EDNE.EQ-package: Implements the EDNE-Test for Equivalence
In EDNE.EQ: Implements the EDNE-Test for Equivalence
Description
Details
Author(s)
References
Examples
Description
Package implements the EDNE-test for equivalence
according to Hoffelder et al. (2015) <DOI:10.1080/10543406.2014.920344>.
"EDNE" abbreviates "Euclidean Distance between the
Non-standardized Expected values".
The EDNE-test for equivalence is a multivariate two-sample equivalence test.
Distance measure of the test is the Euclidean distance.
The test is an asymptotically valid test for the family of distributions
fulfilling the assumptions of the multivariate central limit theorem
(see Hoffelder et al.,2015).
The function EDNE.EQ() implements the EDNE-test for equivalence
according to Hoffelder et al. (2015).
The function EDNE.EQ.dissolution.profiles() implements a variant
of the EDNE-test for equivalence analyses of dissolution profiles
(see Suarez-Sharp et al.,2020 <DOI:10.1208/s12248-020-00458-9>).
EDNE.EQ.dissolution.profiles() checks whether the quadratic mean of the
differences of the expected values of both dissolution profile populations
is statistically significantly smaller than 10 [% of label claim].
The current regulatory standard approach for equivalence analyses of
dissolution profiles is the similarity factor f2.
The statistical hypotheses underlying EDNE.EQ.dissolution.profiles()
coincide with the hypotheses for f2 (see Hoffelder et al.,2015,
Suarez-Sharp et al., 2020).
Details
The DESCRIPTION file:
This package was not yet installed at build time.
Index: This package was not yet installed at build time.
Author(s)
Thomas Hoffelder
Maintainer: Thomas Hoffelder <thomas.hoffelder@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
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# A recalculation of the three-dimensional EDNE example evaluation
# in Hoffelder et al. (2015) can be done with the following code:
data(ex_data_JoBS)
REF_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='REF'), ]
[c("Diss_15_min","Diss_20_min","Diss_25_min")])
TEST_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='TEST'), ]
[c("Diss_15_min","Diss_20_min","Diss_25_min")])
equivalence_margin_EDNE_JoBS <- 297
test_EDNE_JoBS <- EDNE.EQ(X=REF_JoBS
, Y=TEST_JoBS
, eq_margin=equivalence_margin_EDNE_JoBS
, print.results = TRUE)
# 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
EDNE.EQ documentation built on Oct. 23, 2020, 6:21 p.m.
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Description Details Author(s) References Examples
Description
Package implements the EDNE-test for equivalence according to Hoffelder et al. (2015) <DOI:10.1080/10543406.2014.920344>. "EDNE" abbreviates "Euclidean Distance between the Non-standardized Expected values". The EDNE-test for equivalence is a multivariate two-sample equivalence test. Distance measure of the test is the Euclidean distance. The test is an asymptotically valid test for the family of distributions fulfilling the assumptions of the multivariate central limit theorem (see Hoffelder et al.,2015). The function EDNE.EQ() implements the EDNE-test for equivalence according to Hoffelder et al. (2015). The function EDNE.EQ.dissolution.profiles() implements a variant of the EDNE-test for equivalence analyses of dissolution profiles (see Suarez-Sharp et al.,2020 <DOI:10.1208/s12248-020-00458-9>). EDNE.EQ.dissolution.profiles() checks whether the quadratic mean of the differences of the expected values of both dissolution profile populations is statistically significantly smaller than 10 [% of label claim]. The current regulatory standard approach for equivalence analyses of dissolution profiles is the similarity factor f2. The statistical hypotheses underlying EDNE.EQ.dissolution.profiles() coincide with the hypotheses for f2 (see Hoffelder et al.,2015, Suarez-Sharp et al., 2020).
Details
The DESCRIPTION file:
This package was not yet installed at build time.
Index: This package was not yet installed at build time.
Author(s)
Thomas Hoffelder
Maintainer: Thomas Hoffelder <thomas.hoffelder@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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | # A recalculation of the three-dimensional EDNE example evaluation
# in Hoffelder et al. (2015) can be done with the following code:
data(ex_data_JoBS)
REF_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='REF'), ]
[c("Diss_15_min","Diss_20_min","Diss_25_min")])
TEST_JoBS <- cbind(ex_data_JoBS[ which(ex_data_JoBS$Group=='TEST'), ]
[c("Diss_15_min","Diss_20_min","Diss_25_min")])
equivalence_margin_EDNE_JoBS <- 297
test_EDNE_JoBS <- EDNE.EQ(X=REF_JoBS
, Y=TEST_JoBS
, eq_margin=equivalence_margin_EDNE_JoBS
, print.results = TRUE)
# 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
|
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