Introduction to bootf2
In bootf2: Simulation and Comparison of Dissolution Profiles

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#"
)

library(bootf2)

ema1 <- "https://www.ema.europa.eu/en/documents/scientific-guideline/"
ema2 <- "guideline-investigation-bioequivalence-rev1_en.pdf#page=21"
ema3 <- paste0(ema1, ema2)
fda  <- "https://www.fda.gov/media/70936/download#page=12"
fda2 <- "https://www.gmp-compliance.org/files/guidemgr/UCM070246.pdf#page=12"
fdamr <- "https://www.fda.gov/media/70956/download#page=37"
canada1 <- "https://www.canada.ca/en/health-canada/services/drugs-health"
canada2 <- "-products/drug-products/applications-submissions/guidance"
canada3 <- "-documents/post-notice-compliance-changes/quality-document/"
canada4 <- paste0(canada1, canada2, canada3, "guidance.html#a5")
ca1 <- "https://www.canada.ca/en/health-canada/services/drugs-health-"
ca2 <- "products/drug-products/applications-submissions/guidance-documents/"
ca3 <- "canadian-reference-product-guidance.html#app2"
ca4 <- paste0(ca1, ca2, ca3)
who1 <- "https://apps.who.int/iris/bitstream/handle/10665/258720/"
who2 <- "9789241210034-eng.pdf?sequence=1&isAllowed=y#page=244"
who3 <- paste0(who1, who2)
#anvisa1 <- "https://bvsms.saude.gov.br/bvs/saudelegis/anvisa/2010/"
anvisa1a <- "https://web.archive.org/web/20190806045126/http://bvsms.saude."
anvisa1b <- "gov.br/bvs/saudelegis/anvisa/2010/res0031_11_08_2010.html"
anvisa2  <- paste0(anvisa1a, anvisa1b)

Introduction

Because of the prominent roles dissolution profiles played in the pharmaceutical industry, it is important to have a reliable method to compare dissolution profiles. Over the years, many model-dependent and -independent methods were developed; but owing to its simplicity, similarity factor $f_2$ is the most widely used one, and it is recommended in many regulatory guidelines [@EMA-2010-INV.BE; @USFDA-1997-08-DISSO.IR.SOLID.ORAL; @HealthCanada-2017; @WHO-2017; @MHLW2012; @ANVISA2010; @CDENMPA-2016].

However, to apply the $f_2$ method, several conditions have to be fulfilled due to certain drawbacks associated with it. When $f_2$ method is not applicable for the failure of fulfilling regulatory conditions, other methods should be used.

The package bootf2 was developed to compare the dissolution profiles using confidence interval of $f_2$ by bootstrap method as recommended recently by several regulatory agencies [@EMA-2018-09-QA.MSD.DISSO; @Davit-2013-03-BA; @Lum-2019-05-WS; @Mandula-2019-05-WS].

There are 4 main functions in the package:

sim.dp() to simulate dissolution profile using mathematical models or multivariate normal distribution.
calcf2() to calculate similarity factor $f_2$ according to different regulatory rules.
sim.dp.byf2() to find a dissolution profile that, when compared to a given reference profile, has $f_2$ value equal to the predefined target $f_2$.
bootf2() to estimate the confidence intervals of $f_2$s using bootstrap method.

The details of functions are explained in their respective manual and vignettes. Some common topics are discussed in this document.

Regulatory rules for $f_2$

To apply the traditional $f_2$ method, several conditions have to be fulfilled. Unfortunately, different regulatory agencies described those conditions differently. Some of the conditions are same across different guidelines, such as 1.) same dissolution condition and same time points for both test and reference, 2.) use 12 units, and 3.) use at least 3 time points for the calculation of $f_2$, while others are either slightly different, or are actually the same but different interpretation exist due to the ambiguous wording in the guideline.

The last two scenarios are detailed below with direct quotes from guidelines (with hyper links) as they affect the implementation of the functions calcf2().

20%/10% CV Rule
- EMA [@EMA-2010-INV.BE]:
"The relative standard deviation or coefficient of variation of any product should be less than 20% for the first point and less than 10% from second to last time point."

If the the time points in the dissolution is 5 min, 10 min, 15 min, ..., strict interpretation is that the 20% CV is for the first time point 5 min only. From time point 10 min onward, the CV% criteria is 10%. From an unofficial communication with an EU regulator, the practical use is 20% CV for all time points till 10 min, 10% for the rest points. It seems that, due to high variability asociated to the early point, many companies deleted 5 min time points from their dissolution profile, even though this point should be presented according to their method. Obviously this is a kind of bad practice, so the relaxed criterion of 20% CV up to 10 min can be considered as encouragement for the company not to delete any data points.
- US FDA [@USFDA-1997-08-DISSO.IR.SOLID.ORAL]:
"To allow use of mean data, the percent coefficient of variation at the earlier time points (e.g., 15 minutes) should not be more than 20%, and at other time points should not be more than 10%."

While the guidance indicating 15 min as an example for cutting points of earlier points (20% CV), FDA seems take more liberal approach. In an unofficial communication, an example of dissolution profiles having 5, 10, 20, 30 min, ..., time points was given where the first 2 or 3 points (that's 20 min!) having CV% within 10% and 20%. In such cases, FDA will review thew data for test and reference, but it is likely that the traditional $f_2$ method could still be used.
- Health Canada:
The older guidance [@HealthCanada-2017] states that:

"To use mean data, the % coefficient of variation at the first time point should not be more than 20% and at other time points should not be more than 10%."

So that would be the same as the EMA's guideline when interpreted strictly. However, the newer guidance [@HealthCanada-2019-07-Quality] has the following statement:

"To use mean data, the % coefficient of variation at the earlier point should be not more than 20% and at other time points should be not more than 10%."

So it is not clear right now which time points could be considered as earlier points. In the function calcf2(), the same rule as EMA's was implemented.
- WHO [@WHO-2017]:
"To use mean data the percentage coefficient of variation at time-points up to 10 minutes should be not more than 20% and at other time-points should be not more than 10%;"

This is the same as the "new" interpretation of the EMA's guideline.
- Brazil [@ANVISA2010]:
"para permitir o uso de médias, os coeficientes de variação para os primeiros pontos de coleta não podem exceder 20%. Para os demais pontos considera-se o máximo de 10%. São considerados como primeiros pontos de coleta o correspondente a 40% do total de pontos coletados. Por exemplo, para um perfil de dissolução com cinco tempos de coleta, consideram-se primeiros pontos os dois primeiros tempos de coleta." (Translation: to allow the use of averages, the coefficients of variation for the first collection points cannot exceed 20%. For the other points, a maximum of 10% is considered. The first collection points correspond to 40% of the total collected points. For example, for a dissolution profile with five collection times, the first two collection times are considered first points.)

The next condition caused different interpretations among many.

More than 85% dissolution time points
- EMA [@EMA-2010-INV.BE]:
"Not more than one mean value of > 85% dissolved for any of the formulations."
- US FDA [@USFDA-1997-08-DISSO.IR.SOLID.ORAL]:
"Only one measurement should be considered after 85% dissolution of both the products."

There is no ambiguity associated with EMA's rule. But because of the phrase "both the products" in FDA's guidance, many interpreted that all time points should be included until both test and reference dissolved more than 85%. For example, with the following dissolution profiles, many would interpret that while time points 5, 10, 15, and 20 min should be included according to EMA's rule, all time points should be included according to FDA's rule because both test and reference dissolve more than 85% only at 60 min, not at earlier points.

r fda85 <- data.frame(Time = c(5, 10, 15, 20, 30, 45, 60), Test = c(7, 15, 50, 69, 82, 84, 86), Ref = c(10, 20, 55, 86, 90, 95, 97)) knitr::kable(fda85, booktabs = TRUE)

However, this is a misinterpretation. Because if this is true, then there will be 4 time points included in the reference profile where dissolution is more than 85%, which is in direct contradiction to the same sentence that "Only one measurement should be considered after ...".

In an unofficial communication using this example, an FDA staff confirmed that only the first 4 time points would be used. In other words, the same as EMA's rule.
- Health Canada [@HealthCanada-2019-07-Quality]:
"Because f2 values are sensitive to the number of dissolution time points, only one measurement should be considered after 85% dissolution of the product."
- WHO [@WHO-2017]:
"a maximum of one time point should be considered after 85% dissolution of the reference (comparator) product has been reached;"

If reference dissolves faster than test does, WHO's rule would be the same as the EMA/FDA rule; if not, then there might be several time points with more than 85% dissolved for test product. This would be different from EMA/FDA approach, but at least the guideline is very clear and leaves no room for ambiguity.
- Brazil [@ANVISA2010]:
"para fins de cálculo F2, incluir apenas um ponto da curva após ambos os medicamentos atingirem a média de 85% de dissolução;" (Translation: for F2 calculation purposes, include only one point on the curve after both drugs average 85% dissolution;)

The phrasing is very similar to FDA's so it could also open to be misinterpreted. However, with the same logic as discussed above, ANVISA's rule should also be the same as EMA's.

To summarize, EMA, US FDA, Canada, and Brazil should have the same rule in this regard; only WHO has slightly different rule.

There is another regulatory scenario regarding the use of $f_2$, or rather, the not use of it.

When $f_2$ is unnecessary

For immediate-release formulation, sometimes it is unnecessary to calculate $f_2$ and the profiles can still be declared similar if the products dissolve quick enough, typically more than 85% at 15 min.
- EMA [@EMA-2010-INV.BE]:
"For immediate release formulations, ..., Where more than 85% of the drug is dissolved within 15 minutes, dissolution profiles may be accepted as similar without further mathematical evaluation. "
- US FDA [@USFDA-2017-12-WAIVER.BABE.IR.BCS]:
"In addition, when both test and reference products dissolve 85 percent or more of the label amount of the drug in 15 minutes using all three dissolution media recommended above, the profile comparison with an f2 test is unnecessary."
- Health Canada [@HealthCanada-2019-07-Quality]:
"If the individual data for both the test and reference products show more than 85% dissolution within 15 minutes, the profiles are considered similar (no calculations are necessary)."

Canadian rule is stricter than EMA's and FDA's since the latter two use mean value while the former use individual data.
- WHO [@WHO-2017]:
"If both the test and reference (comparator) products show more than 85% dissolution in 15 minutes the profiles are considered similar (no calculations required)."
- Brazil [@ANVISA2010]:
"Quando a substância ativa apresentar alta solubilidade e a formulação for de liberação imediata, apresentando dissolução muito rápida para ambos os medicamentos, o fator F2 perde o seu poder discriminativo e, portanto, não é necessário calculá- lo. Nesses casos deve-se comprovar a dissolução muito rápida dos produtos, por meio do gráfico da curva, realizando coletas em, por exemplo: 5, 10, 15, 20 e 30 minutos. O coeficiente de variação no ponto de 15 minutos que não pode exceder 10%." (Translation: When the active substance presents high solubility and the formulation is immediate release, presenting very fast dissolution for both drugs, the F2 factor loses its discriminative power and, therefore, it is not necessary to calculate it. In these cases, the very fast dissolution of the products must be proved by means of the dissolution curve, carrying out collections in, for example: 5, 10, 15, 20 and 30 minutes. The coefficient of variation at the 15-minute point that cannot exceed 10%.)

Another point worth mentioning, even though it is not related to the calculation of $f_2$, is a scenario described in US FDA's SUPAC-MR guidance [@USFDA-1997-09-SUPAC.MR.CMC.DISSO.BE]:

"Also, the average difference at any dissolution sampling time point should not be greater than 15% between the changed drug product and the biobatch or marketed batch (unchanged drug product) dissolution profiles."

This rule has not been implemented in the function calcf2().