymptotical-MH")
    }

  
###########################################################################################
    study.ci=NULL

    if(studyCI==T)
      {data.mi=data.orginal
       n=length(data.mi[,1])
 
       study.ci=matrix(0, n, 4)
       colnames(study.ci)=c("est", "lower CI", "upper CI", "p")
       rownames(study.ci)=1:n

       for(kk in 1:n) 
          {xx1=data.mi[kk,1]
           xx2=data.mi[kk,2]
           ee1=data.mi[kk,3]
           ee2=data.mi[kk,4] 
           fit=ci.RateR(xx1, xx2, ee1, ee2, cov.prob=cov.prob, midp=midp)        
           study.ci[kk,2]=fit$lower
           study.ci[kk,3]=fit$upper
           study.ci[kk,1]=fit$est
           study.ci[kk,4]=fit$p
           

           rownames(study.ci)[kk]=paste("study ", kk)
           }
       }


    return(list(ci.fixed=ci, study.ci=study.ci, precision=paste("+/-", (max(log(delta.grd))-min(log(delta.grd)))/BB.grdnum)))
 }