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If this article is perceived as overly
focused on statistics, I apologize. This is due to my professional
background, which has led me to be less skilled at crafting engaging
narratives.
I have to confess that
»Short« in the title is a euphemism…
‘Bioavailability’ (a portmanteau of ‘biologic availability’) in its current meaning was coined in 1971^{1} and ‘Bioequivalence’ saw the light of day in 1975.^{2}
The MeSH term ‘Biological Availability’ was introduced in 1979.
“The extent to which the active ingredient of a drug dosage form becomes available at the site of drug action or in a biological medium believed to reflect accessibility to a site of action.
The site of action (i.e., a receptor) is practically always
inaccessible. There should be no space for believes in
science.
The best definition of bioequivalence (BE) is given by the International
Council for Harmonisation of Technical Requirements for Pharmaceuticals
for Human Use (ICH).^{3}
“Two drug products containing the same drug substance(s) are considered bioequivalent if their relative bioavailability (BA) (rate and extent of drug absorption) after administration in the same molar dose lies within acceptable predefined limits. These limits are set to ensure comparable in vivo performance, i.e., similarity in terms of safety and efficacy.
We will use a two-treatment two-sequence two-period (2×2×2) crossover design as an example. \[\small{\begin{array}{cccc} \textsf{Table I}\phantom{0}\\ \text{subject} & \text{sequence} & \text{T} & \text{R}\\\hline \phantom{1}1 & \text{RT} & 71 & 81\\ \phantom{1}2 & \text{TR} & 61 & 65\\ \phantom{1}3 & \text{RT} & 80 & 94\\ \phantom{1}4 & \text{TR} & 66 & 74\\ \phantom{1}5 & \text{TR} & 94 & 54\\ \phantom{1}6 & \text{RT} & 97 & 63\\ \phantom{1}7 & \text{RT} & 70 & 85\\ \phantom{1}8 & \text{TR} & 76 & 90\\ \phantom{1}9 & \text{TR} & 54 & 53\\ 10 & \text{RT} & 99 & 56\\ 11 & \text{RT} & 83 & 90\\ 12 & \text{TR} & 51 & 68\\\hline \end{array}}\]
Problems were reported with formulations of Narrow Therapeutic Index Drugs (NTIDs) like phenytoin,^{4} ^{5} ^{6} ^{7} digoxin,^{1} ^{8} ^{9} ^{10} ^{11} ^{12} warfarin,^{13} theophylline,^{14} primidone.^{15} Some show nonlinear pharmacokinetics (phenytoin) or are auto-inducers (warfarin).
Generic drugs in the current sense did not yet exist at that time; only the content had to meet the USP requirements.
“Although in 1969 Professor John Wagner demonstrated to the Bureau of Medicine, methods for comparing areas under the serum versus time curve (AUC) to estimate bioequivalence, his approach was ignored inasmuch as the FDA hierarchy did not believe a problem existed, and therefore such studies would not be neccessary. For their part the Offices of Pharmaceutical Research and Compliance in the Bureau of Medicine and the Commissioner’s Office believed that the “Bioavailability Problem” as some called it was a “Content Uniformity Problem”.^{16} In 1971 for example, when notified of a “Bioavailability Problem” with a generic digoxin product, FDA investigated and ascertained that one manufacturer first added all the excipients into a 55-gal drum, then added digoxin, closed the lid, and mixed it by rolling the drum across the floor a few times. The content uniformity of those tablets varied from 10% to 156%.
Following a ‘Conference on Bioavailability of Drugs’ held at the National Academy of Sciences of the United States in 1971, a guideline was published the following year.^{18}
© 2008 hobvias sudoneighm @ flickr
“[…] the mean of AUC of the generic had to be within 20% of the mean AUC of the approved product. At first this was determined by using serum versus time plots on specially weighted paper, cutting the plot out and then weighing each separately.
Methods and procedures for in vivo testing to determine bioavailability (BA) for new drugs were proposed by the FDA on June 20, 1975. Several terms were defined:^{19}
The “site of drug action” was questioned but kept in the regulation of 1977 and is used ever since by the FDA.^{20}
“[A] comment also recommended that the phrase “becomes available to the site of drug action” be deleted since it is overly optimistic to presume that bioavailability data consisting of estimates of parent drug […] concentration in body fluids […] provides, as a general rule, an estimate of the availability of the therapeutic moiety at the site of drug action.
The Commissioner agrees that bioavailability data alone do not estimate the availability of the therapeutic moiety at the site of drug action. It is scientifically valid to assume, however, that if an active drug ingredient or therapeutic moiety reaches a reasonable extent of systemic circulation at a reasonable rate, the therapeutic moiety will also become available at the site of drug action […]. For this reason, the Commissioner concludes that reference to availability at site of drug action should not be deleted. He also believes that omission of such a reference would incorrectly focus the definition of bioavailability exclusively on absorption of the active drug ingredient or therapeutic moiety from the drug product. Even where such absorption is total, the product may not be bioavailable because an insufficient amount of the active drug ingredient or therapeutic moiety reaches the systemic circulation. In certain instances, e.g., high first-pass metabolism in the liver or rapid renal clearance, the active drug ingredient or therapeutic moiety must be absorbed at a rate sufficient to overcome the metabolic or elimination mechanism and reach the systemic circulation so that the therapeutic moiety will become available at the site of drug action in sufficient amounts to elicit the intended therapeutic effect.
top of section ↩︎ previous section ↩︎
The FDA’s
80/20 Rule or ‘Power Approach’ (at least 80% power to detect a 20%
difference) of 1972 consisted of testing the hypothesis of no difference
at the \(\small{\alpha=0.05}\) level of
significance.^{17} ^{21} \[H_0:\;\mu_\text{T}-\mu_\text{R}=0\;vs\;H_1:\;\mu_\text{T}-\mu_\text{R}\neq
0,\tag{1}\] where \(\small{H_0}\) is the null
hypothesis of equivalence and \(\small{H_1}\) the alternative
hypothesis of inequivalence. \(\small{\mu_\text{T}}\) and \(\small{\mu_\text{R}}\) are the (true) means
of \(\small{\text{T}}\) and \(\small{\text{R}}\), respectively. In order
to pass the test, the estimated (post hoc, a
posteriori, retrospective) power had to be at least 80%. The power
depends on the true value of \(\small{\sigma}\), which is unknown. There
exists a value of \(\small{\sigma_{\,0.80}}\) such that if
\(\small{\sigma\leq\sigma_{\,0.80}}\),
the power of the test of no difference \(\small{H_0}\) is greater or equal to 0.80.
Since \(\small{\sigma}\) is unknown, it
has to be approximated by the sample standard deviation \(\small{s}\). The Power Approach in a simple
2×2×2 crossover design then consists of rejecting \(\small{H_0}\) and concluding that \({\small{\mu_\text{T}}}\) and \({\small{\mu_\text{R}}}\) are equivalent if
\[-t_{1-\alpha/2,\nu}\leq\frac{\bar{x}_\text{T}-\bar{x}_\text{R}}{s\sqrt{\tfrac{1}{2}\left(\tfrac{1}{n_1}+\tfrac{1}{n_2}\right)}}\leq
t_{1-\alpha/2,\nu}\:\textsf{and}\:s\leq\sigma_{0.80}\textsf{,}\tag{2}\]
where \(\small{n_1,\,n_2}\) are the
number of subjects in sequences 1 and 2, the degrees of freedom \(\small{\nu=n_1+n_2-2}\), and \(\small{\bar{x}_\text{T},\bar{x}_\text{R}}\)
are the means of \(\small{\text{T}}\)
and \(\small{\text{R}}\),
respectively.
Note that this procedure is based on estimated power \(\small{\widehat{\pi}}\), since the
true power is a function of the unknown \(\small{\sigma}\). It was the only approach
based on post hoc power and
was never implemented in any other jurisdiction.
For the example we estimate a power of only 46.4% to detect a 20% difference and the study would fail.
First proposals by the biostatistical community were published.^{22} ^{23} ^{24} ^{25}
The analysis was performed on untransformed data (i.e., by an additive model assuming normal distributed data) and bioequivalence was concluded if the 95% confidence interval (CI) of the point estimate (PE) was entirely within 80 – 120%.^{22 25}
We get for our example in R:
<- data.frame(subject = rep(1:12, each = 2),
example treatment = c("R", "T", "T", "R", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R"),
period = rep(1:2, 12),
Y = c(81, 71, 61, 65, 94, 80, 66, 74,
94, 54, 63, 97, 85, 70, 76, 90,
54, 53, 56, 99, 90, 83, 51, 68))
<- c("subject", "period", "treatment")
facs <- lapply(example[facs], factor) # factorize the data
example[facs] # additive model (untransformed data, differences); sequence not in the model!
<- lm(Y ~ subject + period + treatment, data = example)
muddle <- as.numeric(confint(muddle, level = 0.95)["treatmentT", ])
CI <- coef(muddle)[["treatmentT"]]
PE # percentages (flawed!)
<- mean(example$Y[example$treatment == "T"])
mean.T <- mean(example$Y[example$treatment == "R"])
mean.R <- 100 * mean.T / mean.R
PE.pct <- 100 * (CI + mean.R) / mean.R
CI.pct <- data.frame(method = c("differences", "percentages"),
result PE = c(sprintf("%+.3f", PE),
sprintf("%6.2f%%", PE.pct)),
lower = c(sprintf("%+.3f", CI[1]),
sprintf("%.2f%%", CI.pct[1])),
upper = c(sprintf("%+.3f", CI[2]),
sprintf("%6.2f%%", CI.pct[2])),
BE = c("", "fail"))
if (CI.pct[1] >= 80 & CI.pct[2] <= 120) result$BE[2] <- "pass"
names(result)[3:4] <- c("lower CL", "upper CL")
print(result, row.names = FALSE)
# method PE lower CL upper CL BE
# differences +2.417 -12.777 +17.611
# percentages 103.32% 82.44% 124.21% fail
If data are analyzed by an additive model the result are differences. It is a fundamental error to naïvely transform differences to percentages – it would require Fieller’s CI.^{26} ^{27} However, this was not done back in the day. We get a 95% CI of 82.44 – 124.21%, and the study would fail because the upper confidence limit (CL) is > 120%.
Westlake^{23} mused that the shortest CI – which is symmetrical about the PE – would be too difficult to comprehend by non-statisticians. He suggested to split the t-values in such a way that the probability of the two tails sums to \(\small{\alpha}\) and the respective CI is symmetrical around 0 (or 100%). In the example we obtain ±21.80%, and the study would fail as well because the confidence limits are > ±20%. As above, calculating a percentage is flawed.
However, such a result is misleading. The information about the location of the difference is lost; one cannot know any more whether the average BA of \(\small{\text{T}}\) is lower or higher than the one of \(\small{\text{R}}\). Therefore, the method was criticized^{24} and never implemented in practice. It took me years to convince Certara to remove Westlake’s CI from the results in Phoenix WinNonlin. In 2016, I was successful with version 6.4… Since then the differences are given in the additive model.
The ‘Approved Drug Products with Therapeutic Equivalence Evaluations’ (the ‘Orange Book’ named after its ugly cover) was first published in 1980 and is annually updated^{28} with monthly supplements.^{29} It gives information about the originator’s approval (with a ‘New Drug Application’ – NDA), as well as which originator’s product and strength (called Reference Listed Drug – RLD) has to be used in studies of generics in an ‘Abbreviated New Drug Application’ – ANDA. Generic prescription drugs are coded as follows:
AA
, AN
,
AO
, AP
, or AT
, depending on the
dosage form; or
AB
.
BC
,
BD
, BE
, BN
, BP
,
BR
, BS
, BT
, BX
, or
B*
.
See also information about the ‘Electronic Orange Book’ below.
The generic boom started 1984 in the U.S. with the ‘Drug Price Competition and Patent Term Restoration Act’ (informally known as ‘Hatch-Waxman Act’).^{30}
The approval process was different for innovator (originator) and generic companies.
Innovators:There was an early agreement that pharmaceutical equivalence (content, in vitro) is too permissive and therapeutic equivalence (like in phase III) would require extremely large studies in patients.^{31} Hence, comparing BA in healthy volunteers seemed to be a reasonable compromise.^{32}
“What is the justification for studying bioequivalence in healthy volunteers?
“Variability is the enemy of therapeutics” and is also the enemy of bioequivalence. We are trying to determine if two dosage forms of the same drug behave similarly. Therefore we want to keep any other variability not due to the dosage forms at a minimum. We choose the least variable “test tube”, that is, a healthy volunteer.
Disease states can definitely change bioavailability, but we are testing for bioequivalence, not bioavailability.
Whereas in PK by bioavailability exclusively the Area under Curve extrapolated to infinite time \(\small{(AUC_{0-\infty}})\) is meant, the FDA introduced in 1975 two new terms, namely
The former is understood as a surrogate for the absorption rate \(\small{k\,_\text{a}}\) in a PK model. I prefer – like the ICH^{3} and the FDA since 2003^{33} – rate and extent of absorption, in order not to contaminate the original meaning of BA in PK. Whereas the FDA and China’s CDE require for single dose studies \(\small{AUC_{0-\text{t}}}\) and \(\small{AUC_{0-\infty}}\), in all other jurisdictions only \(\small{AUC_{0-\text{t}}}\) is required.
Let us consider the basic equation of pharmacokinetics \[\frac{f\cdot D}{CL}=\frac{f\cdot D}{V\cdot k_\text{ el}}=AUC_{0-\infty}=\int_{0}^{\infty}C(t)\,dt\textsf{,}\tag{3}\] where \(\small{f}\) is the fraction absorbed (we are interested in the comparison of formulations), \(\small{D}\) is the dose, \(\small{CL}\) is the clearance, \(\small{V}\) is the apparent volume of distribution, \(\small{k\,_\text{el}}\) is the elimination rate constant, and \(\small{C(t)}\) is the plasma concentration with time. We see immediately that for identical^{34} doses and invariate^{35} \(\small{CL}\), \(\small{V}\), \(\small{k\,_\text{el}}\) (which are drug-specific), comparing the \(\small{AUC}\text{s}\) allows to compare the fractions absorbed.
“Pharmacokinetics: one of the magic arts of divination whereby needles are stuck into dummies in an attempt to predict profits.
It must be mentioned that \(\small{C_\text{max}}\) is not sensitive to even substantial changes in the rate of absorption \(\small{k\,_\text{a}}\), since it is a composite metric.^{36} In a one compartment model it depends on \(\small{k\,_\text{a}}\), \(\small{f}\) and both the elimination rate constant \(\small{k\,_\text{el}}\) and \(\small{V}\) (or \(\small{CL}\) if you belong to the other church). Whereas \(\small{k\,_\text{a}}\) and \(\small{f}\) are properties of the formulation – we are interested in – the others are properties of the drug.^{37} \[\eqalign{ t_\textrm{max}&=\frac{\log_{e}(k\,_\text{a}/k\,_\text{el})}{k\,_\text{a}-k\,_\text{el}}\\ C_\textrm{max}&=\frac{f\cdot D\cdot k\,_\text{a}}{V\cdot (k\,_\text{a}-k\,_\text{el})}\large(\small\exp(-k\,_\text{el}\cdot t_\textrm{max})-\exp(-k\,_\text{a}\cdot t_\textrm{max})\large)\tag{4}}\] Therefore, when using it as a surrogate for the absorption rate one must keep in mind that formulations with different fractions absorbed and absorption rate constants will show a T/R-ratio of \(\small{C_\text{max}}\) which differs from the one of \(\small{AUC}\) (which is independent from \(\small{k\,_\text{a}}\) and thus, unbiased with regard to \(\small{f}\)).
An assessment of \(\small{t_\text{max}}\) would not necessarily help; in this example it is 2.71 h for the formulation with \(\small{k\,_\text{a}=0.74}\) / h and 2.78 h for the one with \(\small{k\,_\text{a}=0.71}\) / h. A difference of only four minutes cannot be detected with common sampling schedules.
It took ten years before the alternative metric \(\small{C_\text{max}/AUC}\) (based on theoretical considerations and simulations) was proposed.^{38} ^{39} ^{40} Apart from being less biased than \(\small{C_\text{max}}\), it is also substantially less variable. Regrettably, it was never implemented in any guideline.
In the early 1980s originators failed in trying to falsify the concept (i.e., comparing BE in healthy volunteers to large therapeutic equivalence (TE) studies in patients): If BE passed, TE passed as well and vice versa. If they would have succeeded (BE passed while TE failed), generic companies would have to demonstrate TE in order to get products approved. Such studies would have to be much larger than the originators’ phase III studies, making them economically infeasible.^{31} Essentially, that would have meant an early end of the young generic industry.
However, comparative BA is also used by originators in scale-up of formulations used in phase III to the to-be-marketed formulation, supporting post-approval changes, in line extensions of approved products, and for testing of drug-drug interactions or food effects. Hence, a substantial part of BE trials are performed by originators. If they had been successful to refute the concept, they would have shot into their own foot.
In the mid 1980s a consensus was reached, i.e., that generic approval should only be acceptable after suitable in vivo equivalence. It must be mentioned that BE relies on current Good Manufacturing Practices (cGMP). If drugs are not manufactured according to cGMP, the entire concept would collapse.
The main assumption in BE was
(and still is) that ‘similar’ plasma concentrations in healthy
volunteers will lead to similar concentrations at the target site
(i.e., a receptor) and thus, to similar effects in patients. It
was an open issue whether BE should
be interpreted as a surrogate of clinical efficacy/safety or a measure
of pharmaceutical quality. Whereas in the 1980s the former was
prevalent, since the 1990s the latter is mainstream.
A somewhat naïve interpretation of the
PK metrics is that \(\small{AUC}\) directly translates to
efficacy and \(\small{C_\text{max}}\)
to safety. Especially the latter is not correct because any difference
in \(\small{C_\text{max}}\) leads to a
relatively smaller difference in the maximum effect \(\small{E_\text{max}}\).
There was no consensus about the definition of ‘similarity’ and the statistical methodology to compare plasma profiles. Two early methods are outlined in the following.
top of section ↩︎ previous section ↩︎
This was an approach employed by the FDA. Two drugs were considered bioequivalent if at least 75% of subjects show \(\small{\text{T}/\text{R}\textsf{-}}\)ratios within 75 – 125%.^{17} ^{41} ^{42} It is not a statistic and, thus, was immediately criticized because variable formulations or studies with some extreme values may pass the criterion by pure chance.^{43}
We get for our example in R:
<- data.frame(subject = rep(1:12, each = 2),
example treatment = c("R", "T", "T", "R", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R"),
Y = c(81, 71, 61, 65, 94, 80, 66, 74,
94, 54, 63, 97, 85, 70, 76, 90,
54, 53, 56, 99, 90, 83, 51, 68))
75.75 <- reshape(example, idvar = "subject", timevar = "treatment",
rule.direction = "wide")
75.75 <- rule.75.75[c("subject", "Y.T", "Y.R")]
rule.names(rule.75.75)[2:3] <- c("T", "R")
75.75$T.R <- 100 * (rule.75.75$T / rule.75.75$R)
rule.for (i in 1:nrow(rule.75.75)) {
if (rule.75.75$T.R[i] >= 75 & rule.75.75$T.R[i] <= 125) {
75.75$BE[i] <- TRUE
rule.75.75$within[i] <- "yes"
rule.else {
} 75.75$BE[i] <- FALSE
rule.75.75$within[i] <- "no"
rule.
}
}names(rule.75.75)[c(4, 6)] <- c("T/R (%)", "±25%")
if (sum(rule.75.75$BE) / nrow(rule.75.75) >= 0.75) {
<- "Passed BE by the"
BE else {
} <- "Failed BE by the"
BE
}print(rule.75.75[, c(1:4, 6)], row.names = FALSE); cat(BE, "75/75 Rule.\n")
# subject T R T/R (%) ±25%
# 1 71 81 87.65432 yes
# 2 61 65 93.84615 yes
# 3 80 94 85.10638 yes
# 4 66 74 89.18919 yes
# 5 94 54 174.07407 no
# 6 97 63 153.96825 no
# 7 70 85 82.35294 yes
# 8 76 90 84.44444 yes
# 9 54 53 101.88679 yes
# 10 99 56 176.78571 no
# 11 83 90 92.22222 yes
# 12 51 68 75.00000 yes
# Passed BE by the 75/75 Rule.
Nine of the twelve subjects (75%) have a \(\small{\text{T}/\text{R}\textsf{-}}\)ratio within 75 – 125% and the study would pass, despite the three subjects with high \(\small{\text{T}/\text{R}\textsf{-}}\)ratios.
Another suggestion was testing for a statistically significant difference at level \(\small{\alpha=0.05}\) with a t-test. The null hypothesis was that formulations are equal, i.e., \(\small{\mu_\text{T}-\mu_\text{R}=0}\).
Let’s assess our example in R again:
<- data.frame(subject = rep(1:12, each = 2),
example treatment = c("R", "T", "T", "R", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R"),
Y = c(81, 71, 61, 65, 94, 80, 66, 74,
94, 54, 63, 97, 85, 70, 76, 90,
54, 53, 56, 99, 90, 83, 51, 68))
<- reshape(example, idvar = "subject", timevar = "treatment",
tt direction = "wide")
<- tt[c("subject", "Y.T", "Y.R")] # change for clarity
tt $T.R <- tt[, 2] - tt[, 3] # difference
ttnames(tt)[2:4] <- c("T", "R", "T–R") # cosmetics
4] <- sprintf("%+0.f", tt[, 4])
tt[, <- t.test(x = tt$T, y = tt$R, paired = TRUE)$p.value
p if (p >= 0.05) {BE <- "Passed BE" } else {BE<- "Failed BE" }
print(tt, row.names = FALSE); cat(sprintf("%s by a paired t-test (p = %.4f).\n", BE, p))
# subject T R T–R
# 1 71 81 -10
# 2 61 65 -4
# 3 80 94 -14
# 4 66 74 -8
# 5 94 54 +40
# 6 97 63 +34
# 7 70 85 -15
# 8 76 90 -14
# 9 54 53 +1
# 10 99 56 +43
# 11 83 90 -7
# 12 51 68 -17
# Passed BE by a paired t-test (p = 0.7193).
We calculate a \(\small{p}\)-value of 0.7193, which is statistically not significant and the study would pass again.
However, we face a similar problem like with the 75/75 Rule. If the differences show high variability, the study would pass. On the other hand, if there is low variability in the differences, the study would fail. This is counterintuitive and actually the opposite of what regulators want.
One of my early sins^{44} – it was not the last…
After phenytoin intoxications in Austria^{45} we compared three
generics (containing the free acid like the originator, Na-, or Ca-salt)
to the reference in a crossover design. All formulations have been
approved and were marketed in Austria. Although at that time I already
calculated a 95% CI, the
reviewers of our manuscript insisted in testing for a significant
difference »because it is state of the art«.
The \(\small{AUC}\)s of two generics
were statistically significant different from the reference (\(\small{\text{T}_1}\) containing the free
acid like the originator and \(\small{\text{T}_3}\) containing the
Ca-salt). \(\small{\text{T}_2}\)
containing the Na-salt was statistically not significant different and,
thus, considered equivalent – despite its high \(\small{\text{T}/\text{R}\textsf{-}}\)ratio
(Table II). \[\small{
\begin{array}{ccccc}
\textsf{Table II}\phantom{00000}\\
\text{formulation} & \text{T}/\text{R (%)} & p & &
\text{BE}\\\hline
\text{T}_1 & 146.65 & 0.0195\phantom{6} & \text{*} &
\text{fail}\\
\text{T}_2 & 133.67 & 0.151\phantom{96} & \text{n.s.} &
\text{pass}\\
\text{T}_3 & \phantom{1}27.97 & 0.00596 & \text{**} &
\text{fail}\\\hline
\end{array}}\] If we would evaluate the study according to
current standards (i.e., by the 90%
CI inclusion approach based on
\(\small{\log_{e}\textsf{-}}\)transformed
data and acceptance limits of 80.00 – 125.00%), all generics would fail.
\(\small{\text{T}_3}\) would even be
bioinequivalent because its upper
CL is way below 80% (Table III).
\[\small{\begin{array}{ccccc}
\textsf{Table III}\phantom{0000}\\
\text{formulation} & \text{PE (%)} &
\text{CL}_\text{lower}\text{(%)} & \text{CL}_\text{upper}\text{
(%)} & \text{BE}\\\hline
\text{T}_1 & 151.12 & 118.75 & 192.32 & \text{fail
(inconclusive)}\\
\text{T}_2 & 139.39 & \phantom{1}95.91 & 202.60 &
\text{fail (inconclusive)}\\
\text{T}_3 & \phantom{1}21.67 & \phantom{1}10.25 &
\phantom{2}45.81 & \text{fail (inequivalent)}\\\hline
\end{array}}\] Given the nonlinear
PK of phenytoin,^{46} ^{47} switching a patient
from the originator to the generics with high \(\small{\text{T}/\text{R}\textsf{-}}\)ratios
would be problematic – potentially leading to toxicity after multiple
doses. Even worse would be switching from the generic \(\small{\text{T}_3}\) with its low \(\small{\text{T}/\text{R}\textsf{-}}\)ratio
to any of the other formulations.
An Analysis of Variance (ANOVA) instead of a t-test allows to take period-effects into account.^{48} ^{49} ^{50} This decade was also the heyday of Bayesian methods.^{51} ^{52} ^{53} ^{54} Nomograms for sample size estimation were also Bayesian^{55} but happily misused by frequentists. New parametric^{56} ^{57} as well as nonparametric methods entered the stage.^{57} ^{58} PK metrics to compare controlled release formulations in steady state were proposed.^{59} ^{60} ^{61} The first software to evaluate 2×2×2 crossover studies was released in the public domain.^{62}
The acceptance range in bioequivalence is based on a ‘clinically relevant difference’ \(\small{\Delta}\), i.e., for data following a lognormal distribution \[\left\{\theta_1,\theta_2\right\}=\left\{100\,(1-\Delta),100\,(1-\Delta)^{-1}\right\}\tag{5}\] It must be mentioned that the commonly applied \(\small{\Delta=20\%}\)^{63} leading to \(\small{\{80.00\%,}\) \(\small{125.00\%\}}\) is arbitrary (as is any other).
An important leap forward was the Two One-Sided Tests Procedure (TOST)^{21} – although it was never implemented in its original form \(\small{(6)}\) in regulatory practice. Instead, the confidence interval inclusion approach \(\small{(7)}\) made it to the guidelines. Although these approaches are operationally identical (i.e., their outcomes [pass | fail] are the same), these are statistically different methods:
The TOST Procedure gives two \(\small{p}\)-values, namely \(\small{p(\theta_0\geq\theta_1)}\) and \(\small{p(\theta_0\leq\theta_2)}\).
\[\begin{matrix}\tag{6} H_\textrm{0L}:\frac{\mu_\textrm{T}}{\mu_\textrm{R}}\leq\theta_1\:vs\:H_\textrm{1L}:\frac{\mu_\textrm{T}}{\mu_\textrm{R}}>\theta_1\\ H_\textrm{0U}:\frac{\mu_\textrm{T}}{\mu_\textrm{R}}\geq\theta_2\:vs\:H_\textrm{1U}:\frac{\mu_\textrm{T}}{\mu_\textrm{R}}<\theta_2 \end{matrix}\]
The two-sided \(\small{1-2\,\alpha}\) confidence interval is assessed for inclusion in the acceptance range \(\small{\left\{\theta_1,\theta_2\right\}}\).
\[H_0:\frac{\mu_\textrm{T}}{\mu_\textrm{R}}\not\subset\left\{\theta_1,\theta_2\right\}\:vs\:H_1:\theta_1<\frac{\mu_\textrm{T}}{\mu_\textrm{R}}<\theta_2\tag{7}\]
Evaluating our example for \(\small{\left\{\theta_1,\theta_2\right\}=\left\{80\%,120\%\right\}}\)
by \(\small{(6)}\)
we get \(\small{p(\theta_0\geq\theta_1)=0.0160}\)
and \(\small{p(\theta_0\leq\theta_2)=0.0528}\).
Since one of the \(\small{p\textsf{-}}\)values is \(\small{>\alpha}\), the study would fail.
Assessing it by \(\small{(7)}\) we get a
CI of 82.44 – 124.21%. The
study would fail because the upper
CL is > 120%.
Although the study failed, repeating it in a larger sample size
(with higher power) would likely allow us to demonstrate
BE, since the outcome was
inconclusive.
If assessing the example by \(\small{(7)}\) according to current standards (i.e., of \(\small{\log_e\textsf{-}}\)transformed data for \(\small{\left\{\theta_1,\theta_2\right\}=}\) \(\small{\{80\%,}\) \(\small{125\%\}}\)), we would get a 90% CI of 87.40 – 121.73% and the study would pass. The Times They Are a-Changin’.
It is a misconception that a certain CI of a sample (i.e., a particular study) contains the – true but unknown – population mean \(\small{\mu}\) with \(\small{1-\alpha}\) probabilty. Let’s simulate some studies and evaluate them by \(\small{(7)}\):
invisible(library(PowerTOST))
set.seed(123) # for reproducibility of simulations
<- 1 # true population mean
mue <- 0.25
CV <- 100
studies <- sampleN.TOST(CV = CV, theta0 = mue, targetpower = 0.8, print = FALSE)
x <- x[["Sample size"]]
subjects <- x[["Achieved power"]]
power # simulate subjects within studies, lognormal distribution
<- data.frame(study = rep(1:studies, each = subjects * 2),
samples subject = rep(rep(1:subjects, studies), each = 2),
period = rep(rep(1:2, studies), 2),
sequence = rep(c(rep(c("TR"), subjects),
rep(c("RT"), subjects)), studies),
treatment = c(rep(c("T", "R"), subjects / 2),
rep(c("R", "T"), subjects / 2)),
Y = rlnorm(n = subjects * studies * 2,
meanlog = log(mue) - 0.5 * log(CV^2 + 1),
sdlog = sqrt(log(CV^2 + 1))))
<- c("subject", "period", "treatment")
facs <- lapply(samples[facs], factor) # factorize the data
samples[facs] <- data.frame(study = 1:studies, PE = NA_real_,
result lower = NA_real_, upper = NA_real_,
BE = FALSE, contain = TRUE)
<- numeric(studies)
grand.PE for (i in 1:studies) {
<- samples[samples$study == i, ]
temp <- lm(log(Y) ~ period + subject + treatment, data = temp)
heretic $PE[i] <- 100 * exp(coef(heretic)[["treatmentT"]])
result3:4] <- 100 * exp(confint(heretic, level = 0.90)["treatmentT", ])
result[i, if (round(result[i, 3], 2) >= 80 & round(result[i, 4], 2) <= 125)
$BE[i] <- TRUE
resultif (result$lower[i] > 100 * mue | result$upper[i] < 100 * mue) result$contain[i] <- FALSE
<- mean(result$PE[1:i]) # (cumulative) grand means
grand.PE[i]
}dev.new(width = 4.5, height = 4.5)
<- par(no.readonly = TRUE)
op par(mar = c(3.05, 2.9, 1.4, 0.75), cex.axis = 0.9, mgp = c(2, 0.5, 0))
<- range(c(min(result$lower), 1e4 / min(result$lower),
xlim max(result$upper), 1e4 / max(result$upper)))
plot(1:2, 100 * rep(mue, 2), type = "n", log = "x", xlab = "PE [90% CI]",
ylab = "study #", axes = FALSE,
xlim = xlim, ylim = range(result$study))
abline(v = 100 * c(0.8, mue, 1.25), lty = c(2, 1, 2))
axis(1, at = c(125, pretty(xlim)),
labels = sprintf("%.0f%%", c(125, pretty(xlim))))
axis(2, at = c(1, pretty(1:studies)[-1]), las = 1)
axis(3, at = 100 * mue, label = expression(mu))
box()
lines(grand.PE, 1:studies, lwd = 2)
for (i in 1:studies) {
if (result$BE[i]) { # pass
<- "blue"
clr else { # fail
} if (result$contain[i]) {# mue within CI
<- "magenta"
clr else { # mue not in CI
} <- "red"
clr
}
}lines(c(result$lower[i], result$upper[i]), rep(i, 2), col = clr)
points(result$PE[i], i, pch = 16, cex = 0.6, col = clr)
}par(op)
In 7% of studies the population mean \(\small{\mu}\) is not contained in
the 90% CI (red lines). In
other words, given the result of a single study we can never
know where \(\small{\mu}\) lies. Only
the grand mean (mean of sample means \(\small{\frac{1}{n}\sum_{i=1}^{i=n}\overline{x_i}}\))
approaches \(\small{\mu}\) for a large number
of samples. After the 100^{th} study it is with 99.44%
pretty close to \(\small{\mu}\) (for
geeks: The convergence is poor; if simulating 25,000 studies, it is
100.23%). However, nobody would repeat a – passing – study (blue lines)
for such a rather uninteresting information, right?
This explains also why a particular study might fail by pure
chance even if a formulation is equivalent (here 15% of
studies; red or magenta lines). Such cases are related to the producer’s
risk (Type II
Error = 1 – power), which is for the given conditions 16.3%. On the
other hand, it is also possible that a formulation which is not
equivalent might pass. These cases are related to the patient’s
risk (Type I
Error).
For details see the articles about hypotheses, treatment effects, post hoc power, and sample size
estimation. Science is a cruel mistress.
At a hearing in 1986 the FDA confirmed that \(\small{(6)}\) or \(\small{(7)}\) of untransformed data should be used with \(\small{\Delta=20\%}\). If clinically relevant, tighter limits (\(\small{\Delta=10\%}\)) might be needed.^{64}
The first German guideline was drafted by the International Association for Pharmaceutical Technology (Arbeitsgemeinschaft für Pharmazeutische Verfahrenstechnik) in 1985.^{65} It was presented and discussed in 1987.^{66} ^{67} ^{68}
In 1988 wider acceptance limits of 70 – 130% were proposed for \(\small{C_\text{max}}\) due to its inherent high variability^{69} (as a one-point metric practically always larger than the one of the integrated metric \(\small{AUC}\)).
The Australian draft guideline was published in 1988.^{70} It was the first covering not only the design and evaluation but also validation of bioanalytical methods. The model with effects period, subject, treatment^{25 50} was recommended and a test for sequence-effects was not considered necessary. The problematic conversion of differences to percentages was acknowledged and Fieller’s CI^{26 27} discussed. Kudos to both!
In 1989 a loose-leaf collection was started.^{71} It contained raw-data of generic drugs marketed in Germany, the evaluation provided by companies, as well as results recalculated by the ZL (Central Laboratory of German Pharmacists). Including the 6^{th} supplement of 1996 it contained more than 2,000 pages… It was an indispensible resource for planning new studies and also showed the ‘journey’ of dossiers (i.e., the same study being used by different companies).
The BioInternational conference series set milestones in the development of testing for bioequivalence. The first in Toronto 1989 dealt with the \(\small{\log_{e}\textsf{-}}\)transformation of data and the definition of Highly Variable Drugs (HVDs).^{72} There was a poll among the participants about the \(\small{\log_{e}\textsf{-}}\)transformation of data. Outcome: ⅓ never, ⅓ always, ⅓ case by case (i.e., perform both analyses and report the one with narrower CI ‘because it fits the data better’). Let’s be silent about the last team.^{73} HVDs were defined as drugs with intra-subject variabilities of more than 30% but problems might be evident already at 25%.
The original acceptance range was symmetrical around 100%. In \(\small{\log_{e}\textsf{-}}\)scale it should be symmetrical around \(\small{0}\) (because \(\small{\log_{e}1=0}\)). What happens to our \(\small{\Delta}\), which should still be 20%? Due to the positive skewness of the lognormal distribution a lively discussion started after early publications proposing 80 – 125%.^{25 50} Keeping 80 – 120% would have been flawed because the maximum power should be obtained at \(\small{\mu_\text{T}/\mu_\text{R}=1}\) for \[\exp\left((\log_{e}\theta_1+\log_{e}\theta_2)/2\right),\tag{8}\] which works only if \(\small{\theta_2=\theta_1^{-1}}\) or \(\small{\theta_1=\theta_2^{-1}}\). Keeping the original limits, maximum power would be obtained at \(\small{\mu_\text{T}/\mu_\text{R}=}\) \(\small{\exp((\log_{e}0.8+\log_{e}1.2)/2)}\) \(\small{\approx0.979796}\).
There were three parties (all agreed that the acceptance range should be symmetrical in \(\small{\log_{e}\textsf{-}}\)scale and consequently asymmetrical when back-transformed). These were their arguments and suggestions:
\[\left\{\theta_1,\theta_2\right\}=\left\{100\,(1-\Delta),100/(1-\Delta)\right\}=80-125\%\tag{11}\]
The 90% CI inclusion approach \(\small{(7)}\) based on \(\small{\log_{e}\textsf{-}}\)transformed data with acceptance limits of 80.00 – 125.00% \(\small{(5)}\) was the winner.
either too low, i.e., \(\small{p(\text{BA}<\phantom{1}80\%)>5\%}\)
or too high, i.e., \(\small{p(\text{BA}>125\%)>5\%}\)
but evidently not at the same time. Hence, the 90% CI controls the risk for the population of patients. Therefore, if a study passes, the risk for patients does still not exceed 5%. Note that at the BE limits \(\small{\left\{\theta_1,\theta_2\right\}}\) power, i.e., the chance to pass, is 5%. Therefore, the patient’s risk (type I error) is controlled.
First sample size tables for the multiplicative model with the acceptance range 80 – 125% were published^{74} and extended for narrower (\(\small{\Delta=10\%}\): 90.00 – 111.11%) and wider (\(\small{\Delta=30\%}\): 70.00 – 142.86%) acceptance ranges.^{75} The nonparametric method was improved taking period-effects into account.^{76} ^{77} Drug-drug and food-interaction studies should be assessed for equivalence.^{78} The general applicability of average BE was challenged and the concept of individual and population bioequivalence outlined.^{79} ^{80} ^{81} The first textbook dealing exclusively with BA/BE was published.^{82}
This was also the decade of updated and new guidelines. A European
draft guidance was published in 1990;^{83} the final guideline
was published in December 1991 and came into force in June 1992.^{84} The 90%
CI inclusion approach of \(\small{\log_{e}\textsf{-}}\)transformed
data with an acceptance range of 80 – 125% was recommended and for
NTIDs the
acceptance range may need to be tightened. Due to its inherent higher
variability a wider acceptance range may be acceptable for \(\small{C_\text{max}}\). If inevitable and
clinically acceptable, a wider acceptance range may also be used for
\(\small{AUC}\). Only if clinically
relevant, a nonparametric analysis of \(\small{t_\text{max}}\) was
recommended.
An in vivo study was not required if the new
formulation is
Similar statements about solutions were given in all later guidelines. The second lead to application of the Biopharmaceutic Classification System (BCS).^{85} More about that further down.
“The almost classical 1977 FDA notice […] defined bioavailability as the rate and extent to which the active drug ingredient of therapeutic moiety is absorbed from a drug product and becomes available at the site of action.^{20} However, in the majority of cases substances are intended to exhibit a systemic therapeutic effect, and a more practical definition can be given, taking into account that the substance in the general circulation is in exchange with the substance at the site of action. Therefore, the European 1991 guidance on bioavailability and bioequivalence^{84} gave the following definition: Bioavailability is understood as to be the extent and rate to which the a substance or its therapeutic moiety is delivered from the pharmaceutical form into the general circulation.
In July 1992 a guidance of the FDA was published.^{87} An ANOVA of \(\small{\log_{e}\textsf{-}}\)transformed data was recommended and the nested subject(sequence) term in the statistical model entered the scene. It must be mentioned that in comparative BA studies subjects are usually uniquely coded. Hence, the term subject(sequence) is a bogus one^{88} and could be replaced by the simple subject as well (see below for an example). Alas, this model was implemented in all global guidelines ever since.
In the same year the Canadian guidance for Immediate Release (IR) formulations was published.^{89} To that time is was the most extensive one because it gave not only the method of evaluation, but information about the study design, sample size, ethics, bioanalytics, etc. It differed from the others in the relaxed requirement for \(\small{C_\text{max}}\), where only the \(\small{\text{T}/\text{R}\textsf{-}}\)ratio has to lie within 80 – 125% (instead of its CI). The guidance for MR formulations followed in 1996.^{90}
In 1998 the World Health Organization published its first guideline,^{91} which was similar to the European one.
Table IV shows the result of the example evaluated by various methods. \[\small{\begin{array}{lcccc} \textsf{Table IV}\phantom{0}\\ \phantom{0}\text{Method} & \text{Model} & \text{PE} & \text{power},p,\text{CI, etc.} & \text{BE?}\\\hline \text{80/20 Rule} & \text{additive} & - & 46.40<80\% & \text{fail}\\ t\text{-test} & \text{additive} & +2.417\;(103.32\%) & 0.7193\geq0.05 & \text{pass}\\ \text{TOST} & \text{additive} & +2.417\;(103.32\%) & 0.0160\leq0.05,\,0.0528>0.05 & \text{fail}\\ \text{95% CI} & \text{additive} & +2.417\;(103.32\%) & -12.777\,,+17.611\;(82.44-124.21\%) & \text{fail}\\ \text{Westlake} & \text{additive} & \pm0.000\;(100.00\%) & \pm2.944\;(\pm21.80\%) & \text{fail}\\\hline \text{80/20 Rule} & \text{multiplicative} & - & 72.90<80\% & \text{fail}\\ \text{75/75 Rule} & - & - & 9/12=75\% & \text{pass}\\ t\text{-test} & \text{multiplicative} & 103.14\% & 0.7317\geq0.05 & \text{pass}\\ \text{TOST} & \text{multiplicative} & 103.14\% & 0.0097\leq0.05,\,0.0309\leq0.05 & \text{pass}\\ {\color{Blue} {90\%\,\text{CI}}} & {\color{Blue} {\text{multiplicative}}} & {\color{Blue} {103.14\%}} & {\color{Blue} {87.40-121.73\%}} & {\color{Blue} {\text{pass}}}\\ \text{Westlake} & \text{multiplicative} & 100.00\% & \pm18.09\% & \text{pass}\\ \text{75/75 Rule} & \text{multiplicative} & - & 75\%\subset \pm25\% & \text{pass}\\\hline \end{array}}\] In the additive model the acceptance range was 80 – 120%, whereas in the multiplicative model it is 80 – 125%. Since in the former differences are assessed, the wrong percentages are given in brackets.
At the time being only the 90% CI inclusion approach is globally accepted. Our example in R again:
<- data.frame(subject = rep(1:12, each = 2),
example sequence = c("RT", "RT", "TR", "TR", "RT",
"RT", "TR", "TR", "TR", "TR",
"RT", "RT", "RT", "RT", "TR",
"TR", "TR", "TR", "RT", "RT",
"RT","RT", "TR", "TR"),
treatment = c("R", "T", "T", "R", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R",
"T", "R", "R", "T", "R", "T", "T", "R"),
period = rep(1:2, 12),
Y = c(81, 71, 61, 65, 94, 80, 66, 74,
94, 54, 63, 97, 85, 70, 76, 90,
54, 53, 56, 99, 90, 83, 51, 68))
<- c("subject", "sequence", "treatment", "period")
facs <- lapply(example[facs], factor) # factorize the data
example[facs] <- paste("nested model : period, subject(sequence), treatment",
txt "\nsimple model : period, subject, sequence, treatment",
"\nheretic model: period, subject, treatment\n\n")
<- data.frame(model = c("nested", "simple", "heretic"),
result PE = NA, lower = NA, upper = NA, BE = "fail", na = 0)
for (i in 1:3) {
if (result$model[i] == "nested") { # bogus nested model (guidelines)
<- lm(log(Y) ~ period +
nested %in% sequence +
subject data = example)
treatment, $PE[i] <- 100 * exp(coef(nested)[["treatmentT"]])
result3:4] <- 100 * exp(confint(nested, level = 0.90)["treatmentT", ])
result[i, 6] <- sum(is.na(coef(nested)))
result[i,
}if (result$model[i] == "simple") { # simple model (subjects are uniquely coded)
<- lm(log(Y) ~ period +
simple +
subject +
sequence data = example)
treatment, $PE[i] <- 100 * exp(coef(simple)[["treatmentT"]])
result3:4] <- 100 * exp(confint(simple, level = 0.90)["treatmentT", ])
result[i, 6] <- sum(is.na(coef(simple)))
result[i,
}if (result$model[i] == "heretic") { # heretic model (without sequence)
<- lm(log(Y) ~ period +
heretic +
subject data = example)
treatment, $PE[i] <- 100 * exp(coef(heretic)[["treatmentT"]])
result3:4] <- 100 * exp(confint(heretic, level = 0.90)["treatmentT", ])
result[i, 6] <- sum(is.na(coef(heretic)))
result[i,
}# rounding acc. to guidelines
if (round(result[i, 3], 2) >= 80 & round(result[i, 4], 2) <= 125)
$BE[i] <- "pass"
result
}# cosmetics
$PE <- sprintf("%6.2f%%", result$PE)
result$lower <- sprintf("%6.2f%%", result$lower)
result$upper <- sprintf("%6.2f%%", result$upper)
resultnames(result)[c(3:4, 6)] <- c("lower CL", "upper CL", "NE")
cat(txt); print(result, row.names = FALSE)
# nested model : period, subject(sequence), treatment
# simple model : period, subject, sequence, treatment
# heretic model: period, subject, treatment
#
# model PE lower CL upper CL BE NE
# nested 103.14% 87.40% 121.73% pass 13
# simple 103.14% 87.40% 121.73% pass 1
# heretic 103.14% 87.40% 121.73% pass 0
As already outlined above, the nested model
recommended in all [sic] guidelines is over-specified because
subjects are uniquely coded. In the example we get 13 not estimable
(aliased) effects (in the output of R lines
with NA
, in SAS
.
, and in Phoenix
WinNonlin not estimable
). Correct, because we are asking
for something the data cannot provide.^{88}
In the simple model only one effect cannot be estimated. Even
sequence can be removed from the model. I call it
heretic because regulators will grill you if you are using it.
It was proposed by Westlake^{25 50} and I employed it in hundreds (‼) of
studies and some cases are published.^{92}
Note that the results of all models are identical; if you don’t
believe me, try it with one of your studies.
A ‘Positive List’ was published by the German regulatory authority, i.e., for 90 drugs BE was not required.^{93} In order to comply with the European Note for Guidance of 2001^{94} it had to be removed by the BfArM.
The FDA published guidance for ‘Scale-Up and Postapproval Changes’ (SUPAC)^{95} ^{96} defining three ‘Levels’ of changes:
Under certain conditions of Level 2, demonstration of in vitro similarity by \(\small{f_2\geq 50\%}\)^{97} in the application/compendial medium at 15, 30, 45, 60 and 120 minutes (or until an asymptote is reached) of at least 12 units is sufficient.
\[f_2=50\,\log_{10}\left\{100\,\sqrt{1+\frac{1}{n}\sum_{i=1}^{i=n}(\text{R}_i-\text{T}_i)^2}\right\}\small{\textsf{,}}\tag{12}\]
where \(\small{\text{R}_i}\) and
\(\small{\text{T}_i}\) are the
cumulative percent dissolved at \(\small{1\ldots\ n}\) time points of \(\small{\text{R}}\) and \(\small{\text{T}}\), respectively.
For Level 3 changes in vivo testing
(BE) is mandatory.
It must be mentioned that comparing formulations by \(\small{f_2}\) can be problematic, especially if the shapes of dissolution curves are different and/or if they intersect. \(\small{f_2}\) is not a statistic and, therefore, it is impossible to evaluate false positive and negative rates of decisions for approval of drug products based on it.^{98}
Two (of five) sessions of the BioInternational ’92 conference in Bad
Homburg dealt with BE of Highly
Variable Drugs.^{99} ^{100} Various approaches have been discussed:
Multiple dose instead of single dose studies, metabolite instead of the
parent compound, stable isotope techniques,^{101} add-on designs,
and – for the first time – replicate designs.
Although the BioInternational 2 in Munich 1994 was with over 600 participants the largest in the series, no substantial progress for HVD(P)s was achieved.^{102} Following a suggestion^{103} at a joint AAPS/FDA workshop in 1995 widening the conventional acceptance limits of 80.00 – 125.00% was considered.^{104}
“For some highly variable drugs and drug products, the bioequivalence standard should be modified by changing the BE limits while maintaining the current confidence interval at 90%. […] the bioequivalence limits should be determined based in part upon the intrasubject variability for the reference product.
A hot topic ever since… Why are we discussing it for 35 (‼) years (since the first BioInternational conference)? Is it really that complicated^{105} or are we too stupid?
Studies in steady-state were proposed as an option for HVD(P)s in a European draft guideline^{106} in order to reduce variability, but it was removed from the final version of 2001.^{94}
Validation of bioanalytical methods^{107} ^{108} ^{109} ^{110} was partly covered in Australia and Canada. However, no specific guideline existed. A series of conferences (informally known as ‘Crystal City’) was initiated in 1990.^{111} Procedures stated in the conference report^{112} were discussed at the BioInternational 2 in Munich 1994 and quickly adopted by bioanalytical sites.
Poland happily adopted Germany’s ‘Positive List’^{93} only when it wanted to join the European Union
to learn that in the meantime Germany abandoned it to comply with the
2001 guideline.^{94}
Until 2015 a similar (but shorter) list existed in The Netherlands for
»strict national market authorisation«. Must have been a
schizophrenic situation for assessors of the
MEB: In the morning a
dossier for national MA
without any in vivo comparison → . In the afternoon another
dossier of the same product in the course of a European
submission. A comparative BA study
performed, but 90% CI
80.00–125.01% → . Outright bizarre.
Until 2012 Denmark required for
NTIDs that the 90%
CI had to include 100%
(i.e., that there is no significant treatment effect). Bizarre
as well. For details see Example 3 in this
article.
In February 2005 the FDA published the Electronic Orange Book (EOB), which is updated daily. It can be searched by: Proprietary name, active ingredient, applicant (company), application number, dosage form, route of administration, patent number. It gives also a list of newly added or delisted patents.
The series of ‘Crystal City’ meetings continued.^{113} ^{114} Incurred sample reanalysis (ISR) was proposed^{114} and details subsequently outlined.^{115} The first bioanalytical method validation guidance was published by the FDA in 2001 and revised in 2018.^{116} ^{117} Before the EMA’s draft guideline was published in 2009,^{118} some European inspectors raised an eyebrow if sites worked according to a ‘foreign’ (i.e., the FDA’s) guidance.
“The validation of bioanalytical methods and the analysis of study samples should be performed in accordance with the principles of Good Laboratory Practice (GLP). However, as human bioanalytical studies fall outside of the scope of GLP […], the sites conducting the human studies are not required to be monitored as part of a national GLP compliance programme.
Well roared, lions! My CRO (in Austria) was GLP-certified since 1991, although we performed only phase I studies. In other countries (e.g., Spain), this was not possible. In Germany GLP is subject to state law. Hence, it was possible to get certified in one federal state but not in another… However, this ‘issue’ was resolved with the final guideline published in 2011^{119} and the ICH M10 guideline of 2022,^{120} ^{121} superseding all local guidelines.
In June 2010 the
FDA started to
publish Product-Specific Guidances (PSGs).^{122} They are available
online
(with May 16, 2024 an amazing 2,213) and can be searched by active
ingredient or RLD. Many
PSGs remain drafts for a
long time. For example, of the 131
PSGs starting with the
letter P
, only ten are final and some are for 13 years
still in draft state.
The EMA requires for
prolonged and multiphasic release products both a single dose
study and a study in steady state.^{123} The steady state study can be waived if
there is no ‘risk’ of accumulation (\(\small{AUC_{0-\tau}>90\%AUC_{0-\infty}}\),
where \(\small{\tau}\) is the intended
dosing interval). However, for prolonged release products this option is
rarely – if ever – possible… Different
PK metrics to assess the minimum
concentration in steady-state are required for originators and generic
companies. The former have to assess the minimum concentration within
the dosing interval \(\small{(C_\text{ss,min})}\), whereas the
latter have to assess the minimum concentration at the end of the dosing
interval \(\small{(C_{\text{ss}\,,\tau})}\). If there
is a lag-time, the latter is more difficult due to its higher
variability.^{124} Why double standards?
For prolonged release products with no ‘risk’ of accumulation and
multiphasic release products the cut-off times for partial \(\small{AUC\textsf{s}}\) have to be
pre-specified based on PK, which
is a rather difficult feat. Furthermore,
BE has not only to be demonstrated
for \(\small{AUC_{0-\text{t}}}\) and
all partial \(\small{AUC\textsf{s}}\)
but also for \(\small{C_\text{max}}\)
in each of the sections. This gives for one cut-off time \(\small{\text{tc}}\) already a whopping six
PK metrics (\(\small{AUC_{0-\text{t}}}\), \(\small{AUC_{0-\infty}}\), \(\small{AUC_{0-{\text{tc}}}}\), \(\small{AUC_{\text{tc}-\text{t}}}\), \(\small{C_{\text{max,t}\leq \text{tc}}}\),
\(\small{C_{\text{max,t}>\text{tc}}}\)).
At least reference-scaling (see below) is acceptable
for all PK metrics – except for
\(\small{AUC_{0-\text{t}}}\) and \(\small{AUC_{0-\infty}}\).^{123} That’s different to the few
PSGs of the
FDA
(e.g., methylphenidate,
zolpidem),
where the cut-off times are based on
PD and – apart from the partial
\(\small{AUC\textsf{s}}\) and \(\small{AUC_{0-\infty}}\) – only the
global \(\small{C_\text{max}}\) is required.
top of section ↩︎ previous section ↩︎
Whereas Average Bioequivalence (ABE) is bijective (if \(\small{T}\) is equivalent to \(\small{R}\), \(\small{R}\) is also equivalent to \(\small{T}\)), this holds in all variants of Scaled Average Bioequivalence (SABE) only if \(\small{CV_\text{wT}=CV_\text{wR}}\). Therefore, switching from \(\small{R}\) to \(\small{T}\) is tolerable if \(\small{CV_\text{wT}<CV_\text{wR}}\) but in such a case switching from \(\small{T}\) to \(\small{R}\) might be problematic.
After a wealth of – controversal – publications in the 1990s,^{79 80 81} ^{125} ^{126} ^{127} ^{128} ^{129} ^{130} ^{131} ^{132} ^{133} the FDA introduced two new concepts as alternatives to ABE, namely Population Bioequivalence (PBE) and Individual Bioequivalence (IBE).^{134} ABE focuses only on the comparison of population averages of the PK metrics and not the variances of formulations. It does also not assess a subject-by-formulation interaction variance, that is, the variation in the average \(\small{\text{T}}\) and \(\small{\text{R}}\) difference among individuals. In contrast, PBE and IBE include comparisons of both averages and variances of PK metrics. The PBE approach assesses total variability of the PK metrics in the population. The IBE approach assesses within-subject variability for the \(\small{\text{T}}\) and \(\small{\text{R}}\) formulations, as well as the subject-by-formulation interaction.
Demonstrated PBE would support ‘Prescribability’ (i.e., a drug naïve patient could start treatment), whereas IBE support ‘Switchability’ (i.e., a patient could switch formulations during treatment).^{133} Contrary to ABE, both PBE and IBE require studies in a full replicate design, which means that both \(\small{\text{T}}\) and \(\small{\text{R}}\) are administered twice. The acceptance limits for ABE were kept at 80.00 – 125.00% but for the others scaling to the variability of the reference was possible. That would mean an incentive for test formulations with a lower variability than the one of the reference but a penalty for ones with a higher variability.
However, the underlying statistical concepts were not trivial and the
result practically incomprehensible for non-statisticians. Furthermore,
both approaches had a discontinuity (when moving from constant- to
reference-scaling), which lead to an inflated type I error (patient’s
risk) of approximately 6.5%.^{130 131 134} ^{135} ^{136}
PBE/IBE
faced criticism, e.g.,
responses [to the guidance] were still doubt-filled as to whether the new bioequivalence criteria really provided added value compared to average bioequivalence^{137}
and was regarded a‘theoretical’ solution to a ‘thoretical’ problem^{138} ^{139}
leading to its omission from a subsequent guidance,^{140} and a return to conventional ABE.^{141}
“Average bioequivalence should suffice based upon grounds of ‘practicality, plausibility, historical adequacy, and purpose’ and ‘because we have better things to do.’ […] ‘Statisticians have a bad track record in bioequivalence, […] the literature is full of ludicrous recommendations from statisticians, […] regulatory recommendations (of dubious validity) have been hastily implemented, and practical realities have been ignored’. “Individual bioequivalence is a promising, clinically relevant method that should theoretically provide further confidence to clinicians and patients that generic drug products are indeed equivalent in an individual patient.
Even today, considering the studies summarized and analyzed by the FDA, the data is inadequate to validate the theoretical approach and provide confidence to the scientific community that the methodology required and the expense entailed are justified.
At this time, individual bioequivalence still remains a theoretical solution to solve a theoretical clinical problem. We have no evidence that we have a clinical problem, either a safety or an efficacy issue, and we have no evidence that if we have the problem that individual bioequivalence will solve the problem.
I remember a Dutch regulator standing up in the BioInternational conference in London 2003, saying:
I’m glad that PBE and IBE are dead. I never understood them.
We don’t see a problem, our database search showed that even HVDPs comply with the usual BE criteria.
However, this observation was based on its requirement that only the PE of \(\small{C_\text{max}}\) has to lie within 80.0–125.0%.^{90}
Benet proposed in a keynote at the BioInternational 1994 that innovators should perform replicate studies as part of the new drug application and provide information on intra- and inter-subject measures of extent and rate of BA in the PK section of the package insert.^{102} SABE was also discussed at the BioInternational 2005.^{143}
The EMA published a concept paper in 2006, containing valuable points for discussion.^{144}
Application of SABE was not limited to a certain PK metric. Furthermore, a comparison of \(\small{s_{\text{wT}}^{2}}\) with \(\small{s_{\text{wR}}^{2}}\) would require a full replicate design.
“Who controls the past controls the future: who controls the present controls the past.
SABE was introduced 2010 first by the EMA,^{145} shortly after by the FDA,^{146} ^{147} in 2017 by the WHO,^{148} and in 2018 by Health Canada.^{149}
Terminology:
The concept of SABE is based on the following considerations:
The conventional model of ABE by \(\small{(7)}\) is modified in SABE to \[H_0:\;\frac{\mu_\text{T}}{\mu_\text{R}}\Big{/}\sigma_\text{wR}\not\subset\left\{\theta_{\text{s}_1},\theta_{\text{s}_2}\right\}\;vs\;H_1:\;\theta_{\text{s}_1}<\frac{\mu_\text{T}}{\mu_\text{R}}\Big{/}\sigma_\text{wR}<\theta_{\text{s}_2},\tag{13}\] where \(\small{\sigma_\text{wR}}\) is the standard deviation of the reference. The scaled limits \(\small{\left\{\theta_{\text{s}_1},\theta_{\text{s}_2}\right\}}\) of the acceptance range depend on conditions given by the agency.
Reference-Scaled Average Bioequivalence (RSABE)^{153} is recommended by the FDA and China’s CDE. Average Bioequivalence with Expanding Limits (ABEL)^{154} is another variant of SABE and recommended in all other jurisdictions. In order to apply the methods following conditions have to be fulfilled:
In all methods a point estimate-constraint is imposed. Even if a study would pass the scaled limits, the PE has to lie within 80.00 – 125.00% in order to pass. Whilst the PE-constraint is statistically not justified, it was implemented in all jurisdictions ‘for political reasons’.^{156}
“
- There is no scientific basis or rationale for the point estimate recommendations
- There is no belief that addition of the point estimate criteria will improve the safety of approved generic drugs
- The point estimate recommendations are only “political” to give greater assurance to clinicians and patients who are not familiar (don’t understand) the statistics of highly variable drugs
Compared to ABE, SABE leads to a substantial reduction in sample sizes (see this article). However, both RSABE and ABEL may result in an inflated type I error (patient’s risk),^{105} which was already described in 2009^{154} ^{157} (before [sic] SABE was implemented) and is still an unresolved issue^{158} ^{159} (see also this article).
top of section ↩︎ previous section ↩︎
The FDA
published SAS
code^{146 153} but it is a mystery why a fixed-effects
model for the partial replicate design and a mixed-effects model
for a full replicate design was recommended. If you understand why,
please let me know.
If \(\small{s_\text{wR}<0.294}\),
ABE has to be assessed by \(\small{(7)}\) and
\(\small{\Delta=20\%}\) (90%
CI entirely within 80.00 –
125.00%).
It must be mentioned that if the study was performed in a partial
replicate design, the model is over-specified and the optimizer of any
(‼) software might not converge (for details see this article).
If \(\small{s_\text{wR}\geq0.294}\),
RSABE
should be applied. The regulatory constant is given by \[\theta_\text{s}=\frac{\log_{e}1.25}{s_0}\approx
0.8925742\ldots\small{\textsf{,}}\tag{14}\] where \(\small{s_0}\) is the regulatory switching
condition \(\small{0.25}\). The point
estimate \(\small{PE}\) is given by
\(\small{\overline{Y}_\text{T}-\overline{Y}_\text{R}}\),
where \(\small{\overline{Y}_\text{T}}\)
and \(\small{\overline{Y}_\text{R}}\)
are the means of \(\small{\log_{e}}\)-transformed
PK-metrics obtained for the test
and reference products, respectively. The standard error \(\small{se}\) of the \(\small{PE}\) is \[se=\sqrt{\frac{\widehat{s}}{{N_{s}}^{2}}\sum
\frac{1}{n_i}}\small{\textsf{,}}\tag{15}\] where \(\small{\widehat{s}}\) is the model’s
residual mean squares error, \(\small{N_\text{s}}\) are the number of
sequences, and \(\small{n_i}\) the
number of subjects in sequence \(\small{i}\). We start with the
SABE model \(\small{(13)}\) and
work with \(\small{\log_{e}\textsf{-}}\)transformed
values for convenience \[-\theta_\text{s}\leq\frac{\mu_\text{T}-\mu_\text{R}}{\sigma_\text{wR}}\leq\theta_\text{s}\tag{16}\]
and use its squared and linearized form \[\left(\mu_\text{T}-\mu_\text{R}\right)^2-{\theta_{s}}^{2}\cdot{\sigma_{\text{wR}}}^{2}\leq0\small{\text{.}}\tag{17}\]
Upon inspecting part of the SAS
code in the
FDA’s
guidance…^{153}
pointest=exp(estimate); x=estimate**2-stderr**2; theta=((log(1.25))/0.25)**2; y=-theta*s2wr;
…we see that stderr**2, i.e., \(\small{se^2}\) from \(\small{(15)}\), is inserted in the left-hand side of \(\small{(17)}\) – which is formulated in the true parameters – yielding for the estimates \[PE^2-se^2-{\theta_{s}}^{2}\cdot {s_{\text{wR}}}^{2}\leq0\small{\textsf{.}}\tag{18}\] This is not stated as such in the formulas of the guidance. We are aware of only one reference,^{160} which is – regrettably – not in the public domain.
“The statistical approach we use is very similar to that proposed by Tothfalusi, Endrenyi, et al. 2001,^{161} with a minor difference (use of an unbiased estimator for \(\small{\left(\mu_\text{T}-\mu_\text{R}\right)^2})\).
Then \[\eqalign{ E_\text{m}&=PE^2-se^2\\ E_\text{s}&={\theta_{s}}^{2}-{s_{\text{wR}}}^{2} }\tag{19}\] are calculated, where \(\small{E_\text{m}}\) and \(\small{E_\text{s}}\) are the estimates of the true parameters (\(\small{se^2}\) acts again as a bias correction). Since their distributions are known, their upper confidence limits \(\small{C_\text{m}}\) and \(\small{C_\text{s}}\) can be calculated by \[\eqalign{ C_\text{m}&=\left(\left|PE\right|+t_{1-\alpha,\,\nu}\cdot se\right)^2\\ C_\text{s}&=E_\text{s}\cdot \nu\big{/}\chi_{1-\alpha,\,\nu}^{2}\small{\textsf{,}} }\tag{20}\] where \(\small{\nu}\) are the degrees of freedom given by \(\small{\sum n-N_\text{s}}\). A modification^{162} of Howe’s approximation^{163} is used in order to get the CI of a sum of random variables from the individual CIs. The squared lengths of the individual CIs are: \[\eqalign{ L_\text{m}&=\left(C_\text{m}-E_\text{m}\right)^2\\ L_\text{s}&=\left(C_\text{s}-E_\text{s}\right)^2\small{\textsf{.}} }\tag{21}\] Finally we calculate the 95% upper confidence bound: \[\small{\textsf{bound}}=E_\text{m}-E_\text{s}+\sqrt{\left(L_\text{m}-L_\text{m}\right)^2}\tag{22}\]
In order to pass RSABE:
Although the EMA’s
concept paper stated^{144} that the
statistical and computational methods will be given in the guideline,
this was not the case.^{145}
SAS
code and two example data sets were published later in
a Q&A document.^{164} The
evaluation has to be done with a simple
ANOVA, i.e., assuming
identical within-subject variances of the test and reference products.
Methods to identify and handle outliers were not given.
If \(\small{CV_\text{wR}\leq30\%}\), ABE has to be demonstrated by \(\small{(7)}\) and \(\small{\Delta=20\%}\) (90% CI entirely within 80.00 – 125.00%).
Otherwise, ABEL can be applied and the limits expanded to \(\small{\left\{L,U\right\}=100\exp(\mp k\cdot s_\text{wR})}\), with the regulatory constant \(\small{k=0.76}\). The scaling is capped at 50% for all agencies (maximum expansion 69.84 – 143.19%), except for Health Canada at ≈57.382% (67.7 – 150.0%).
invisible(library(PowerTOST))
<- 100 * sort(c(seq(0.3, 0.6, 0.05), 0.57382))
CVwR <- data.frame(CVwR = CVwR,
EL EMA.uc = c(rep("no", 4), rep("yes", 4)),
EMA.L = NA_real_, EMA.U = NA_real_,
HC.uc = c(rep("no", 6), rep("yes", 2)),
HC.L = NA_real_, HC.U = NA_real_)
<- scABEL(CV = CVwR / 100, regulator = "EMA")
EMA <- scABEL(CV = CVwR / 100, regulator = "HC")
HC 1] <- sprintf("%.3f%%", EL[, 1])
EL[, 3:4] <- sprintf("%.2f%%", 100 * EMA)
EL[, 6:7] <- sprintf("%.1f%%", 100 * HC)
EL[, names(EL)[2:7] <- c("capped", "L (EMA)", "U (EMA)",
"capped", "L (HC)", "U (HC)")
print(EL, row.names = FALSE)
# CVwR capped L (EMA) U (EMA) capped L (HC) U (HC)
# 30.000% no 80.00% 125.00% no 80.0% 125.0%
# 35.000% no 77.23% 129.48% no 77.2% 129.5%
# 40.000% no 74.62% 134.02% no 74.6% 134.0%
# 45.000% no 72.15% 138.59% no 72.2% 138.6%
# 50.000% yes 69.84% 143.19% no 69.8% 143.2%
# 55.000% yes 69.84% 143.19% no 67.7% 147.8%
# 57.382% yes 69.84% 143.19% yes 66.7% 150.0%
# 60.000% yes 69.84% 143.19% yes 66.7% 150.0%
It has to be demonstrated that the high \(\small{CV_\text{wR}}\) is not caused by
outliers. If outliers are detected, they have to be excluded and \(\small{CV_\text{wR}}\) as well as \(\small{\left\{L,U\right\}}\) recalculated.
However, the 90% CI has to be
calculated with complete data.
In order to pass ABEL:
Based on \(\small{\Delta=10\%}\) for Narrow Therapeutic Index Drugs (EMA) and Critical Dose Drugs (Health Canada) the BE limits may need to be narrowed^{145 148 149} or scaled.^{153} ^{165}
With the regulatory switching condition \(\small{s_0=0.10}\) we get the regulatory
constant by \[\theta_\text{s}=\frac{\log_{e}1.11111}{s_0}\approx
1.053595\ldots\tag{23}\] The 95% upper confidence bound is
determined with \(\small{\theta_\text{s}}\) by \(\small{(15)-(22)}\).
The upper CL for \(\small{\sigma_\text{wT}/\sigma_\text{wR}}\)
is calculated by \[\frac{s_\text{wT}/s_\text{wR}}{\sqrt{F_{{1-\alpha/2},\nu_1,\nu_2}}}\small{\textsf{,}}\tag{24}\]
where \(\small{s_\text{wT}}\) ist the
estimate of \(\small{\sigma_\text{wT}}\) with \(\small{\nu_1}\) degrees of freedom, \(\small{s_\text{wR}}\) ist the estimate of
\(\small{\sigma_\text{wR}}\) with \(\small{\nu_2}\) degrees of freedom, and
\(\small{F}\) is the value of the F-distribution
with \(\small{\nu_1}\) (numerator) and
\(\small{\nu_2}\) (denominator) for
\(\small{\alpha=0.1}\).
In order to pass:
The last condition is operationally equivalent to capping the ‘implied’ limits \(\small{\left\{L,U\right\}}\) of RSABE at \(\small{CV_\text{wR}\geq}\) \(\small{\approx21.42\%}\). Otherwise, for any larger \(\small{CV_\text{wR}}\) they would by wider than 80.00 – 125.00%. Of course, that is not what we want for an NTID. We can show that numerically.
<- function(x, Delta, sigma.0) { # x is CVwR
fun <- log(Delta) / sigma.0 # regulatory constant
theta.s <- sqrt(log(x^2 + 1)) # within subject standard deviation of R
swR <- exp(theta.s * swR) # upper ‘implied’ (scaled) limit
U <- U - 1.25 # target zero
objective return(objective)
}<- 1.11111 # approximate acc. to the guidance (not the exact 1/0.9)
Delta .0 <- 0.10 # regulatory switching condition
sigma# numerically find the CVwR where U ~1.25
<- 100 * uniroot(fun, interval = c(0, 0.3), tol = 1e-8,
CVcap .0)$root
Delta, sigma# check the ‘implied’ limits
<- sort(c(CVcap / 100, seq(0.05, 0.3, 0.05)))
CVwR <- data.frame(CVwR = CVwR, L.implied = NA_real_, U.implied = NA_real_,
comp L.capped = NA_real_, U.capped = NA_real_)
<- c(-1, +1)
f for (i in seq_along(CVwR)) {
2:5] <- sprintf("%.2f%%", 100 * exp(f * log(Delta) / sigma.0 *
comp[i, sqrt(log(CVwR[i]^2 + 1))))
if (comp$CVwR[i] >= CVcap / 100) {
4:5] <- sprintf("%.2f%%", 100 * exp(f * log(Delta) / sigma.0 *
comp[i, sqrt(log((CVcap / 100)^2 + 1))))
}
}$CVwR <- sprintf("%.2f%%", 100 * comp$CVwR)
comp<- sprintf("The ‘implied’ limits in RSABE are capped at CVwR %.9g%%.\n", CVcap)
txt cat(txt); print(comp, row.names = FALSE)
# The ‘implied’ limits in RSABE are capped at CVwR 21.4189888%.
# CVwR L.implied U.implied L.capped U.capped
# 5.00% 94.87% 105.41% 94.87% 105.41%
# 10.00% 90.02% 111.08% 90.02% 111.08%
# 15.00% 85.46% 117.02% 85.46% 117.02%
# 20.00% 81.17% 123.20% 81.17% 123.20%
# 21.42% 80.00% 125.00% 80.00% 125.00%
# 25.00% 77.15% 129.62% 80.00% 125.00%
# 30.00% 73.40% 136.25% 80.00% 125.00%
Introduced by the FDA in 2000,^{170} ^{140} the EMA in 2010,^{145} the WHO in 2017,^{148} and adopted by the ICH in 2019^{171} as an alternative for in vivo testing of IR products based on the Biopharmaceutic Classification System, where drugs are classified by their solubility and permeability.^{85}
\[\small{\begin{array}{cc}\hline \textbf{Class I} & \textbf{Class II}\\\hline \text{High solubility} & \text{Low solubility}\\ \text{High permeability} & \text{High permeability}\\\hline \textbf{Class III} & \textbf{Class IV}\\\hline \text{High solubility} & \text{Low solubility}\\ \text{Low permeability} & \text{Low permeability}\\\hline\end{array}}\]
The idea behind waiving an in vivo study is based on the fact that such studies are not required for aqueous solutions (see above). Thus, if a drug product dissolves very rapidly, it can be expected to behave similar to a solution.
A BCS-based biowaiver may be acceptable if the drug substance has been proven to exhibit high solubility and complete absorption (Class I) and either very rapid (> 85% within 15 min) or similarly rapid (85% within 30 min) in vitro dissolution characteristics of the test and reference product has been demonstrated considering specific requirements and excipients that might affect BA are qualitatively and quantitatively the same. In general, the use of the same excipients in similar amounts is preferred.
BCS-based biowaivers may also be acceptable if the drug substance has been proven to exhibit high solubility and limited absorption (Class III) and very rapid (> 85% within 15 min) in vitro dissolution of the test and reference product has been demonstrated considering specific requirements, excipients that might affect BA are qualitatively and quantitatively the same, and other excipients are qualitatively the same and quantitatively very similar.
The following conditions should be employed in the comparative dissolution studies to characterize the dissolution profile of the products:^{171}
When high variability or coning is observed in the paddle apparatus at 50 rpm for both reference and test products, the use of the basket apparatus at 100 rpm is recommended. Additionally, alternative methods (e.g., the use of sinkers or other appropriately justified approaches) may be considered to overcome issues such as coning, if scientifically substantiated.^{171}
The evaluation of the similarity factor \(\small{f_2}\) is based on the following conditions:^{171}
A risk assessment of potential bioinequivalence by application of a biowaiver has be provided, which has to be more strict for Class III than for Class I drugs.^{145} Biowaivers for NTIDs are not possible.
Alas, approaches are still not harmonized – after eight BioInternational conferences 1989–2008 and six GBHI workshops 2015–2024…
Agency | Uncomplicated drug | HVD(P) | NTID |
---|---|---|---|
FDA^{153} |
ABE (any metric) 90% CI within 80.00–125.00% |
RSABE (any metric) \(\small{\textsf{bound}\leq 0}\) PE within 80.00–125.00% |
RSABE (any metric) \(\small{\textsf{bound}\leq 0}\) upper CL of \(\small{\sigma_\text{wT}/\sigma_\text{wR} \leq 2.5}\) 90% CI within 80.00–125.00% |
EMA^{145 123} |
ABE (any metric) 90% CI within 80.00–125.00% |
ABEL (\(\small{C_\text{max}}\), \(\small{\textsf{p}AUC}\)) \(\small{uc}\) 50% PE within 80.00–125.00% |
ABE: 90% CI within
90.00–111.11% PSGs: Only for \(\small{AUC}\) |
WHO^{148} ^{172} |
ABE (any metric) 90% CI within 80.00–125.00% |
ABEL (\(\small{C_\text{max}}\), \(\small{AUC}\)) \(\small{uc}\) 50% PE within 80.00–125.00% |
ABE: 90% CI within 90.00–111.11% |
Health Canada^{149} |
ABE \(\small{AUC}\): 90% CI within 80.0–125.0% \(\small{C_\text{max}}\): PE within 80.0–125.0% |
ABEL (\(\small{AUC}\), \(\small{uc}\) 57.382%) ABE (\(\small{C_\text{max}}\): PE within 80.0–125.0%)^{149} |
ABE \(\small{AUC}\): 90% CI within 90.0–112.0% \(\small{C_\text{max}}\): 90% CI within 80.0–125.0% |
This lack of harmonization leads to the paradox (though hypothetical) situation that the same study will pass in one jurisdiction but fail in another.^{105 158}
Still unresolved, outlook:
<nitpick>
No other jurisdiction contains such a ridiculous statement.
“Those people who think they know everything
are a great annoyance to those of us who do.
</nitpick>
top of section ↩︎ previous section ↩︎
See also a – somewhat outdated – collection of guidelines, my presentations, and further readings.^{136 137 179} ^{233} ^{234} ^{235} ^{236} ^{237} ^{238} ^{239} ^{240} ^{241} ^{242} ^{243} ^{244} ^{245} To whom it may concern.^{246} ^{247} ^{248}
A word of warning: The textbooks dealing mainly with statistics (marked with ★) are rather tough cookies and not recommended for beginners.
In gratitude to László Endrényi, whose work on pharmacokinetic metrics and the bioequivalence of Highly Variable Drugs inspired many scientists in the field.
Helmut Schütz 2024
,
PowerTOST
, and
Rüdiger Appel’s station-clock
GPL 3.0,
klippy
MIT,
pandoc
GPL 2.0.
1^{st} version April 9, 2024. Rendered July 31, 2024 21:35 CEST
by rmarkdown
via pandoc in 0.16 seconds.
Abbreviation | Meaning |
---|---|
AAPS | American Association of Pharmaceutical Scientists |
ABE | Average Bioequivalence |
ABEL | Average Bioequivalence with Expanding Limits |
ANAMED | Agencia Nacional de Medicamentos (competent authority of Chile) |
ANDA | Abbreviated New Drug Application (generics; FDA term) |
ANOVA | Analyis of Variance |
ANVISA | Agência Nacional de Vigilância Sanitária (competent authority of Brazil) |
AOAC | (U.S.) Association of Official Analytical Chemists |
APhA | (U.S.) Academy of Pharmaceutical Sciences |
API | Active Pharmaceutical Ingredient |
APV | Arbeitsgemeinschaft für Pharmazeutische Verfahrenstechnik (International Association for Pharmaceutical Technology) |
\(\small{AUC}\) | Area Under the Curve |
\(\small{AUC_{0-\text{t}}}\) | \(\small{AUC}\) from the time of administration to the time of the last measurable concentration |
\(\small{AUC_{0-72\text{h}}}\) | \(\small{AUC}\) from the time of administration to 72 hours (IR products) |
\(\small{AUC_{0-\infty}}\) | \(\small{AUC}\) from the time of administration extrapolated to infinite time |
BA | Bioavailability |
BCS | Biopharmaceutic Classification System |
BE | Bioequivalence |
BfARM | Bundesinstitut for Arzneimittel und Medizinprodukte (competent authority of Germany) |
\(\small{\textsf{bound}}\) | 95% upper confidence bound in RSABE |
\(\small{C}\) | Concentration |
CDE | Center for Drug Evaluation (China) |
CDER | Center for Drug Evaluation and Research (FDA) |
CFR | Code of Federal Regulations (U.S.) |
cGMP | curent Good Manufacturing Practices |
CHMP | Committee for Medicinal Products for Human Use (of the EMA) |
CI | Confidence Interval |
CL | Confidence Limit |
\(\small{CL}\) | Clearance |
\(\small{C_\text{max}}\) | Maximum concentration |
CPMP | Committee for Proprietary Medicinal Products (of the EMEA) |
CRO | Contract Research Organization |
\(\small{C_\text{ss,min}}\) | Minimum concentration in steady-state within the dosing interval \(\small{\tau}\) |
\(\small{C_{\text{ss}\,,\tau}}\) | Concentration in steady-state at the end of the dosing interval \(\small{\tau}\) |
\(\small{C_{\text{t}_\text{last}}}\) | Last measured concentration |
\(\small{\widehat{C}_{\text{t}_\text{last}}}\) | Estimated concentration at \(\small{t_\text{last}}\) |
CVM | Center for Veterinary Medicine (FDA) |
\(\small{CV_\text{wR},CV_\text{wT}}\) | Observed within-subject Coefficient of Variation of the Reference and Test product |
\(\small{D}\) | Dose |
EMA | European Medicines Agency |
\(\small{E_\text{max}}\) | Maximum effect |
EMEA | European Agency for the Evaluation of Medicinal Products (rebranded to EMA in Dec. 2009) |
EOB | Electronic Orange Book (FDA) |
EUFEPS | European Federation for Pharmaceutical Sciences |
\(\small{f}\) | Fraction absorbed |
\(\small{f_2}\) | Similarity factor |
FDA | (U.S.) Food and Drug Administration |
FDC | Fixed Dose Combination (product) |
FIP | Federation International Pharmaceutique (International Pharmaceutical Federation) |
GBHI | Global Bioequivalence Harmonisation Initiative |
GLP | Good Laboratory Practice |
GSD | Group-Sequential Design |
\(\small{H_0}\) | Null hypothesis |
\(\small{H_1}\) | Alternative hypothesis (also \(\small{H_\text{a}}\)) |
HPFB | Health Products and Food Branch (competent authority of Canada) |
HVD(P) | Highly Variable Drug (Product) |
IBE | Individual Bioequivalence |
ICH | International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use |
IR | Immediate Release (product) |
ISR | Incurred sample reanalysis |
IV | Intravenous |
\(\small{k}\) | Regulatory constant in ABEL: 0.76 |
\(\small{k\,_\text{a}}\) | Absorption rate constant (also \(\small{k_\text{01}}\)) |
\(\small{k\,_\text{el}}\) | Elimination rate constant (also \(\small{k_\text{10}}\)) |
\(\small{L}\) | Lower expanded limit in ABEL |
LALA | Locally applied, locally acting (product) |
\(\small{\log_{e}}\) | Natural logarithm (base e ≈ 2.71828…) |
\(\small{\log_{10}}\) | Decadic logarithm (base 10) |
\(\small{L,U}\) | Expanded limits in ABEL |
MA | Market Authorisation |
MEB | Medicines Evaluation Board (competent authority of The Netherlands) |
MR | Modified release (product) |
\(\small{n}\) | Sample size |
\(\small{n_1,n_2}\) | Number of subjects in sequences 1 and 2 of a 2×2×2 crossover design |
NDA | New Drug Application (originators; FDA term) |
NTID | Narrow Therapeutic Index Drug (Canada: Critical Dose Drug) |
OGD | Office of Generic Drugs (FDA) |
OGDP | Office of Generic Drug Policy (FDA) |
\(\small{p(x)}\) | Probability of \(\small{x}\) |
\(\small{\text{p}AUC}\) | Partial \(\small{AUC}\) |
PBE | Population Bioequivalence |
PD | Pharmacodynamics |
PE | Point Estimate of \(\small{\mu_\text{T}/\mu_\text{R}}\) |
PQT | Prequalification Team (WHO) |
PK | Pharmacokinetics |
PKWP | Pharmacokinetics Working Party (of the EMA’s CHMP) |
PQT | Prequalification Team (WHO) |
PSG | Product-Specific Guidance |
\(\small{\text{R}}\) | Reference product |
RLD | Reference Listed Drug (FDA term) |
RSABE | Reference-Scaled Average Bioequivalence |
\(\small{s}\) | Sample standard deviation |
\(\small{s_0}\) | Switching condition in RSABE: for HVD(P)s 0.25 and for NTIDs 0.1 |
SABE | Scaled Average Bioequivalence |
SUPAC | Scale-Up and Postapproval Changes (FDA) |
\(\small{s_\text{wR},s_\text{wT}}\) | Observed within-subject standard deviation of the Reference and Test product |
\(\small{s_{\text{wR}}^{2},s_{\text{wT}}^{2}}\) | Observed within-subject variance of the Reference and Test product |
\(\small{t}\) | Time |
\(\small{\text{T}}\) | Test product |
\(\small{\text{tc}}\) | Cut-off time (multiphasic release products) |
TE | Therapeutic Equivalence |
TGA | Therapeutic Goods Administration (competent authority of Australia) |
\(\small{t_\text{last}}\) | Time of the last measured concentration \(\small{C_{\text{t}_\text{last}}}\) |
\(\small{t_\text{max}}\) | Time of \(\small{C_\text{max}}\) |
TIE | Type I Error |
TOST | Two One-Sided Tests |
TSD | Two-Stage Design |
\(\small{U}\) | Upper expanded limit in ABEL |
\(\small{uc}\) | Upper cap of expansion in ABEL |
URL | Uniform Resource Locator |
\(\small{V}\) | Apparent volume of distribution |
WHO | World Health Organization |
\(\small{\bar{x}_\text{T},\bar{x}_\text{R}}\) | Arithmetic means of \(\small{\text{T}}\) and \(\small{\text{R}}\) |
\(\small{\alpha}\) | Nominal level of the test, probability of Type I Error (patient’s risk) |
\(\small{\beta}\) | Probability of Type II Error (producer’s risk), where \(\small{\beta=1-\pi}\) |
\(\small{\Delta}\) | Clinically relevant difference |
\(\small{\theta_\text{s}}\) | Regulatory constant in RSABE: for HVD(P)s 0.8925742… and for NTIDs 1.053595… |
\(\small{\theta_0}\) | True (in sample size estimation assumed) \(\small{\text{T}/\text{R}}\)-ratio |
\(\small{\theta_1,\theta_2}\) | Fixed lower and upper limits of the BE acceptance range |
\(\small{\theta_{\text{s}_1},\theta_{\text{s}_2}}\) | Scaled lower and upper limits of the BE acceptance range |
\(\small{\widehat{\lambda}_\text{z}}\) | Apparent terminal rate constant (estimated) |
\(\small{\mu_\text{T}/\mu_\text{R}}\) | True \(\small{\text{T}/\text{R}}\)-ratio |
\(\small{\nu}\) | Degrees of freedom |
\(\small{\pi}\) | Prospective (a priori) power, where \(\small{\pi=1-\beta}\) |
\(\small{\widehat{\pi}}\) | Estimated (a posteriori, post hoc, retrospective) power |
\(\small{\sigma}\) | Population standard deviation |
\(\small{\sigma_\text{wR},\sigma_\text{wT}}\) | True within-subject standard deviation of the Reference and Test product |
\(\small{\tau}\) | Dosing interval |
2×2×2 | Two treatment two sequence two period crossover design |
FAX
-machines. Some books
are out of print; perhaps you can get them used. No, I will not sell any
of them.Vitti TG, Banes D, Byers TE. Bioavailability of Digoxin. N Engl J Med. 1971; 285(25): 1433–4. doi:10.1056/NEJM197112162852512.↩︎
DeSante KA, DiSanto AR, Chodos DJ, Stoll RG. Antibiotic Batch Certification and Bioequivalence. JAMA. 1975; 232(13): 1349–51. doi:10.1001/jama.1975.03250130033016.↩︎
ICH. Bioequivalence for Immediate-Release Solid Oral Dosage Forms. M13A. Draft version 20 December 2022. Online.↩︎
Hall DG, In: Hearing Before the Subcommittee on Monopolies Select Committee on Small Business. U.S. Senate, Government Printing Office, Washington D.C. 1967: 258–81.↩︎
Tyrer JH, Eadie MJ, Sutherland JM, Hooper WD. Outbreak of anticonvulsant intoxication in an Australian city. Br Med J. 1970; 4: 271–3. doi:10.1136/bmj.4.5730.271. Open Access.↩︎
Bochner F, Hooper WD, Tyrer JH, Eadie MJ. Factors involved in an outbreak of phenytoin intoxications. J Neurol Sci. 1972; 16(4): 481–7. doi:10.1016/0022-510x(72)90053-6.↩︎
Lund L. Clinical significance of generic inequivalence of three different pharmaceutical preparations of phenytoin. Eur J Clin Pharmacol. 1974; 7: 119–24. doi:10.1007/bf00561325.↩︎
Lindenbaum J, Mellow MH, Blackstone MO, Butler VP. Variations in biological activity of digoxin from four preparations. N Engl J Med. 1971; 285(24): 1344–7. doi:10.1056/NEJM197112092852403.↩︎
Wagner JG, Christensen M, Sakmar E, Blair D, Yates JD, Willis PW 3^{rd}, Sedman AJ, Stoll RG. Equivalence lack in digoxin plasma levels. JAMA, 1973; 224(2): 199–204. PMID 4739492.↩︎
Lindenbaum J, Preibisz JJ, Butler VP Jr., Saha JR. Variation in digoxin bioavailabity: a continuing problem. J Chron Dis. 1973; 16: 749–54. doi:10.1056/nejm197112092852403.↩︎
Levy G, Gibaldi M. Bioavailability of Drugs. Focus on Digoxin. Circulation. XLIX(3); 1974: 391–4. doi:10.1161/01.CIR.49.3.391. Open Access.↩︎
Jounela AJ, Pentikäinen PJ, Sothmann. Effect of particle size on the bioavalability of digoxin. Eur J Clin Pharmacol. 1975; 8(5): 365–70. doi:10.1007/BF00562664.↩︎
Richton-Hewett S, Foster E, Apstein CS. Medical and Economic Consequences of a Blinded Oral Anticoagulant Brand Change at a Municipal Hospital. Arch Intern Med. 1988; 148(4): 806–8. doi:10.1001/archinte.1988.00380040046010.↩︎
Weinberger M, Hendeles L, Bighley L, Speer J. The Relation of Product Formulation to Absorption of Oral Theophylline. N Engl J Med. 1978; 299(16): 852–7. doi:10.1056/nejm197810192991603.↩︎
Bielmann B, Levac TH, Langlois Y, L Tetreault L. Bioavailability of primidone in epileptic patients. Int J Clin Pharmacol. 1974; 9(2): 132–7. PMID 4208031↩︎
Skelly JP, Knapp G. Biologic availability of digoxin tablets. JAMA. 1973; 224(2): 243. doi:10.1001/jama.1973.03220150051015.↩︎
Skelly JP. A History of Biopharmaceutics in the Food and Drug Administration 1968–1993. AAPS J. 2010; 12(1): 44–50. doi:10.1208/s12248-009-9154-8. Free Full Text.↩︎
APhA. Guidelines for Biopharmaceutic Studies in Man. Washington D.C. February 1972.↩︎
Skelly JP. Bioavailability and Bioequivalence. J Clin Pharmacol. 1976; 16(10/2): 539–45. doi:10.1177/009127007601601013.↩︎
Gardener S (Acting Commissioner of Food and Drugs). CFR, Title 21, Vol. 5, Chapter I, Part 320. Bioavailability and Bioequivalence Requirements. Procedures for Determining the In Vivo Bioavailability of Drug Products. December 30, 1976. Effective July 7, 1977, In: FR, Vol. 42, No. 5. January 7, 1977. Online.↩︎
Schuirmann DJ. A comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. J Pharmacokin Biopharm. 1987; 15(6): 657–80. doi:10.1007/BF01068419.↩︎
Metzler CM. Bioavailability – A Problem in Equivalence. Biometrics. 1974; 30(2): 309–17. PMID 4833140.↩︎
Westlake WJ. Symmetrical Confidence Intervals for Bioequivalence Trials. Biometrics. 1976; 32(4): 741–4. PMID 1009222.↩︎
Mantel N. Do We Want Confidence Intervals Symmetrical About the Null Value? Biometrics. 1977; 33: 759–60. [Letter to the Editor]↩︎
Westlake WJ. Design and Evaluation of Bioequivalence Studies in Man. In: Blanchard J, Sawchuk RJ, Brodie BB, editors. Principles and perspectives in Drug Bioavailability. Basel: Karger; 1979. ISBN 3-8055-2440-4. p. 192–210.↩︎
Fieller EC. Some Problems In Interval Estimation. J Royal Stat Soc B. 1954; 16(2): 175–85. doi:10.1111/j.2517-6161.1954.tb00159.x.↩︎
Locke CS. An Exact Confidence Interval from Untransformed Data for the Ratio of Two Formulation Means. J. Pharmacokin. Biopharm. 1984; 12(6): 649–55. doi:10.1007/bf01059558.↩︎
U.S. Department of Health and Human Services, FDA, Office of Medical Products and Tobacco, CDER, OGD, OGDP. Approved Drug Products with Therapeutic Equivalence Evaluations. 44^{th} Edition. 2024. Download.↩︎
U.S. Department of Health and Human Services, FDA, Office of Medical Products and Tobacco, CDER, OGD, OGDP. Approved Drug Products with Therapeutic Equivalence Evaluations. Cumulative Supplement. Download.↩︎
US Government Publishing Office. Drug Price Competition and Patent Term Restoration Act of 1984. Public Law 98-117. Sept. 24, 1984. Online.↩︎
In phase III we try to demonstrate that verum performs ‘better’ than placebo, i.e., one-sided tests for non-inferiority (effect) and non-superiority (adverse reactions). Such studies are already large: Approving statins and COVID-19 vaccines required ten thousands volunteers. Can you imagine how many it would need to detect a 20% difference between two treatments?↩︎
Benet LZ. Why Do Bioequivalence Studies in Healthy Volunteers? Presentation at: 1^{st} MENA Regulatory Conference on Bioequivalence, Biowaivers, Bioanalysis and Dissolution. Amman; 23 September 2013. Internet Archive.↩︎
Office of the Federal Register. Code of Federal Regulations, Title 21, Part 320, Subpart A, § 320.23(a)(1) Online.↩︎
This is an assumption, i.e., based on the labelled content instead of the measured potency.↩︎
Yet another assumption. Incorrect for highly variable drugs and, thus, inflates the confidence interval.↩︎
Tóthfalusi L, Endrényi L. Estimation of C_{max} and T_{max} in Populations After Single and Multiple Drug Administration. J Pharmacokin Pharmacodyn. 2003; 30(5): 363–85. doi:10.1023/b:jopa.0000008159.97748.09.↩︎
These formulas are only valid for a one-compartment model with zero order absorption and first order elimination. In all other models \(\small{t_\text{max}}\) (and thus, \(\small{C_\text{max}}\)) cannot be analytically derived. In software numeric optimization is employed to locate the maximum of the function.↩︎
Endrényi L, Fritsch S, Yan W. C_{max}/AUC is a clearer measure than C_{max} for absorption rates in investigations of bioequivalence. Int J Clin Pharmacol Ther Toxicol. 1991; 29(10): 394–9. PMID 1748540.↩︎
Schall R, Luus HG. Comparison of absorption rates in bioequivalence studies of immediate release drug formulations. Int J Clin Pharmacol Ther Toxicol. 1992; 30(5): 153–9. PMID 1592542.↩︎
Endrényi L, Yan W. Variation of C_{max} and C_{max}/AUC in investigations of bioequivalence. Int J Clin Pharm Ther Toxicol. 1993; 31(4): 184–9. PMID 8500920.↩︎
Haynes JD. Statistical simulation study of new proposed uniformity requirement for bioequivalency studies. J Pharm Sci. 1981; 70(6): 673–5. doi:10.1002/jps.2600700625.↩︎
Cabana BE. Assessment of 75/75 Rule: FDA Viewpoint. Pharm Sci. 1983; 72(1): 98–9. doi:10.1002/jps.2600720127.↩︎
Haynes JD. FDA 75/75 Rule: A Response. Pharm Sci. 1983; 72(1): 99–100.↩︎
Nitsche V, Mascher H, Schütz H. Comparative bioavailability of several phenytoin preparations marketed in Austria. Int J Clin Pharmacol Ther Toxicol. 1984; 22(2): 104–7. PMID 6698663.↩︎
Klingler D, Nitsche V, Schmidbauer H. Hydantoin-Intoxikation nach Austausch scheinbar gleichwertiger Diphenylhydantoin-Präparate. Wr Med Wschr. 1981; 131: 295–300. [German]↩︎
Glazko AJ, Chang T, Bouhema J, Dill WA, Goulet JR, Buchanan RA. Metabolic disposition of diphenylhydantoin in normal human subjects following intravenous administration. Clin Pharmacol Ther. 1969; 10(4): 498–504. doi:10.1002/cpt1969104498.↩︎
Bochner F, Hooper WD, Tyrer JH, Eadi MJ. Effect of dosage increments on blood phenytoin concentrations. J Neurol Neurosurg Psychiatr. 1972; 35(6): 873–6. doi:10.1136/jnnp.35.6.873.↩︎
Kirkwood TBL. Bioequivalence Testing—A Need to Rethink [reader reaction]. Biometrics. 1981, 37: 589—91. doi:10.2307/2530573.↩︎
Westlake WJ. Response to Bioequivalence Testing—A Need to Rethink [reader reaction response]. Biometrics. 1981, 37: 591–3.↩︎
Westlake WJ. Bioavailability and Bioequivalence of Pharmaceutical Formulations. In: Pearce KE, editor. Biopharmaceutical Statistics for Drug Development. New York: Marcel Dekker; 1988. ISBN 0-8247-7798-0. p. 329–53.↩︎
Rodda BE, Davis RL. Determining the probability of an important difference in bioavailability. Clin Pharmacol Ther. 1980; 28: 247–52. doi:10.1038/clpt.1980.157.↩︎
Mandallaz D, Mau J. Comparison of Different Methods for Decision-Making in Bioequivalence Assessment. Biometrics. 1981; 37: 213–22. PMID 6895040.↩︎
Fluehler H, Hirtz J, Moser HA. An Aid to Decision-Making in Bioequivalence Assessment. J Pharmacokin Biopharm. 1981; 9: 235–43. doi:10.1007/BF01068085.↩︎
Selwyn MR, Hall NR. On Bayesian Methods for Bioequivalence. Biometrics. 1984; 40: 1103–8. PMID 6398710.↩︎
Fluehler H, Grieve AP, Mandallaz D, Mau J, Moser HA. Bayesian Approach to Bioequivalence Assessment: An Example. J Pharm Sci. 1983; 72(10): 1178–81. doi:10.1002/jps.2600721018.↩︎
Anderson S, Hauck WW. A New Procedure for Testing Bioequivalence in Comparative Bioavailability and Other Clinical Trials. Commun Stat Ther Meth. 1983; 12(23): 2663–92. doi:10.1080/03610928308828634.↩︎
Steinijans VW, Diletti E. Statistical Analysis of Bioavailability Studies: Parametric and Nonparametric Confidence Intervals. Eur J Clin Pharmacol. 1983; 24: 127–36. doi:10.1007/BF00613939.↩︎
Steinijans VW, Diletti E. Generalization of Distribution-Free Confidence Intervals for Bioavailability Ratios. Eur J Clin Pharmacol. 1985; 28: 85–8. doi:10.1007/BF00635713.↩︎
Steinijans VW, Schulz H-U, Beier W, Radtke HW. Once daily theophylline: multiple-dose comparison of an encapsulated micro-osmotic system (Euphylong) with a tablet (Uniphyllin). Int J Clin Pharm Ther Toxicol. 1986; 24(8): 438–47. PMID 3759279.↩︎
Steinijans VW. Pharmacokinetic Characteristics of Controlled Release Products and Their Biostatistical Analysis. In: Gundert-Remy U, Möller H, editors. Oral Controlled Release Products – Therapeutic and Biopharmaceutic Assessment. Stuttgart: Wissenschaftliche Verlagsgesellschaft; 1988, ISBN 978-3804710429. p. 99–115.↩︎
Blume H, Siewert M, Steinijans V. Bioäquivalenz von per os applizierten Retard-Arzneimitteln; Konzeption der Studien und Entscheidung über Austauschbarkeit. Pharm Ind. 1989; 51: 1025–33. [German]↩︎
Wijnand HP, Timmer CJ. Mini-computer programs for bioequivalence testing of pharmaceutical drug formulations in two-way cross-over studies. Comput Programs Biomed. 1983; 17(1–2): 73–88. doi:10.1016/0010-468x(83)90027-2.↩︎
Where did it come from? Two stories:
Les Benet told
that there was a poll at the FDA and – essentially based on gut
feeling – the 20% saw the light of day.
I’ve heard another one,
which I like more. Wilfred J. Westlake, one of the pioneers of
BE was a statistician at
SKF. During a
coffee and cig break (everybody was smoking in the 1970s) he asked his
fellows of the clinical pharmacology department »Which difference in
blood concentrations do you consider relevant?« Yep, the 20% were
born.↩︎
Rheinstein P. Report by the Bioequivalence Task Force on Recommendations from the Bioequivalence Hearing conducted by the Food and Drug Administration. September 29 – October 1986. January 1988.↩︎
APV. Richtlinie und Kommentar. Pharmazeutische Industrie. 1985; 47(6): 627–32. [German]↩︎
Arbeitsgemeinschaft Pharmazeutische Verfahrenstechnik (APV). International Symposium. Bioavailability/Bioequivalence, Pharmaceutical Equivalence and Therapeutic Equivalence. Würzburg. 9–11 February, 1987.↩︎
Junginger H. APV-Richtlinie – »Untersuchungen zur Bioverfügbarkeit, Bioäquivalenz« Pharm Ztg. 1987; 132: 1952–5. [German]↩︎
Junginger H. Studies on Bioavailability and Bioequivalence – APV Guideline. Drugs Made in Germany. 1987; 30: 161–6.↩︎
Blume H, Kübel-Thiel K, Reutter B, Siewert M, Stenzhorn G. Nifedipin: Monographie zur Prüfung der Bioverfügbarkeit / Bioäquivalenz von schnell-freisetzenden Zubereitungen (1). Pharm Ztg. 1988; 133(6): 398–93. [German]↩︎
TGA. Guidelines for Bioavailability and Bioequivalency Studies. Draft C06:6723c (29/11/88).↩︎
Blume H, Mutschler E. Bioäquivalenz – Qualitätsbewertung wirkstoffgleicher Fertigarzneimittel: Anleitung-Methoden-Materialien. Frankfurt/Main: Govi-Verlag; 1989. [German]↩︎
McGilveray IJ, Midha KK, Skelly JP, Dighe S, Doluiso JT, French IW, Karim A, Burford R. Consensus Report from “Bio International ’89”: Issues in the Evaluation of Bioavailability Data. J Pharm Sci. 1990; 79(10): 945–6. doi:10.1002/jps.2600791022.↩︎
Keene ON. The log transformation is special. Stat Med. 1995; 14(8): 811–9. doi:10.1002/sim.4780140810. Open Access.↩︎
Diletti E, Hauschke D, Steinijans VW. Sample size determination for bioequivalence assessment by means of confidence intervals. Int J Clin Pharm Ther Toxicol. 1991; 29(1): 1–8. PMID 2004861.↩︎
Diletti E, Hauschke D, Steinijans VW. Sample size determination: Extended tables for the multiplicative model and bioequivalence ranges of 0.9 to 1.11 and 0.7 to 1.43. Int J Clin Pharm Ther Toxicol. 1992; 30(Suppl.1): S59–62. PMID 1601533.↩︎
Hauschke D, Steinijans VW, Diletti E. A distribution-free procedure for the statistical analysis of bioequivalence studies. Int J Clin Pharm Ther Toxicol. 1990; 28(2): 72–8.↩︎
Steinijans VW, Hauschke D. Update on the statistical analysis of bioequivalence studies. Int J Clin Pharm Ther Toxicol. 1990; 28(3): 105–10. PMID 2318545.↩︎
Steinijans VW, Hartmann M, Huber R, Radtke HW. Lack of pharmacokinetic interaction as an equivalence problem. Int J Clin Pharm Ther Toxicol. 1991; 29(8): 323–8. PMID 1835963.↩︎
Anderson S, Hauck WW. Consideration of individual bioequivalence. J Pharmacokinet Biopharm 1990; 18(3): 259–73. doi:10.1007/bf01062202.↩︎
Schall R, Luus HG. On population and individual bioequivalence. Stat Med 1993; 12(12): 1109–24. doi:10.1002/sim.4780121202.↩︎
Schall R. A unified view of individual, population, and average bioequivalence. In: Blume HH, Midha KK, editors. Bio-International 2. Bioavailability, Bioequivalence and Pharmacokinetic Studies. Stuttgart: medpharm; 1995. ISBN 3-88763-040-8. p. 91–106.↩︎
Chow S-C, Liu J-p. Design and Analysis of Bioavailability and Bioequivalence Studies. New York: Marcel Dekker; 1992. ISBN 0-8247-8682-3. ★↩︎
CPMP Working Party. Investigation of Bioavailability and Bioequivalence: Note for Guidance. III/54/89-EN, 8^{th} Draft. June 1990.↩︎
Commission of the European Community. Investigation of Bioavailabilty and Bioequivalence. Brussels. December 1991. BEBAC Archive.↩︎
Amidon GL, Lennernäs H, Shah VV, Crison JR. A Theoretical Basis for a Biopharmaceutic Drug Classification: The Correlation of in Vitro Drug Product Dissolution and in Vivo Bioavailability. Pharm Res. 1995; 12(3): 413–20. doi:10.1023/a:1016212804288. Open Access.↩︎
Steinijans VW, Hauschke D. International Harmonization of Regulatory Bioequivalence Requirements. Clin Res Reg Aff. 1993; 10(4): 203–20.↩︎
FDA, CDER. Guidance for Industry. Statistical Procedures for Bioequivalence Studies using a Standard Two-Treatment Crossover Design. Rockville. Jul 1992. Internet Archive.↩︎
If Subject 1 is randomized to sequence \(\small{\text{TR}}\), there is not another Subject 1 randomized to sequence \(\small{\text{RT}}\). Randomization is not like Schrödinger’s cat. Hence, the nested term in the guidelines is an insult to the mind.↩︎
Health Canada, HPFB. Guidance for Industry. Conduct and Analysis of Bioavailability and Bioequivalence Studies – Part A: Oral Dosage FormulationsUsed for Systemic Effects. Ottawa. 1992. BEBAC Archive.↩︎
Health Canada, HPFB. Guidance for Industry. Conduct and Analysis of Bioavailability and Bioequivalence Studies – Part B: Oral Modified Release Formulations. Ottawa. 1996. BEBAC Archive.↩︎
WHO Marketing Authorization of Pharmaceutical Products with Special Reference to Multisource (Generic) Products: A Manual for Drug Regulatory Authorities. Geneva. 1998. Internet Archive.↩︎
Elkoshi Z, Behr D, Mirimsky A, Tsvetkov, Danon A. Multiple-Dose Studies can be a More Sensitive Assessment for Bioequivalence than Single-Dose Studies. The Case with Omeprazole. Clin Drug Invest. 2002; 22(9): 585–92. doi:10.2165/00044011-200222090-00003.↩︎
Gleiter CH, Klotz U, Kuhlmann J, Blume H, Stanislaus F, Harder S, Paulus H, Poethko-Müller C, Holz-Slomczyk M. (1998), When Are Bioavailability Studies Required? A German Proposal. J Clin Pharmacol. 1998 38: 904–11. doi:10.1002/j.1552-4604.1998.tb04385.x. Open Access.↩︎
EMEA, CPMP. Note for Guidance on the Investigation of Bioavailability and Bioequivalence. London. 26 July 2001. Online.↩︎
FDA, CDER. Guidance for Industry. Immediate Release Solid Oral Dosage Forms. Scale-Up and Postapproval Changes: Chemistry, Manufacturing, and Controls, In Vitro Dissolution Testing, and In Vivo Bioequivalence Documentation. Rockville. November 1995. Download.↩︎
FDA, CDER. Guidance for Industry. SUPAC-MR: Modified Release SolidOral Dosage Forms. Scale-Up and Postapproval Changes: Chemistry, Manufacturing, and Controls, In Vitro Dissolution Testing, and In Vivo Bioequivalence Documentation. Rockville. September 1997. Download.↩︎
Shah VP, Tsong Y, Sathe P, Liu J-p. In vitro dissolution profile comparison – statistics and analysis of the similarity factor f_{2}. Pharm Res. 1998; 15: 889–96. doi:10.1023/a:1011976615750.↩︎
Liu J-p, Ma M-C, Chow S-C. Statistical Evaluation of Similarity Factor f_{2} as a Criterion for Assessment of Similarity Between Dissolution Profiles. Drug Inf J. 1997; 31: 1255–71. doi:10.1177/009286159703100426.↩︎
Midha KK, Blume HH, editors. Bio-International. Bioavailability, Bioequivalence and Pharmacokinetics. Stuttgart: medpharm; 1993. ISBN 3-88763-019-X.↩︎
Blume HH, Midha KK. Bio-International 92, Conference on Bioavailability, Bioequivalence, and Pharmacokinetic Studies. J Pharm Sci. 1993; 82(11): 1186–9. doi:10.1002/jps.2600821125.↩︎
Simultaneous administration of a stable isotope labelled IV dose would allow to calculate the true clearance in each period. Then it would not be necessary to assume identical clearances in \(\small{(3)}\) any more and the problem of highly variable drugs (inflating the CI) could be avoided. However, it would require that the IV formulation is manufactured according to the rules of cGMP and different from the internal standard in MS, which is generally not feasible. Such an approach is only mentioned in Japanese guidelines.↩︎
Blume HH, Midha KK, editors. Bio-International 2. Bioavailability, Bioequivalence and Pharmacokinetic Studies. Stuttgart: medpharm; 1995. ISBN 3-88763-040-8.↩︎
Boddy AW, Snikeris FC, Kringle RO, Wei GCG, Opperman JA, Midha KK. An approach for widening the bioequivalence acceptance limits in the case of highly variable drugs. Pharm Res. 1995; 12(12): 1865–8. doi:10.1023/a:1016219317744.↩︎
Shah VP, Yacobi A, Barr WH, Benet LZ, Breimer D, Dobrinska MR, Endrényi L, Fairweather W, Gillespie W, Gonzalez MA, Hooper J, Jackson A, Lesko LL, Midha KK, Noonan PK, Patnaik R, Williams RL. Workshop Report. Evaluation of Orally Administered Highly Variable Drugs and Drug Formulations. Pharm Res. 1996; 13(11): 1590–4. doi:10.1023/a:1016468018478.↩︎
Schütz H, Labes D, Wolfsegger MJ. Critical Remarks on Reference-Scaled Average Bioequivalence. J Pharm Pharmaceut Sci. 25: 285–96. doi:10.18433/jpps32892.↩︎
EMEA Human Medicines Evaluation Unit / CPMP. Note for Guidance on the Investigation of Bioavailability and Bioequivalence. Draft. London. 17 December 1998.↩︎
Brooks MA, Weifeld RE. A Validation Process for Data from the Analysis of Drugs in Biological Fluids. Drug Devel Ind Pharm. 1985; 11: 1703–28.↩︎
Pachla LA, Wright DS, Reynolds DL. Bioanalytical Considerations for Pharmacokinetic and Biopharmaceutic Studies. J Clin Pharmacol. 1986; 26(5): 332–5. doi:10.1002/j.1552-4604.1986.tb03534.x.↩︎
Buick AR, Doig MV, Jeal SC, Land GS, McDowall RD, Method Validation in the Bioanalytical Laboratory. J Pharm Biomed Anal. 1990; 8(8–12): 629–37. doi:10.1016/0731-7085(90)80093-5. Open Access.↩︎
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