Bioequivalence and Bioavailability Forum

Hi Anu,

❝ I have worked out that unpaired t-test was the right decision (is it?),

I don’t think so.

❝ and I have done that using R.

Great. Before you run into testing have a look at your data:

D   <- c(1, 1/5, 1/25)
R   <- c(132.43,  76.25 ,  27.28 )
T   <- c( 21.28,  14.125,  5.5603)
M   <- c(160   , 122.54 ,  18.19 )
x   <- log(D)
mR  <- lm(R ~ x); summary(mR)
mT  <- lm(T ~ x); summary(mT)
mM  <- lm(M ~ x); summary(mM)
new <- data.frame(x=seq(from=min(x), to=max(x), length.out=100))
mR.conf <- predict(mR, new, interval="confidence", level=0.95)
mT.conf <- predict(mT, new, interval="confidence", level=0.95)
mM.conf <- predict(mM, new, interval="confidence", level=0.95)
plot(x, R, ylim=c(0, max(R, T, M)),
  xlab="log(Dilution)", ylab="Titre", las=1, pch=0)
points(x, T, pch=1, col="red")
points(x, M, pch=2, col="blue")
abline(mR, lwd=2)
abline(mT, lwd=2, col="red")
abline(mM, lwd=2, col="blue")
abline(h=10, lty=2)
for(i in 2:3) lines(new$x, as.numeric(mR.conf[, i]), lty=3)
for(i in 2:3) lines(new$x, as.numeric(mT.conf[, i]), lty=3, col="red")
for(i in 2:3) lines(new$x, as.numeric(mM.conf[, i]), lty=3, col="blue")
legend("topleft", c("Reference", "Test", "Market"),
  pch=0:2, col=c("black", "red", "blue"))

What do you see? What do the confidence intervals (especially mM.conf) tell you?

❝ Kindly help me with how to find superiority and the other query. I am not getting the exact procedure for that

You could compare the slope and intercepts of the models (see any statistical textbook). Looking at your data (even without plotting) I have some doubts whether you need any test at all.
IMHO you need more dilutions (at least five?). BTW, the variability of the Market vaccine is awful (compare e.g., summary(mM)$sigma with summary(mR)$sigma).

Concerning your question #3, what about:

cat(sprintf("%s%.2f%s", "Titre 10: Estimated dilution of Test = 1:",
  1/exp((10-coef(mT)[1])/coef(mT)[2]), ".\n"))