Bioequivalence and Bioavailability Forum • Desperate reader

Helmut
★★★

Vienna, Austria,
2021-08-27 17:51
(1144 d 20:56 ago)

Posting: # 22550
Views: 5,545

Desperate reader [Regulatives / Guidelines]

Post reply

Dear all (and esp. ElMaestro),

with great interest I read two recent papers.^1,2

On the author posted:

$\small{V }$

$\small{V = ZGZ^t + R}$

Work with the wrong model and the software may not converge.
Work with the right model but major stats packages do not support it, and
they do not derive a CI for T/R.

That is an agonizing choice.

I absolutely agree with this statement.
However, what can we do? We need the bloody confidence interval. At the end of the day we are [image]

left out in the rain if we are dealing with a partial replicate design and the study has to be evaluated for average bioequivalence (according to the [image]

’s wishful thinking if $\small{s_\textrm{wR}<0.294}$).
To obtain the variance components which are estimable and the point estimate is just not enough. As long as we can’t get the standard error of the treatment difference and its associated degrees of freedom, we are at a loss. Hence, I repeat my mantra:

Avoid the partial replicate design
if intended for RSABE and if
there is even the slightest chance that you have to assess it for ABE.

Of note: I used the supplementary [image]

script and got for

res <- Run.REML() PE <- 100 * exp(res$Fixed.eff[["TrtT", 1]] - res$Fixed.eff[["TrtR", 1]]) print(res); cat("PE", PE, "\n") $Outcome [1] "The model converged." $LogLikelihood [1] 15.33728 $Fixed.eff [,1] TrtT 8.02569184 TrtR 8.00330042 Per1 -0.04811877 Per2 -0.04682231 SeqRTR 0.00385480 SeqRRT -0.05092437 $Random.eff Var.Component Ini.guess REML.Estimate 1 varT 0.06841615 0.07049570 2 varBR 0.03576077 0.03621596 3 varWR 0.01240137 0.01324664 4 varBRT 0.03576077 0.04563785 PE 102.2644

Pretty close to the modified script we discussed last year (given at the end). Much faster than mine. :-D

Nelder-Mead optimization (31.6 seconds) LogLikelihood 75.98722 Evaluations 239 Successful completion. Component Initial Estimate sigma²(T) 0.06841615 0.07049451 sigma²(bR) 0.03576077 0.03621602 sigma²(wR) 0.01240137 0.01324648 covar(bTbR) 0.05208846 0.04563728 Parameter Estimate sigma(T) 0.2655080 CV(T) 27.026% sigma(bR) 0.1903051 CV(bR) 19.204% sigma(wR) 0.1150934 CV(wR) 11.548% PE 102.2644%

[image]

Fuglsang A. Professor Endrenyi’s Legacy: An Evaluation of the Regulatory Requirement “Fixed Effects, Rather Than Random Effects, Should Be Used for All Terms”. J Pharm Pharm Sci. 2021; 24: 413–20. doi:10.18433/jpps31872. Open access.
Fuglsang A. Mitigation of the convergence issues associated with semi-replicated bioequivalence data. Pharm Stat. 2021. Early View. doi:10.1002/pst.2142.

###########################

# Section 1: Housekeeping #

###########################

library(PowerTOST)

library(TeachingDemos)

GetData <- function(path, sep, dec) {

  # read data from a CSV-file

  if (missing(sep)) sep <- ","

  if (!sep %in% c(",", ";", "t"))

    stop("Column separator must be any of ',', ';', 't'.")

  if (sep == "t") sep <- "\t"

  if (missing(dec)) dec <- "."

  if (!dec %in% c(".", ","))

    stop("Decimal separator must be '.', or ','.")

  # strip quotes and skip eventual commentary lines

  D        <- read.csv(path, sep = sep, dec = dec,

                       quote = "", comment.char = "#")

  names(D) <- c("Subj", "Per", "Seq", "Trt", "Y")

  cols     <- c("Subj", "Per", "Seq", "Trt")

  D[cols]  <- lapply(D[cols], factor)

  return(invisible(D))

}



CreateX <- function(D) {

  # first the two treatments

  TrtT <- as.numeric(as.character(D$Trt) == "T")

  TrtR <- as.numeric(as.character(D$Trt) == "R")

  X <- cbind(TrtT, TrtR)

  R <- qr(X)$rank

  # now the periods

  for (p in unique(D$Per)) {

    v  <- as.numeric(D$Per == p)

    XX <- data.frame(X, v)

    names(XX)[ncol(XX)] <- paste0("P", p)

    rnk <- qr(XX)$rank

    if (rnk > R) {

      X <- XX

      R <- rnk

    }

  }

  for (q in unique(D$Seq)) {

    v  <- as.numeric(D$Seq == q)

    XX <- data.frame(X, v)

    names(XX)[ncol(XX)] <- paste0("Q", q)

    rnk <- qr(XX)$rank

    if (rnk > R) {

      X <- XX

      R <- rnk

    }

  }

  return(as.matrix(X))

}

Create.CovM <- function(Params) {

  # block diagonal covariance matrix

  varT  <- Params[1]


  varBR <- Params[2]


  varWR <- Params[3]


  varRT <- Params[4]


  Nobs  <- length(D$Y)

  V     <- matrix(0, ncol = Nobs, nrow = Nobs)

  for (iRow in 1:Nobs) {

    for (iCol in 1:Nobs) {

      if (iCol == iRow) { # diagonal elements

        if (D$Trt[iRow] == "T") {

          V[iRow, iCol] <- V[iRow, iCol] + varT

        } else {

          V[iRow, iCol] <- V[iRow, iCol] + varWR + varBR

        }

      } else {            # off diagonal elements

        if (D$Subj[iRow] == D$Subj[iCol]) {

          if (D$Trt[iCol] == D$Trt[iRow]) {

            V[iRow, iCol] <- V[iRow, iCol] + varBR

          } else {

            V[iRow, iCol] <- V[iRow, iCol] + varRT

          }

        }

      }

    }

  }

  return(V)

}



############################

# Section 2: Matrix things #

############################

Obj.F12 <- function(Pars) {

  j <<- j + 1

  int[[j]] <<- Pars

  # this is line 3 of page 10 of:

  # http://people.csail.mit.edu/xiuming/docs/tutorials/reml.pdf

  CovM  <- Create.CovM(Pars)

  A     <- -0.5*log(det(CovM))

  # Note: NaNs can be proceded in the next line.

  B     <- suppressWarnings(-0.5*log(det(t(X) %*% solve(CovM) %*% X)))

  est.b <- solve(t(X) %*% solve(CovM) %*% X) %*% t(X) %*% solve(CovM) %*% y

  tmp   <- y - X %*% est.b

  C     <- -0.5 *(t(tmp) %*% solve(CovM) %*% tmp)

  C     <- as.numeric(C) # make a scalar for other solvers

  return(A + B + C)

}

Final <- function(Pars) {

  CovM <- Create.CovM(Pars)

  tmp  <- solve(t(X) %*% solve(CovM) %*% X) %*% t(X) %*% solve(CovM) %*% y

  PE   <- exp(as.numeric(tmp["TrtT", ] - tmp["TrtR", ]))

  return(PE)

}



########################

# Section 3: Execution #

########################

Some.Initial.Guesses <- function(check = FALSE) {

  # design (all possible ones, error handling, full or partial)

  subjs <- unique(as.numeric(D$Subj))

  trts  <- sort(unique(as.character(D$Trt)), decreasing = TRUE)

  if (!length(trts) == 2) stop("Only two treatments supported.")

  if (sum(!trts %in% c("T", "R")) !=0)

    stop("treatments must be coded as 'T' and 'R'.")

  seqs  <- sort(unique(as.character(D$Seq)), decreasing = TRUE) # T first

  type  <- paste(seqs, collapse = "|") # identifier

  nseq  <- length(unique(as.character(D$Seq)))

  nper  <- length(unique(as.numeric(D$Per)))

  nsubj <- length(subjs)

  if (nchar(type) == 19) {  # 4-period 4-sequence full replicate designs

    if (nper != 4) stop("4 periods required in this full replicate design.")

    if (nseq != 4) stop("4 sequences required in this full replicate design.")

    des <- "full"

  }

  if (nchar(type) == 9) {  # 4-period full replicate designs

    if (nper != 4) stop("4 periods required in this full replicate design.")

    if (nseq != 2) stop("2 sequences required in this full replicate design.")

    des <- "full"

  }

  if (nchar(type) == 7) {  # 3-period replicates

    if (type %in% c("TRT|RTR", "TRR|RTT")) {

      if (nper != 3) stop("3 periods required in this full replicate design.")

      if (nseq != 2) stop("2 sequences required in this full replicate design.")

      des <- "full"

    }

    if (type == "TRR|RTR") {

      if (nper != 3) stop("3 periods required in the extra-reference design.")

      if (nseq != 2) stop("2 sequences required in the extra-reference design.")

      des <- "partial"

    }

  }

  if (nchar(type) == 11) { # Balaam's design or 3-sequence partial

    if (!type == "TR|RT|TT|RR") { # Balamm's

      if (nper != 3) stop("3 periods required in this partial replicate design.")

      if (nseq != 3) stop("3 sequences required in this partial replicate design.")

      des <- "partial"

    } else {                      # TRT|RTR|RRT

      if (nper != 2) stop("2 periods required in Balaam's design.")

      if (nseq != 4) stop("4 sequences required in Balaam's design.")

      des <- "full"

    }

  }

  if (type == "TR|RT") stop("TR|RT design not supported yet.")

  gm.T <- gm.R <- numeric(nsubj) # vector of geometric means

  for (subj in seq_along(subjs)) {

    gm.T[subj] <- mean(log(D$Y[which(D$Subj == subj & D$Trt == "T")]))

    gm.R[subj] <- mean(log(D$Y[which(D$Subj == subj & D$Trt == "R")]))

  }

  # remove NAs

  gm.T <- gm.T[!is.na(gm.T)]
  

  gm.R <- gm.R[!is.na(gm.R)]
  

  if (des == "partial") { # guess varT (between + within)

    m    <- lm(log(Y) ~ Seq + Per, data = D[D$Trt == "T", ])

    varT <- anova(m)["Residuals", "Mean Sq"]


  } else {                # guess VarWT

    m     <- lm(log(Y) ~ Seq + Per + Subj, data = D[D$Trt == "T", ])

    varWT <- anova(m)["Residuals", "Mean Sq"]


  }

  # guess VarWR

  m     <- lm(log(Y) ~ Seq + Per + Subj, data = D[D$Trt == "R", ])

  varWR <- anova(m)["Residuals", "Mean Sq"]
  # guess varBR

  m     <- lm(log(Y) ~ Seq + Per, data = D[D$Trt == "R", ])

  varBR <- anova(m)["Residuals", "Mean Sq"] - varWR

  # TODO: full replicates

  varRT <- 0.5 * (varT + varBR)

  rslt  <- c(varT, varBR, varWR, varRT)

  return(rslt)

}

MyREML <- function(maxit = 1000, method = "Nelder-Mead") {

  Ini <- Some.Initial.Guesses()

  ptm <- proc.time()[[3]]

  F   <- optim(par = Ini, fn = Obj.F12, method = method,

               control = list(reltol = 1E-12, maxit = maxit,

               fnscale = -1))

  et  <- proc.time()[[3]] - ptm

  Nms <- c("var_T", "var_bR", "var_wR", "covar_bTbR")

  X   <- data.frame(Nms, Ini, F$par)

  names(X) <- c("Component", "Initial", "Estimate")

  if (F$convergence == 0)  msg <- "Successful completion."

  if (F$convergence == 1)  msg <- paste("Iteration limit", maxit, "reached.")

  if (F$convergence == 10) msg <- "Degeneracy of the Nelder–Mead simplex."

  cat(paste0("\nNelder-Mead optimization (", signif(et, 3), " seconds)"),

             "\n  LogLikelihood", F$value,

             "\n  Evaluations  ", F$counts[["function"]], "\n ", msg, "\n")

  return(X)

}



# Data has to have five columns in this order:

#   Subject (numeric), Period (numeric), Sequence (character),

#   Treatment (character), Response (numeric)

# Column separator 'sep' comma (default), semicolon, or t (tab)

# Decimal separator 'dec' period (default) or comma

path <- "https://bebac.at/downloads/ds02.csv" # EMA partial replicate

D    <- res <- PE <- int <- NULL # nullify eventual previous data and results

D    <- GetData(path)

X    <- CreateX(D)

y    <- log(D$Y)

# capture intermediate results:

# https://stackoverflow.com/questions/23975101/getting-more-details-from-optim-function-from-r

j    <- 0

int  <- list()

# the workhorse

#  optional arguments:

#  maxit = X to reduce the number of iterations from the default 1000

#  plot = TRUE for a plot of the progress of optimization

#  print = TRUE to print the progress of optimization

res <- MyREML()

res[, 1]     <- c("sigma\u00B2(T)", "sigma\u00B2(bR)",

                  "sigma\u00B2(wR)", "covar(bTbR)")

fin          <- data.frame(Parameter = c("sigma(T)", "CV(T)",

                                         "sigma(bR)", "CV(bR)",

                                         "sigma(wR)", "CV(wR)", "PE"),

                           Estimate = NA_real_)

for (j in 1:3) {

  fin$Estimate[j * 2 - 1] <- sprintf("%.7f", sqrt(res[j, 3]))

  fin$Estimate[j * 2]     <- sprintf("%3.3f%%", 100 * mse2CV(res[j, 3]))

}

fin$Estimate[7] <- sprintf("%3.4f%%", 100 * Final(res$Estimate))

int          <- data.frame(matrix(unlist(int), nrow = length(int),

                                  byrow = TRUE))

if (is.null(attr(dev.list(), "names"))) windows(width = 6.5, height = 4)

# variance components

lbls <- c(expression(sigma[T]^2),

          expression(sigma[bR]^2),

          expression(sigma[wR]^2),

          expression(italic(cov)(bTbR)))

cols <- c("darkgreen", "blue", "magenta", "red")

op   <- par(no.readonly = TRUE)

par(mar = c(3.3, 3.1, 1.6, 4.1),  mgp = c(2.2, 0.5, 0), lend = 2,

    ljoin = 1, tcl = 0.25, cex.axis = 0.8)

plot(1:nrow(int), int$X1, type = "n", ylim = range(int), log = "x",

     xlab = "Iteration", ylab = "Estimate", main = "Progress of optimization",

     cex.lab = 0.95, cex.main = 1, font.main = 1, axes = FALSE)

grid()

axis(1)

axis(2, las = 1)

box()

ax <- axTicks(1, log = TRUE)

for (j in 1:4) {

  lines(1:nrow(int), int[, j], type="s", lwd = 2, col = cols[j])

  shadowtext(sqrt(2), int[1, j], cex = 0.65, pos = 3,

             labels = signif(int[1, j], 4), col = cols[j],

             bg = "white", r = 0.2)

  shadowtext(nrow(int)*0.9, tail(int[, j], 1), cex = 0.65, pos = 3,

             labels = signif(tail(int[, j], 1), 4), col = cols[j],

             bg = "white", r = 0.2)

  mtext(lbls[j], 4, at = tail(int[, j], 1), cex = 0.8, line = 0.5, las = 1)

}

par(op)

print(res, row.names = FALSE); cat("\n"); print(fin, row.names = FALSE)

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

ElMaestro
★★★

Denmark,
2021-08-28 00:18
(1144 d 14:29 ago)

@ Helmut
Posting: # 22552
Views: 4,287

Desperate reader

Post reply

Hi Hötzi,

❝ We need the bloody confidence interval.

❝ As long as we can’t get the standard error of the treatment difference and its associated degrees of freedom, we are at a loss.

If we look at SAS documentation e.g. here and here, then

I do not understand the underlying math (just try and look into the spectral decomposition things mentioned as part of DDFM derivation; it sends my head spinning).
Whatever SAS does, it seems to require that we work in V through ZGZ^t+R in order to estimate CI's for the fixed effects.

It would be interesting to see someone who has solid understanding of matrix theory and stats to work out the equations when the between and within-variability for T cannot be separated.
However, since FDA now threw the mixed model out for semi-replicate designs, interesting may in reality just mean academically attractive but possible not too useful at this moment. But who knows - until someone does it and explores it, it is not known if there is an advantageous property hidden somewhere.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2021-08-28 01:54
(1144 d 12:54 ago)

@ ElMaestro
Posting: # 22553
Views: 4,474

Misunderstanding?

Post reply

Hi ElMaestro,

❝ If we look at SAS documentation e.g. here and here, then

❝ 1. I do not understand the underlying math (just try and look into the spectral decomposition things mentioned as part of DDFM derivation; it sends my head spinning).

Wooaah!!

❝ 2. Whatever SAS does, it seems to require that we work in V through ZGZ^t+R in order to estimate CI's for the fixed effects.

Seems so.

❝ It would be interesting to see someone who has solid understanding of matrix theory and stats to work out the equations when the between and within-variability for T cannot be separated.

Definitely not me…

❝ However, since FDA now threw the mixed model out for semi-replicate designs, …

What on earth gives you this impression? I’m talking about ABE (Stats guidance Appendix E, Progesterone guidance page 8, ANDA guidance page 29):

The following codes are an example of the determination of unscaled average BE for LAUCT with a partially replicate 3-way BE design:

PROC MIXED data=pk; CLASSES SEQ SUBJ PER TRT; MODEL LAUCT = SEQ PER TRT/ DDFM=SATTERTH; RANDOM TRT/TYPE=FA0(2) SUB=SUBJ G; REPEATED/GRP=TRT SUB=SUBJ; ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1; ods output Estimates=unsc1; title1 'unscaled BE 90% CI - guidance version'; title2 'AUCt'; run; data unsc1; set unsc1; unscabe_lower=exp(lower); unscabe_upper=exp(upper); run;

[image]

If reference-scaling is acceptable (right branch), even a spreadsheet (‼) would do.

❝ … interesting may in reality just mean academically attractive but possible not too useful at this moment.

Nope. Talk to John about his data sets which didn’t converge. Given, FA0(1) did – with a warning – but I think there is a data set posted at Certara’s forum where nothing worked. Study done, no result. THX, [image]

❝ But who knows - until someone does it and explores it, it is not known if there is an advantageous property hidden somewhere.

Might be.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

ElMaestro
★★★

Denmark,
2021-08-28 12:00
(1144 d 02:48 ago)

@ Helmut
Posting: # 22554
Views: 4,258

Misunderstanding?

Post reply

Hi Hötzi,

❝ ❝ However, since FDA now threw the mixed model out for semi-replicate designs, …

❝

❝ What on earth gives you this impression? I’m talking about ABE (Stats guidance Appendix E, Progesterone guidance page 8, ANDA guidance page 29):

Wow, that is actually right.
Page 27: "PROC GLM should be used for partially replicate (3-way) BE studies"
Page 29: "For PK parameters with a s_WR < 0.294, use the unscaled average BE approach." (which implies PROC MIXED in their code)

So, we must start to work out s_WR using the equations. Once we got it, we know whether we need a mixed model or not for the evaluation of BE. We may need the mixed model for one metric, like AUCt and AUCinf, and the equations (ref scaled ABE) for another, like Cmax.
I guess this is also the gist of the decision tree you gave. I wonder if this is truly their intention. The mixed model therefore seems to have been saved by the bell. This really emphasizes the need for a CI solution that allows V estimated without the existence of Z and R separately.

I am curious now - we should make a little study on the type I error in case of missing ref values.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2021-08-28 12:38
(1144 d 02:10 ago)

@ ElMaestro
Posting: # 22555
Views: 4,336

Here we are

Post reply

Hi ElMaestro,

❝ ❝ What on earth gives you this impression? I’m talking about ABE (Stats guidance Appendix E, Progesterone guidance page 8, ANDA guidance page 29):

❝

❝ Wow, that is actually right.

❝ Page 27: "PROC GLM should be used for partially replicate (3-way) BE studies"

And Page 32:

PROC MIXED should be used for fully replicate (4-way) BE studies

Only the

knows why.

❝ Page 29: "For PK parameters with a s_WR < 0.294, use the unscaled average BE approach." (which implies PROC MIXED in their code)

Now you got it. ;-)

Some stuff there.

❝ So, we must start to work out s_WR using the equations.

Yep. At least that’s easy.

❝ Once we got it, we know whether we need a mixed model or not for the evaluation of BE. We may need the mixed model for one metric, like AUCt and AUCinf, and the equations (ref scaled ABE) for another, like Cmax.

Correct.

❝ I guess this is also the gist of the decision tree you gave. I wonder if this is truly their intention.

That’s the interpretation of all authors who assessed the Type I Error. Sent you Mehl.

❝ The mixed model therefore seems to have been saved by the bell.

❝ This really emphasizes the need for a CI solution that allows V estimated without the existence of Z and R separately.

Happy that finally I conveyed the message.

❝ I am curious now - we should make a little study on the type I error in case of missing ref values.

Oh dear, reaching for the stars! So far we have no clue how to come up with a solution for complete data. Appetizer.
Since there were comments on about study costs, see there.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Mahmoud
★

Jordan,
2021-09-17 15:31
(1123 d 23:16 ago)

@ Helmut
Posting: # 22580
Views: 3,663

Papers

Post reply

Dear all

Dr Anders Fuglsang discussed in his paper

Mitigation of the convergence issues associated with semi-replicated bioequivalence data. Pharmaceutical Statistics. 2021;1–3
used the proc mixed in RTR/TRR/RRT design in ABE

I think that using proc mixed to fit RTR/TRR/RRT design is not suitable, because in most cases proc mixed produced Estimated G matrix is not positive definite.

So proc GLM recommended by FDA and Emea is more appropriate in the Semi-replicated designs

M.Youseef

Edit: Post moved. [Helmut]

Helmut
★★★

Vienna, Austria,
2021-09-17 17:15
(1123 d 21:32 ago)

@ Mahmoud
Posting: # 22581
Views: 3,709

FDA: PROC MIXED (‼) for ABE

Post reply

Hi Mahmoud,

❝ I think that using proc mixed to fit RTR/TRR/RRT design is not suitable, because in most cases proc mixed produced Estimated G matrix is not positive definite.

❝

❝ So proc GLM recommended by FDA and Emea is more appropriate in the Semi-replicated designs

Please read the entire thread again. The FDA does recommend PROC MIXED for ABE in all guidances.
That’s the problem.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Mahmoud
★

Jordan,
2021-09-17 17:24
(1123 d 21:24 ago)

@ Helmut
Posting: # 22582
Views: 3,751

FDA: PROC MIXED (‼) for ABE

Post reply

❝ Please read the entire thread again. The FDA does recommend PROC MIXED for ABE in all guidances.

❝ That’s the problem.

Dear Dr Helmut

Draft Guidance on Progesterone

If SAS® is used for statistical analysis
–
PROC MIXED should be used for fully replicated (4-way) BE studies
–
PROC GLM should be used for partially replicated (3-way) BE studies

or other software accomplishes same objectives

Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post #5! [Helmut]

Helmut
★★★

Vienna, Austria,
2021-09-17 19:11
(1123 d 19:36 ago)

@ Mahmoud
Posting: # 22584
Views: 3,886

FDA: PROC MIXED (‼) for ABE

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Dear Mahmoud!

❝ Dear Dr Helmut

Not a doctor. No intentions to become one. Told you that numerous times before.

❝ If SAS® is used for statistical analysis

❝ PROC MIXED should be used for fully replicated (4-way) BE studies

❝ PROC GLM should be used for partially replicated (3-way) BE studies

Since you didn’t bother to read the entire thread as suggested – and not even the subject line of my post – would you mind to digest this one?

Your quote refers to Reference-scaled Average Bioequivalence ($\small{s_\textrm{wR}\geq 0.294}$).
However, for (conventional, unscaled) Average Bioequivalence ($\small{s_\textrm{wR}<0.294}$) PROC MIXED should be used regardless the design.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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