# tools:::Rd_package_title("SE.EQ") tools:::Rd_package_description("SE.EQ") package ## Details The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("SE.EQ") tools:::Rd_package_indices("SE.EQ") ## Author(s) tools:::Rd_package_author("SE.EQ") Maintainer: tools:::Rd_package_maintainer("SE.EQ") ## 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](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](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](http://dx.doi.org/10.1080/10543406.2014.920344) Hoffelder, T. (2019) Equivalence analyses of dissolution profiles with the Mahalanobis distance. **Biometrical Journal**, 61:5, 1120-1137. URL: [https://doi.org/10.1002/bimj.201700257](https://doi.org/10.1002/bimj.201700257) 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](http://dx.doi.org/10.1208/s12248-020-00458-9) ## Examples ```r # A reproduction of the three-dimensional SE 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_SE_JoBS <- 0.74^2 test_SE_JoBS <- SE.EQ(X=REF_JoBS , Y=TEST_JoBS , eq_margin=equivalence_margin_SE_JoBS , print.results = TRUE) # Apart from simulation errors, a recalculation of the SE 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 20 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. # In the result of the simulation the variable empirical.size.se presents the # simulated size obtained by function \code{SE.EQ()} whereas variable # empirical.size.se.disso shows the # simulated size obtained by function \code{SE.EQ.dissolution.profiles()}. # A detailed analysis of the operating characteristics of the SE variant # implemented in \code{SE.EQ.dissolution.profiles()} is the content of # a future paper. 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_SE <- function(disttype , Hom , Var , mu_1 , mu_2 , n_per_group , n_simus ) { n_success_SE <- 0 n_success_SE_disso <- 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 vars_X <- diag(COVMAT_1) # variances of first sample vars_Y <- diag(COVMAT_2) # variances of second sample dist_SE <- sum( (Mean_diff * Mean_diff) / (0.5 * (vars_X + vars_Y) ) ) # true SE distance and equivalence margin for SE.EQ 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_SE:",dist_SE,"\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_SE_disso <- n_success_SE_disso + SE.EQ.dissolution.profiles( X = REF , Y = TEST , print.results = FALSE )$testresult.num n_success_SE <- n_success_SE + SE.EQ( X=REF , Y=TEST , eq_margin = dist_SE , print.results = FALSE )$testresult.num } empirical_succ_prob_SE <- n_success_SE / n_simus empirical_succ_prob_SE_disso <- n_success_SE_disso / n_simus simuresults <- data.frame(dist = disttype , Hom = Hom , Var = Var , dimension = d , em_se = dist_SE , sample.size = n_per_group , empirical.size.se = empirical_succ_prob_SE , empirical.size.se.disso = empirical_succ_prob_SE_disso) } SIMULATION_LOOP_SAMPLE_SIZE <- function(disttype , Hom , Var , mu_1 , mu_2 , n_simus ) { run_10 <- SIMULATION_SIZE_SE(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_SE(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_SE(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_SE(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 ```

SE.EQ-package