SE.EQ {SE.EQ}

The SE-test for equivalence

Description

The function SE.EQ() implements the SE-test for equivalence according to Hoffelder et al. (2015). It is a multivariate two-sample equivalence procedure. Distance measure of the test is the sum of standardized differences between the expected values or in other words: the sum of effect sizes of all components of the two multivariate samples.

Usage

SE.EQ(X, Y, eq_margin, 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.

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.

eq_margin

numeric (>0). The equivalence margin of the test.

alpha

numeric (0<alpha<1). The significance level of the SE-test for equivalence. 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 FALSE no output is created

Details

This function implements the SE-test for equivalence. Distance measure of the test is the sum of standardized differences between the expected values or in other words: the sum of effect sizes of all components of the two multivariate samples. The test is an asymptotically valid test for normally distributed data (see Hoffelder et al.,2015).

Value

a data frame; three columns containing the results of the test

p.value

numeric; the p-value of the SE test for equivalence

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., 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

Examples

# 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)