Bioequivalence and Bioavailability Forum

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1. Model-based approach for group sequential and adaptive designs in parallel and cross-over bioequivalence studies

❝ AFAIK this one is the most interesting. Authors are INSERM and FDA people. But it looks like their adaptive design cannot control TIE. How come?

• 0.0304 is for Pocock’s group-sequential design (fixed N) with one interim at exactly N/2.
  
• The fact that 0.0304 ‘works’ for Potvin’s original ‘Method B’ is a coincidence (other settings of the GMR and power require other alphas).

library(Power2Stage)
alpha <- rep(0.0304, 2)
df    <- data.frame(alpha1=alpha[1], alpha2=alpha[2],
                    CV=rep(0.24, 4), n1=c(12, rep(16, 3)),
                    GMR=rep(c(0.95, 0.9), each=2),
                    power=rep(c(0.8, 0.9), 2), TIE=NA, CL.lo=NA, CL.hi=NA)
for (j in 1:nrow(df)) {
  df$TIE[j]  <- power.tsd(alpha=alpha, CV=df$CV[j], n1=df$n1[j],
                          GMR=df$GMR[j], theta0=1.25,
                          targetpower=df$power[j], nsims=1e6)$pBE
  df[j, 8:9] <- binom.test(df$TIE[j]*1e6, 1e6)[["conf.int"]]
}
adj   <- c(0.0302, 0.0286, 0.0273, 0.0269)
ad    <- data.frame(alpha1=adj, alpha2=adj,
                    CV=rep(0.24, 4), n1=c(12, rep(16, 3)),
                    GMR=rep(c(0.95, 0.9), each=2),
                    power=rep(c(0.8, 0.9), 2), TIE=NA,
                    sig.lim=binom.test(0.05*1e6, 1e6,
                                       alternative="less")[["conf.int"]][2])
for (j in 1:nrow(ad)) {
  ad$TIE[j]  <- power.tsd(alpha=rep(adj[j], 2), CV=ad$CV[j], n1=ad$n1[j],
                          GMR=ad$GMR[j], theta0=1.25,
                          targetpower=ad$power[j], nsims=1e6)$pBE
}
cat("\n\u201Cnatural constant\u201D (one size fits all)\n");print(signif(df, 5), row.names=FALSE)
cat("\nadjusted alphas\n");print(signif(ad, 5), row.names=FALSE)

“natural constant” (one size fits all)
 alpha1 alpha2   CV n1  GMR power      TIE    CL.lo    CL.hi
 0.0304 0.0304 0.24 12 0.95   0.8 0.050270 0.049843 0.050700
 0.0304 0.0304 0.24 16 0.95   0.9 0.052329 0.051893 0.052767
 0.0304 0.0304 0.24 16 0.90   0.8 0.055298 0.054851 0.055748
 0.0304 0.0304 0.24 16 0.90   0.9 0.056219 0.055768 0.056672

adjusted alphas
 alpha1 alpha2   CV n1  GMR power      TIE sig.lim
 0.0302 0.0302 0.24 12 0.95   0.8 0.049987 0.05036
 0.0286 0.0286 0.24 16 0.95   0.9 0.049576 0.05036
 0.0273 0.0273 0.24 16 0.90   0.8 0.049789 0.05036
 0.0269 0.0269 0.24 16 0.90   0.9 0.049794 0.05036

Quote:
→ In most cases TSS and TSA type 1 error estimates
are within the 0.05 prediction interval [0.0326-0.0729]

round(as.numeric(binom.test(0.05*500, 500)[["conf.int"]]), 4)
[1] 0.0326 0.0729

signif(binom.test(0.05*1e6, 1e6, alternative="less")[["conf.int"]][2], 5)
[1] 0.05036

❝ Turned out that >50% had a so-called ‘dry knee’, i.e., no synovia at all.

❝ Given all that, I’m asking myself on which data the FDA’s model is based upon and how reliable they are.