| EDNE.EQ.dissolution.profiles {EDNE.EQ} | R Documentation |
The EDNE-test for equivalence for dissolution profile data
Description
The function EDNE.EQ.dissolution.profiles() implements a variant of the EDNE-test for equivalence with a concrete equivalence margin for analyses of dissolution profiles. It is a multivariate two-sample equivalence procedure. Distance measure of the test is the Euclidean distance. The equivalence margin is compliant with current regulatory requirements. (see Hoffelder et al.,2015).
Usage
EDNE.EQ.dissolution.profiles(X, Y, alpha = 0.05, print.results = TRUE)
Arguments
X |
numeric data matrix of the first sample (REF). The rows of |
Y |
numeric data matrix of the second sample (TEST). The rows of |
alpha |
numeric (0< |
print.results |
logical; if TRUE (default) summary statistics and test results are printed in the output. If NO no output is created |
Details
This function implements a variant of the EDNE-test for equivalence with a concrete equivalence margin for analyses of dissolution profiles. The current regulatory standard approach for comparing dissolution profiles is the similarity factor f2 (see FDA, 1997, EMA, 2010, among others). Analogous to f2 the equivalence margin implemented in this function is defined by a shift of 10 [% of label claim] at all dissolution time points. Thus, the statistical hypotheses of f2 and EDNE.EQ.dissolution.profiles() coincide (see Hoffelder et al.,2015, Suarez-Sharp et al., 2020). The test checks whether the quadratic mean of the differences between REF and TEST mean profiles is statistically significantly smaller than 10%.
With f2, the current regulatory standard approach for comparing dissolution profiles, the type I error cannot be controlled. According to EMA (2010) "similarity acceptance limits should be pre-defined and justified and not be greater than a 10% difference". The functions
-
EDNE.EQ.dissolution.profiles
and f2 have in common that they all check wether a kind of average difference between the expected values is smaller than 10 [% of label claim] (see Suarez-Sharp et al., 2020). Thus, the methods
-
EDNE.EQ.dissolution.profiles
are compliant with current regulatory requirements. In contrast to the standard approach f2 they allow (at least approximate) type I error control.
Value
a data frame; three columns containing the results of the test
p.value |
numeric; the p-value of the equivalence test according to Hoffelder et al. (2015) |
testresult.num |
numeric; 0 (null hypothesis of nonequivalence not rejected) or 1 (null hypothesis of nonequivalence rejected, decision in favor of equivalence) |
testresult.text |
character; test result of the test in text mode |
Author(s)
Thomas Hoffelder <thomas.hoffelder at boehringer-ingelheim.com>
References
EMA (2010). Guidance on the Investigation of Bioequivalence. European Medicines Agency, CHMP, London. Doc. Ref.: CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **. URL: https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-investigation-bioequivalence-rev1_en.pdf
FDA (1997). Guidance for Industry: Dissolution Testing of Immediate Release Solid Oral Dosage Forms. Food and Drug Administration FDA, CDER, Rockville. URL: https://www.fda.gov/media/70936/download
Hoffelder, T., Goessl, R., Wellek, S. (2015). Multivariate Equivalence Tests for Use in Pharmaceutical Development. Journal of Biopharmaceutical Statistics, 25:3, 417-437. URL: http://dx.doi.org/10.1080/10543406.2014.920344
Suarez-Sharp, S., Abend, A., Hoffelder, T., Leblond, D., Delvadia, P., Kovacs, E., Diaz, D.A. (2020). In Vitro Dissolution Profiles Similarity Assessment in Support of Drug Product Quality: What, How, When - Workshop Summary Report. The AAPS Journal, 22:74. URL: http://dx.doi.org/10.1208/s12248-020-00458-9
Examples
# Apart from simulation errors, a recalculation of the EDNE results
# of some parts (normal distribution only) of the simulation study in
# Hoffelder et al. (2015) can be done with the following code. Please note that
# the simulation takes approximately 7 minutes for 50.000 simulation
# runs (number_of_simu_runs <- 50000). To shorten calculation time for
# test users, number_of_simu_runs is set to 100 here and can/should be adapted.
library(MASS)
number_of_simu_runs <- 100
set.seed(2020)
mu1 <- c(41,76,97)
mu2 <- mu1 - c(10,10,10)
SIGMA_1 <- matrix(data = c(537.4 , 323.8 , 91.8 ,
323.8 , 207.5 , 61.7 ,
91.8 , 61.7 , 26.1) ,ncol = 3)
SIGMA_2 <- matrix(data = c(324.1 , 233.6 , 24.5 ,
233.6 , 263.5 , 61.4 ,
24.5 , 61.4 , 32.5) ,ncol = 3)
SIGMA <- matrix(data = c(430.7 , 278.7 , 58.1 ,
278.7 , 235.5 , 61.6 ,
58.1 , 61.6 , 29.3) ,ncol = 3)
SIMULATION_SIZE_EDNE <- function(disttype , Hom , Var , mu_1 , mu_2
, n_per_group , n_simus ) {
n_success_EDNE <- 0
if ( Hom == "Yes" ) {
COVMAT_1 <- SIGMA
COVMAT_2 <- SIGMA
}
else {
COVMAT_1 <- SIGMA_1
COVMAT_2 <- SIGMA_2
}
if ( Var == "Low" ) {
COVMAT_1 <- COVMAT_1 / 4
COVMAT_2 <- COVMAT_2 / 4
}
d <- ncol(COVMAT_1)
Mean_diff <- mu_1 - mu_2 # Difference of both exp. values
dist_edne <- crossprod(Mean_diff) # true EDNE distance and equivalence margin
if ( n_per_group == 10 ) {
cat("Expected value sample 1:",mu_1,"\n",
"Expected value sample 2:",mu_2,"\n",
"Covariance matrix sample 1:",COVMAT_1,"\n",
"Covariance matrix sample 2:",COVMAT_2,"\n",
"EM_EDNE:",dist_edne,"\n")
}
for (i in 1:n_simus) {
if ( disttype == "Normal" ) {
REF <- mvrnorm(n = n_per_group, mu=mu_1, Sigma=COVMAT_1)
TEST<- mvrnorm(n = n_per_group, mu=mu_2, Sigma=COVMAT_2)
}
n_success_EDNE <- n_success_EDNE + EDNE.EQ.dissolution.profiles(X=REF
, Y=TEST
, print.results = FALSE)$testresult.num
}
empirical_succ_prob_EDNE <- n_success_EDNE / n_simus
simuresults <- data.frame(dist = disttype , Hom = Hom , Var = Var
, dimension = d , em_edne = dist_edne
, sample.size = n_per_group
, empirical.size.edne = empirical_succ_prob_EDNE)
}
SIMULATION_LOOP_SAMPLE_SIZE <- function(disttype , Hom , Var , mu_1 , mu_2
, n_simus ) {
run_10 <- SIMULATION_SIZE_EDNE(disttype = disttype , Hom = Hom , Var = Var
, mu_1 = mu_1 , mu_2 = mu_2
, n_per_group = 10 , n_simus = n_simus)
run_30 <- SIMULATION_SIZE_EDNE(disttype = disttype , Hom = Hom , Var = Var
, mu_1 = mu_1 , mu_2 = mu_2
, n_per_group = 30 , n_simus = n_simus)
run_50 <- SIMULATION_SIZE_EDNE(disttype = disttype , Hom = Hom , Var = Var
, mu_1 = mu_1 , mu_2 = mu_2
, n_per_group = 50 , n_simus = n_simus)
run_100 <- SIMULATION_SIZE_EDNE(disttype = disttype , Hom = Hom , Var = Var
, mu_1 = mu_1 , mu_2 = mu_2
, n_per_group = 100 , n_simus = n_simus)
RESULT_MATRIX <- rbind(run_10 , run_30 , run_50 , run_100)
RESULT_MATRIX
}
simu_1 <- SIMULATION_LOOP_SAMPLE_SIZE(disttype = "Normal", Hom = "Yes"
, Var = "High"
, mu_1 = mu1
, mu_2 = mu2
, n_simus = number_of_simu_runs)
simu_2 <- SIMULATION_LOOP_SAMPLE_SIZE(disttype = "Normal", Hom = "Yes"
, Var = "Low"
, mu_1 = mu1
, mu_2 = mu2
, n_simus = number_of_simu_runs)
simu_3 <- SIMULATION_LOOP_SAMPLE_SIZE(disttype = "Normal", Hom = "No"
, Var = "High"
, mu_1 = mu1
, mu_2 = mu2
, n_simus = number_of_simu_runs)
simu_4 <- SIMULATION_LOOP_SAMPLE_SIZE(disttype = "Normal", Hom = "No"
, Var = "Low"
, mu_1 = mu1
, mu_2 = mu2
, n_simus = number_of_simu_runs)
FINAL_RESULT <- rbind(simu_1 , simu_2 , simu_3 , simu_4)
cat("**** Simu results n_simu_runs: ",number_of_simu_runs," **** \n")
FINAL_RESULT