The T^2-test for equivalence for dissolution data

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

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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

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## 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)