bootstrap_f2: Bootstrap f2

In disprofas: Non-Parametric Dissolution Profile Analysis

Description

The function bootstrap_f2() generates R bootstrap replicates of the similarity factor f_2 based on resampling of complete profiles (nonparametric bootstrap) or on resampling per time point the values between profiles (parametric bootstrap). Estimates of “normal”, “basic”, “student”, “percent” and of “bias-corrected, accelerated” (BCa) percentile intervals are returned.

Usage

bootstrap_f2(
  data,
  tcol,
  grouping,
  rand_mode = "complete",
  R = 999,
  each = 12,
  new_seed = 100,
  confid = 0.9,
  use_EMA = "no",
  bounds = c(1, 85),
  ...
)

Arguments

data	A data frame with the dissolution profile data in wide format.
tcol	A vector of indices specifying the columns in data that contain the % release values. The length of tcol must be three or longer.
grouping	A character string specifying the column in data that contains the group names (i.e. a factorial variable, e.g., for the differentiation of batches or formulations of a drug product).
rand_mode	A character string indicating if complete profiles shall be randomised ("complete", the default) or individual data points ("individual").
R	An integer specifying the number of bootstrap replicates. The default is 999.
each	An integer specifying the number of dissolution profiles to be selected per group per randomisation round. The default is 12.
new_seed	An integer for setting the seed for random number generation. The default is 100.
confid	A numeric value between 0 and 1 specifying the confidence limit for the calculation of the bootstrap confidence intervals. The default is 0.9.
use_EMA	A character string indicating if the similarity factor f_2 should be calculated according to the EMA guideline “On the investigation of bioequivalence” ("yes") or not ("no", the default). The default is "no" because the bootstrap f_2 method is one of the possible solutions if the condition concerning the variability between the profiles does not allow the evaluation of f_2 according to the EMA guideline. A third option is "ignore". If use_EMA is "yes" or "no" the appropriate profile portion is determined on the basis of the values of the parameter bounds. If it is "ignore", the complete profiles are used as specified by the parameter tcol.
bounds	A numeric vector of the form c(lower, upper) specifying the “lower” and “upper” limits, respectively, for the % drug release given that use_EMA is "no". The default is c(1, 85). Mean % release values of any of the two groups being compared that are smaller than or equal to the lower bound are ignored and only the first mean % release value that is greater than or equal to the upper bound is included while all the subsequent values are ignored. If use_EMA is "yes" the bounds are c(1, 85) per definition.
...	Named parameters of the functions stat.fun(), ran.fun() and boot().

Details

Information on f_2 can be found in at least three FDA guidances and in the guideline of the European Medicines Agency (EMA) “On the investigation of bioequivalence” (EMA 2010). For the assessment of the similarity of dissolution profiles using the similarity factor f_2 according to the EMA guideline the following constraints do apply:

1. A minimum of three time points (without zero) are necessary.

2. The time points should be the same for the two formulations.

3. For every time point and for each formulation at least 12 data points are required.

4. A maximum of one mean value per formulation may be > 85% dissolved.

5. The coefficient of variation (%CV) should be < 20% for the first time point and < 10% from the second to the last time point for any formulation.

Dissolution profiles are regarded as similar if the f_2 value is between 50 and 100.

One often encountered problem is that the %CV constraint cannot be fulfilled. One possibility in this situation is the use of the bootstrap f_2 method (Shah 1998) by which the distribution of f_2 is simulated to obtain an unbiased estimate of the expected value of f_2 and the variability of the underlying distribution. For the f_2 calculation only those parts of the profiles are taken into account where the means (per formulation) are > d% dissolved (e.g., d = 1) and a maximum of one mean value per formulation is > 85% dissolved. In the literature it is suggested to make use of the lower 90% bias corrected and accelerated (BCa) confidence interval (CI) limit to come to a decision in terms of similarity (Stevens (2015)).

Value

An object of class ‘bootstrap_f2’ is returned, containing the following list elements:

Boot	An object of class ‘boot’ with the corresponding components.
Profile.TP	A named numeric vector of the columns in data specified by tcol and depending on the selection of use_EMA. Given that the column names contain extractable numeric information, e.g., specifying the testing time points of the dissolution profile, it contains the corresponding values. Elements where no numeric information could be extracted are NA.
L	A vector of the Jackknife leave-one-out-values.
CI	An object of class ‘bootci’ which contains the intervals.
BCa_CI	The lower and upper limits of the BCa interval calculated by the boot.ci() function from the ‘boot’ package.
ShahBCa_CI	The lower and upper limits of the BCa interval calculated according to Shah (Shah 1998).

References

United States Food and Drug Administration (FDA). Guidance for industry: dissolution testing of immediate release solid oral dosage forms. 1997.
https://www.fda.gov/media/70936/download

United States Food and Drug Administration (FDA). Guidance for industry: immediate release solid oral dosage form: scale-up and post-approval changes, chemistry, manufacturing and controls, in vitro dissolution testing, and in vivo bioequivalence documentation (SUPAC-IR). 1995.
https://www.fda.gov/media/70949/download

European Medicines Agency (EMA), Committee for Medicinal Products for Human Use (CHMP). Guideline on the Investigation of Bioequivalence. 2010; CPMP/EWP/QWP/1401/98 Rev. 1.
https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-investigation-bioequivalence-rev1_en.pdf

Stevens, R. E., Gray, V., Dorantes, A., Gold, L., and Pham, L. Scientific and regulatory standards for assessing product performance using the similarity factor, f_2. AAPS Journal. 2015; 17(2): 301-306.
doi: 10.1208/s12248-015-9723-y

Shah, V. P., Tsong, Y., Sathe, P., and Liu, J. P. In vitro dissolution profile comparison - statistics and analysis of the similarity factor, f_2. Pharm Res. 1998; 15(6): 889-896.
doi: 10.1023/A:1011976615750

See Also

get_jackknife_values, boot, boot.ci, mimcr, mztia.

disprofas documentation built on Dec. 8, 2021, 5:10 p.m.