Bioequivalence and Bioavailability Forum

Hi Beholder,

❝ An article which might serve as "guideline" for conducting telmisartan BE studies in Russia written by expert organization representative. Open access and abstract in English is available.

THX; interesting. In Table 3 three studies are give twice each. Could reproduce the pooled CV of C_max (43.57%). The upper limit 44.84% is based on a 75% CI. I would use a 80% CL. Given.

library(PowerTOST)
design <- "2x2x2"
n      <- c(85, 36, 40, 59, 60, 50, 40)
CV     <- c(43.27, 32.72, 33.67, 48.35, 49.45, 34.12, 55.34)/100
df     <- n - 2
study <- data.frame(design = "2x2x2", n = n,
                    df = df, CV = CV, CV.CL = NA,
                    stringsAsFactors = FALSE)
for (j in seq_along(CV)) {
  study$CV.CL[j] <- signif(CVCL(CV = study$CV[j], df = study$df[j],
                                side = "upper", alpha = 0.25)[["upper CL"]], 4)
}
print(study); print(CVpooled(study, alpha = 0.25), verbose = TRUE)

#   design  n df     CV  CV.CL
# 1  2x2x2 85 83 0.4327 0.4677
# 2  2x2x2 36 34 0.3272 0.3701
# 3  2x2x2 40 38 0.3367 0.3781
# 4  2x2x2 59 57 0.4835 0.5331
# 5  2x2x2 60 58 0.4945 0.5449
# 6  2x2x2 50 48 0.3412 0.3778
# 7  2x2x2 40 38 0.5534 0.6280
# Pooled CV = 0.4357 with 356 degrees of freedom
# Upper 75% confidence limit of CV = 0.4485

The recommended sample of 20 subjects is for a 2×2×4 design and ABEL based on a GMR of 0.95 and CV 0.45). I would not be that optimistic and suggest a GMR of not better than 0.90 (42 subjects).
Not sure whether it makes sense to work with the pooled CV at all (different sampling schedules and bioanalytical methods).

I like that the experts recommend 2-sequence 4- (TRTR|RTRT) and 3-period (TRT|RTR) full replicate designs and not the lousy partial replicate. Kudos!

Hi Beholder,

following the previous article another one* was published yesterday.

Regrettably designs of studies are again not given (I thought from the other article that the Telmisartan studies were performed in 2×2×2 crossovers). I guess there is a typo in the paper. I could reproduce the pooled CV only when using CV 55.34% of study #7 (and not with the 31.51% of this paper).
Seems that the studies were performed in 4-period full replicates (Candesartan in different designs?). I think that in some cases naïve pooling (and “officially” recommending a sample size based on the upper CL of the pooled CV) is not a good idea. Do you trust in a CV of C_max of Losartan of 6.84% (5/27 studies had <10%)? I doubt it.
Similar Valsartan: Two studies with 7.54% and 8.07% (gimme a break), when the median of the 16 others is already 32.8%.

What I like (p. 681, first paragraph):

The factors contributing to the observed variation that were included in the ANOVA were the sequence, subjects, period, and drug.

(my emphasis)
Hey, no stupid nested subject(sequence)! ElMaestro will be happy.

Since the article is behind Springer’s pay-wall see the R-code at the end.

I’m not worried about differences in the 3^rd decimal figure. The authors used Excel 2016. Hence, it might be a rounding issue (commercial in Excel and scientific in R).
Perhaps there are other typos? Can one of the Russian friends check the original publication?

---

• Romodanovskii DP, Goryachev DV, Khokhlov AL, Miroshnikov AN. Investigation Planning and Bioequivalence evaluation of Angiotensin II Receptor Antagonists. Pharm Chem J. 2019;53(8):680–4. doi:10.1007/s11094-019-02062-4.
  Translated from Khimiko-Farmatsevticheskii Zhurnal. August 2019;53(8):11–5.

---

There would be mismatch for Candesartan when assuming the same design in all studies. Hence I bootstrapped the design (note: other patterns of designs would work as well).

library(PowerTOST)
# Try to guess the Candesartan-designs. Seemingly different ones were used.
# Note: If a 3-period full replicate ("2x2x3") wouldn't matter because the
# same degrees of freedom like the partial replicate "2x3x3"
# Caution: Not a unique (i.e., the 'true') solution!
design      <- c("2x2x2", "2x3x3", "2x2x4")
CV.reported <- 0.230
CL.reported <- 0.238
CVdata <- data.frame(CV = c(24.91, 16.98,  7.92, 15.85, 23.14, 18.45,
                            22.87, 25.37,  7.24, 30.14)/100,
                     n = c(40, 35, 18, 30, 24, 18, 24, 24, 18, 37))
set.seed(123) # uncomment for full random resampling
repeat {
  CVdata$design <- sample(design, nrow(CVdata), replace = TRUE) # bootstrap designs
  x         <- unlist(CVpooled(CVdata = CVdata, alpha = 0.1))
  CV.pooled <- signif(x[["CV"]], 3)
  CV.CL     <- signif(x[["CVupper"]], 3)
  if (abs(CV.pooled - CV.reported) <= 5e-3 &
      abs(CV.CL - CL.reported) <= 1e-3) {
    break # both the pooled CV and its CL are sufficiently close to the reported ones
  }
}
drug  <- c("Losartan", "Valsartan", "Candesartan", "Telmisartan", "Irbesartan")
study <- c(27, 18, 10, 7, 5)
Cmax  <- data.frame(drug = c(rep(drug[1], study[1]), rep(drug[2], study[2]),
                             rep(drug[3], study[3]), rep(drug[4], study[4]),
                             rep(drug[5], study[5])),
                    CV = c(c( 7.39,  7.28, 46.41, 33.67, 10.16, 47.87,
                             37.67, 31.07, 40.28, 28.11, 33.67, 35.37,
                             41.42, 23.07, 40.44,  7.02, 19.51, 23.38,
                              6.84,  8.59, 23.03, 28.26, 41.80, 39.65,
                             22.71, 36.22, 25.43),
                           c(12.79, 32.61, 35.65, 38.41, 36.04, 24.65,
                             31.51, 44.09,  8.07,  7.54, 24.01, 30.54,
                             34.60, 33.02, 28.83, 33.86, 30.73, 35.79),
                           CVdata$CV*100,
                           c(43.27, 32.72, 33.67, 48.35, 49.45, 34.12,
                             55.34), # last CV given in this paper with 31.51%
                           c(20.20, 24.67, 25.12, 15.38, 15.56))/100,
                    n = c(c(24, 24, 40, 18, 18, 24, 26, 44, 72, 30, 18,
                            56, 36, 24, 48, 24, 18, 24, 24, 18, 24, 24,
                            54, 18, 24, 24, 24),
                          c(18, 70, 39, 56, 53, 38, 44, 36, 40, 40, 18,
                            24, 40, 28, 34, 34, 44, 45),
                          CVdata$n,
                          c(85, 36, 40, 59, 60, 50, 40),
                          c(27, 32, 18, 22, 24)),
                   design = c(rep("2x2x4", study[1]), rep("2x2x4", study[2]),
                              CVdata$design,
                              rep("2x2x4", study[4]), rep("2x2x4", study[5])))
# print(Cmax, row.names = FALSE) # uncomment to see the data
res <- data.frame(drug = drug,
                  CV.reported = c(0.327, 0.314, 0.230, 0.435, 0.207),
                  CL.reported = c(0.334, 0.320, 0.238, 0.448, 0.217),
                  CV.pooled = NA, CV.CL = NA)
for (j in seq_along(drug)) {
  x                <- unlist(CVpooled(CVdata = Cmax[Cmax$drug == drug[j], 2:4],
                                      alpha = 0.1))
  res$CV.pooled[j] <- signif(x[["CV"]], 3)
  res$CV.CL[j]     <- signif(x[["CVupper"]], 3)
}
print(res, row.names = FALSE)

Gives:

        drug CV.reported CL.reported CV.pooled CV.CL
    Losartan       0.327       0.334     0.327 0.334
   Valsartan       0.314       0.320     0.314 0.321
 Candesartan       0.230       0.238     0.229 0.238
 Telmisartan       0.435       0.448     0.436 0.449
  Irbesartan       0.207       0.217     0.207 0.218

❝     2. Not only males should be enrolled but females as well (50/50).

This is a rather dubious approach. We test bioequivalence only in the healthy but do not usually in the elderly, the sick, those with renal and liver problems and etc. But we do expand the results of our studies to the aforementioned groups. Moreover, in Russia, bioequivalence studies are usually conducted in relatively young people, less than 50 years old, usually. This is barely a target population. Absolute numbers of PK parameters may differ, but it is very unlikely that the PK of products may differ to bioeinequivalence unless we have information about substantial variability in a specific group. In addition, I saw many trials with only male subjects done in India. They were registered in Europe. But personally, I have not encountered that they were later withdrawn from the market because they were found less efficacious and/or more dangerous in a specific gender or another group. Unfortunately, experts from CIS are infamously known because of their rather questionable and unscientific approaches to BE studies and the registration process.
Also, our population is so so so so different that studies can be done only within the Eurasian Economic Union.