# T2EQ.dissolution.profiles.hoffelder: The T^2-test for equivalence for dissolution data In T2EQ: Functions for Applying the T^2-Test for Equivalence

## Description

The function `T2EQ.dissolution.profiles.hoffelder()` implements a variant of the T^2-test for equivalence analyses of highly variable dissolution profiles (see Hoffelder,2016). It is a multivariate two-sample equivalence procedure. Distance measure of the test is the Mahalanobis distance.

## Usage

 `1` ```T2EQ.dissolution.profiles.hoffelder(X, Y, alpha = 0.05, print.results = TRUE) ```

## Arguments

 `X` numeric data matrix of the first sample (REF). The rows of `X` contain the individual observations of the REF sample, the columns contain the variables/components of the multivariate sample. More precisely, the variables are the measured dissolution time points and the rows contain the individual dissolution profiles. `Y` numeric data matrix of the second sample (TEST). The rows of `Y` contain the individual observations of the TEST sample, the columns contain the variables/components of the multivariate sample. More precisely, the variables are the measured dissolution time points and the rows contain the individual dissolution profiles. `alpha` numeric (0<`alpha`<1). The significance level of the test. Usually set to 0.05 which is the default. `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 T^2-test for equivalence suggested in Hoffelder (2016): The equivalence margin of the test is a compromise between the suggestions of Tsong et al. (1996) and EMA (2010) requirements. See Hoffelder (2016) for a discussion on that equivalence margin.

## 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 (2016) `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

Hoffelder, T. (2016). Highly Variable Dissolution Profiles: Comparison of T^2-Test for Equivalence and f_2 Based Methods. pharmind, 78:4, 587-592. URL: http://www.ecv.de/suse_item.php?suseId=Z|pi|8430

Wellek, S. (2010), Testing Statistical Hypotheses of Equivalence and Noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC.

Tsong, Y., Hammerstrom, T., Sathe, P., Shah, V.P. (1996). Statistical Assessment of Mean Differences between two Dissolution Data Sets. Drug Information Journal, 30:4, 1105-1112. URL: http://dx.doi.org/10.1177/009286159603000427

EMA (2010). Guidance on the Investigation of Bioequivalence. URL: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2010/01/WC500070039.pdf

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## Not run: A recalculation of the results underlying Figure 1 in Hoffelder (2016) can be done with the following code: ## End(Not run) data(ex_data_pharmind) REF_pharmind <- cbind(ex_data_pharmind[ which(ex_data_pharmind\$Group=='REF'), ] [c("Diss_10_min","Diss_20_min","Diss_30_min")]) TEST_pharmind <- cbind(ex_data_pharmind[ which(ex_data_pharmind\$Group=='TEST'), ] [c("Diss_10_min","Diss_20_min","Diss_30_min")]) test_T2EQ.dissolution.profiles.hoffelder_pharmind <- T2EQ.dissolution.profiles.hoffelder(X=REF_pharmind,Y=TEST_pharmind) ```

T2EQ documentation built on May 29, 2017, 12:31 p.m.