LETTER TO THE EDITOR
(wileyonlinelibrary.com) DOI: 10.1002/pst.1677 Published online 21 March 2015 in Wiley Online Library
Letter to the editor by the authors of Exact
Calculation of Power and Sample Size in
Bioequivalence Studies Using Two One-sided
Tests, Pharmaceutical Statistics,
DOI: 10.1002/pst.1666
Meiyu Shen,
a
Estelle Russek-Cohen,
b
and Eric V Slud
c,d
This article reflects the views of the authors and should not be construed to be those of the US Food and Drug Administration.
Copyright © 2015 John Wiley & Sons, Ltd.
Correspondence should be addressed to:
Meiyu Shen,
DBVI, Office of Biostatistics,
Office of Translational Sciences,
Center for Drug Evaluation and Research,
Food and Drug Administration,
10903 New Hampshire Ave,
Silver Spring, MD 20993, USA;
Tel. 3017960995
Email: meiyu.shen@fda.hhs.gov
Our article was posted online in December 2014. We were
contacted by Dr. Phillips [1], one of the authors we cited in
our manuscript. We provided an exact formula for determining
sample size for the two one-sided tests approach for evaluating
bioequivalence as is typically performed for submissions at the
Food and Drug Administration (FDA). We did so because sev-
eral of the earlier papers [1,2] did not provide any explicit
formula for this calculation. We also provided a compari-
son for some approximate methods published after these
earlier papers. Dr. Phillips pointed to an article [3], which
he published in 2009 in the International Journal of Bio-
statistics, an on-line journal, and he pointed to the for-
mula in Hauschke et al.’s book [4] published in 2007. In [3],
Dr. Phillips mentioned the MBESS package [5]. We were not aware
of these, and it is likely others were also not aware of them. Phillips
[3] and Hauschke et al. [4] provide an explicit formula for sample
size assuming equal variances of the test and reference products.
We allow for the variance of the reference and test to differ as
FDA does not explicitly require that they be identical as part of a
bioequivalence study, and our formula would allow one to con-
sider the robustness of the sample size calculation in the presence
of heterogeneity. We would like to acknowledge these earlier con-
tributions and indicate that the results reported by Phillips [1] and
then by Diletti et al. [2] are using an approach comparable to ours
for equal variances. Our article did compare the results of our cal-
culations to Phillips [1] and Diletti et al. [2], and the results did
agree for those values we compared. However, because there was
no formula, we could not validate that the two formulas, ours and
theirs, were equivalent even in the case of homogeneous vari-
ances. We also provide the R code for the power and sample size
based on the formula in our paper. Our original motivation for
writing the article was the result of several submissions to FDA
that used an approximate formula when we believed the exact
formula could easily be calculated.
REFERENCES
[1] Phillips KF. Power of the two one-sided tests procedure in bioe-
quivalence. Journal of Pharmacokinetics and Biopharmaceutics 1990;
18:137–143.
[2] Diletti E, Hauschke D, Steinijans VW. Sample size determination for
bioequivalence assessment by means of confidence intervals. Inter-
national Journal of Clinical Pharmacology Therapy and Toxicology
1991; 29:1–8.
[3] Phillips Kem F. Power for testing multiple instances of the two
one-sided tests procedure. The International Journal of Biostatistics
2009; 5(1):Article 15. DOI: 10.2202/1557-4679.1169.
[4] Hauschke D, Steinijans V, Pigeot I. Bioequivalence studies in drug
development: methods and applications. John Wiley & Sons, Ltd:
Chichester, West Sussex, England, 2007; Chapter 5.
[5] Kelley K, Lai K. MBESS: Methods for the Behavioral, Educational, and
Social Sciences, 2008. 14 February 2008. Available at: http://www3.
nd.edu~kkelley/site/MBESS.html (accessed 13.03.2015).
a
Center for Drug Evaluation and Research, Food and Drug Administration, 10903
New Hampshire Ave, Silver Spring, MD 20993
b
Center for Biologics Evaluation and Research, U.S. Food and Drug Administration,
10903 New Hampshire Ave, Silver Spring, MD 20993
c
Mathematics Department, Mathematics Building, University of Maryland College
Park, MD 20742-4015
d
Center for Statistical Research & Methodology Research and Methodology
Directorate U.S. Census Bureau Washington, D.C. 20233
272
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