a=c(0,15,30,45,60,90,120)
b=c(4.3,6.3,7.9,5.3,4.1,4.6,4.9)

incrementalAUC <- vector()

for (i in 1:(length(a)-1)){

  if((b[i+1]-b[1] >= 0) && (b[i]-b[1] >= 0))
  {incrementalAUC[i] <-((b[i]-b[1]+b[i+1]-b[1])/2)*(a[i+1]-a[i])}

  else if((b[i+1]-b[1] < 0) && (b[i]-b[1] >= 0))
  {incrementalAUC[i] <-(b[i]-b[1])*((b[i]-b[1])/(b[i]-b[i+1])*(a[i+1]-a[i])/2)}

  else if((b[i+1]-b[1] >= 0) && (b[i]-b[1] < 0))
  {incrementalAUC[i] <-(b[i+1]-b[1])*((b[i+1]-b[1])/(b[i+1]-b[i])*(a[i+1]-a[i])/2)}

  else if((b[i]-b[1] < 0) && (b[i+1]-b[1] < 0))
  {incrementalAUC[i] <- 0}
}
incrementalAUC
sum(incrementalAUC)

ID     Group       calculated AUC
 ID=1  Group=1
 ID=1  Group=2
 ID=2  Group=1

a <-rep(c(0,15,30,45,60,90,120), 4)
Id<-rep(1:2,each=14)
group<-rep(1:2,each=7, times = 2)
b=c(4.3,6.3,7.9,5.3,4.1,4.6,4.9,4.3,6.3,7.9,5.6,4.4,4.5,4.8,4.3,6.3,8.9,9.3,4.1,4.6,5.9,4.3,7.3,8.9,7.3,4.1,5.6,4.9)
data<-data.frame(Id,group,a,b)