Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-30T01:58:24.399Z Has data issue: false hasContentIssue false
  • English
  • Français

Equivalence criteria for the safety evaluation of a genetically modified crop: a statistical perspective

Published online by Cambridge University Press:  08 April 2015

C. I. VAHL  and
Q. KANG
C. I. VAHL*
Affiliation:
Department of Statistics, Kansas State University, Manhattan, KS 66506, USA
Q. KANG
Affiliation:
Independent Statistical Consultant, Manhattan, KS 66503, USA
*
*To whom all correspondence should be addressed. Email: vahl@ksu.edu
Get access Rights & Permissions [Opens in a new window]

Summary

Safety evaluation of a genetically modified (GM) crop is accomplished by establishing its substantial equivalence to non-GM reference crops with a history of safe use. Testing hypotheses of equivalence rather than difference is the appropriate statistical approach. A necessary first step in this regard is to specify a reasonable equivalence criterion that includes a measure for discrepancy between the GM and reference crops as well as a regulatory threshold. The present work explored several equivalence criteria and discussed their pros and cons. Each criterion addresses one of three ordered classes of equivalence: super, conditional and marginal equivalence. Their implications were investigated over an array of parameter values estimated from a real-world dataset. Marginal equivalence was identified as adhering most closely to the concept of substantial equivalence. Because conditional equivalence logically implies marginal equivalence and is practically quantifiable from current field designs, the present work recommends conditional equivalence criteria while encouraging producers to improve their design to enable testing marginal equivalence in the future. Contrary to concerns of the ag-biotech industry, empirical evidence from recent publications indicates that a linear mixed model currently implemented by the European Food Safety Authority is adequate for assessing equivalence despite its lack of genotype-by-environment interaction terms.

Type
Crops and Soils Research Papers
Information
The Journal of Agricultural Science , Volume 154 , Issue 3 , April 2016 , pp. 383 - 406
Check for updates
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, S. & Hauck, W. W. (1990). Consideration of individual bioequivalence. Journal of Pharmacokinetics and Biopharmaceutics 18, 259–273.CrossRefGoogle ScholarPubMed
Berger, R. L. (1982). Multiparameter hypothesis testing and acceptance sampling. Technometrics 24, 295–300.CrossRefGoogle Scholar
Berger, R. L. & Hsu, J. C. (1996). Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statistical Science 11, 283–302.CrossRefGoogle Scholar
Berman, K. H., Harrigan, G. G., Riordan, S. G., Nemeth, M. A., Hanson, C., Smith, M., Sorbet, R., Zhu, E. & Ridley, W. P. (2010). Compositions of forage and seed from second-generation glyphosate-tolerant soybean MON 89788 and insect-protected soybean MON 87701 from Brazil are equivalent to those of conventional soybean (Glycine max). Journal of Agricultural and Food Chemistry 58, 6270–6276.CrossRefGoogle ScholarPubMed
Boddy, A. W., Snikeris, F. C., Kringle, R. O., Wei, G. C. G., Oppermann, J. A. & Midha, K. K. (1995). An approach for widening the bioequivalence acceptance limits in the case of highly variable drugs. Pharmaceutical Research 12, 1865–1868.CrossRefGoogle ScholarPubMed
Brink, K., Chui, C. F., Cressman, R. F., Garcia, P., Henderson, N., Hong, B., Maxwell, C. A., Meyer, K., Mickelson, J., Stecca, K. L., Tyree, C. W., Weber, N., Zeng, W. Q. & Zhong, C. X. (2014). Molecular characterization, compositional analysis, and germination evaluation of a high-oleic soybean generated by the suppression of FAD2-1 expression. Crop Science 54, 2160–2174.CrossRefGoogle Scholar
Brown, L. D., Casella, G. & Hwang, J. T. G. (1995). Optimal confidence sets, bioequivalence, and the limaçon of Pascal. Journal of the American Statistical Association 90, 880–889.Google Scholar
Brown, L. D., Hwang, J. T. G. & Munk, A. (1997). An unbiased test for the bioequivalence problem. Annals of Statistics 25, 2345–2367.CrossRefGoogle Scholar
Burch, B. D. (2007). Generalized confidence intervals for proportions of total variance in mixed linear models. Journal of Statistical Planning and Inference 137, 2394–2404.CrossRefGoogle Scholar
Burch, B. D. & Iyer, H. K. (1997). Exact confidence intervals for a variance ratio (or heritability) in a mixed linear model. Biometrics 53, 1318–1333.CrossRefGoogle Scholar
Carrasco, J. L. & Jover, L. (2003). Assessing individual bioequivalence using the structural equation model. Statistics in Medicine 22, 901–912.CrossRefGoogle ScholarPubMed
Casella, G. & Berger, R. L. (2002). Statistical Inference, 2nd edn. Pacific Gove, CA, USA: Duxbery.Google Scholar
Chen, M. L., Patnaik, R., Hauck, W. W., Schuirmann, D. J., Hyslop, T. & Williams, R. (2000). An individual bioequivalence criterion: regulatory considerations. Statistics in Medicine 19, 2821–2842.3.0.CO;2-L>CrossRefGoogle ScholarPubMed
Chervoneva, I., Hyslop, T. & Hauck, W. W. (2007). A multivariate test for population bioequivalence. Statistics in Medicine 26, 1208–1223.CrossRefGoogle ScholarPubMed
Chinchilli, V. M. (1996). The assessment of individual and population bioequivalence. Journal of Biopharmaceutical Statistics 6, 1–14.CrossRefGoogle ScholarPubMed
Chiu, S. T., Tsai, P. Y. & Liu, J. P. (2010). Statistical evaluation of non-profile analyses for the in vitro bioequivalence. Journal of Chemometrics 24, 617–625.CrossRefGoogle Scholar
Chow, S. C., Shao, J. & Wang, H. S. (2003 a). Statistical tests for population bioequivalence. Statistica Sinica 13, 539–554.Google Scholar
Chow, S. C., Shao, J. & Wang, H. S. (2003 b). In vitro bioequivalence testing. Statistics in Medicine 22, 55–68.CrossRefGoogle ScholarPubMed
Chow, S. C., Hsieh, T. C., Chi, E. & Yang, J. (2010). A comparison of moment-based and probability-based criteria for assessment of follow-on biologics. Journal of Biopharmaceutical Statistics 20, 31–45.CrossRefGoogle ScholarPubMed
Chow, S. C., Endrenyi, L. & Lachenbrunch, P. A. (2013). Comments on the FDA draft guidance on biosimilar products. Statistics in Medicine 32, 364–369.CrossRefGoogle ScholarPubMed
Christensen, R. (1996). Exact tests for variance components. Biometrics 52, 309–314.CrossRefGoogle Scholar
Codex Alimentarius Commission (2009). Foods Derived from Modern Biotechnology, 2nd edn. Joint FAO/WHO Food Standards Programme. Rome: FAO & WHO. Available from: http://www.fao.org/docrep/011/a1554e/a1554e00.htm (verified 2 January 2015).Google Scholar
Davit, B. M., Chen, M. L., Conner, D. P., Haidar, S. H., Kim, S., Lee, C. H., Lionberger, R. A., Maklouf, F. T., Nwakama, P. E., Patel, D. T., Schuirmann, D. J. & Yu, L. X. (2012). Implementation of a reference-scaled average bioequivalence approach for highly variable generic drug products by the US Food and Drug Administration. The AAPS Journal 14, 915–924.CrossRefGoogle ScholarPubMed
Dow AgroSciences (2011). Petition for Determination of Nonregulated Status for Herbicide Tolerant DAS-444⊘6-6 Soybean. USDA-APHIS Petition No. 11-234-01p. Indianapolis, IN, USA: Dow AgroSciences LLC. Available from: http://www.aphis.usda.gov/brs/aphisdocs/11_23401p.pdf (accessed January 2015).Google Scholar
Dow AgroSciences (2012). Petition for Determination of Nonregulated Status for Insect-Resistant DAS-81419-2 Soybean. USDA-APHIS Petition No. 12-272-01p. Indianapolis, IN, USA: Dow AgroSciences LLC. Available from: http://www.aphis.usda.gov/brs/aphisdocs/12_27201p.pdf (accessed January 2015).Google Scholar
Dow AgroSciences (2013). Petition for Determination of Nonregulated Status for Herbicide Tolerant DAS-8191⊘−7 Cotton. USDA-APHIS Petition No. 13-262-01p. Indianapolis, IN, USA: Dow AgroSciences LLC. Available from: http://www.aphis.usda.gov/biotechnology/petitions_table_pending.shtml (accessed 2 January 2015).Google Scholar
Dragalin, V., Fedorov, V., Patterson, S. & Jones, B. (2003). Kullback–Leibler divergence for evaluating bioequivalence. Statistics in Medicine 22, 913–930.CrossRefGoogle ScholarPubMed
EFSA (2010). Scientific opinion on statistical considerations for the safety evaluation of GMOs. EFSA panel on genetically modified organisms (GMO). EFSA Journal 8, 1250. doi:10.2903/j.efsa.2010.1250. Available from: http://www.efsa.europa.eu/en/efsajournal/pub/1250.htm (accessed 2 January 2015).Google Scholar
EMA (2010). Guideline on the Investigation of Bioequivalence. CPMP/EWP/QWP/1401/98 Rev. 1/ Corr. London: Committee for Medicinal Products for Human Use, European Medicines Agency. Available from: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500003011.pdf (accessed 2 January 2015).Google Scholar
Endrenyi, L. & Midha, K. K. (1998). Individual bioequivalence – has its time come? European Journal of Pharmaceutical Sciences 6, 271–277.CrossRefGoogle ScholarPubMed
Endrenyi, L., Taback, N. & Tothfalusi, L. (2000). Properties of the estimated variance component for subject-by-formulation interaction in studies of individual bioequivalence. Statistics in Medicine 19, 2867–2878.3.0.CO;2-J>CrossRefGoogle ScholarPubMed
Esinhart, J. D. & Chinchilli, V. M. (1994). Extension to the use of tolerance intervals for the assessment of individual bioequivalence. Journal of Biopharmaceutical Statistics 4, 39–52.CrossRefGoogle Scholar
FAO/WHO (1996). Joint FAO/WHO Expert Consultation on Biotechnology and Food Safety. FAO Food and Nutrition Paper No. 61. Rome: FAO. Available from: http://www.fao.org/ag/agn/food/pdf/biotechnology.pdf (accessed 2 January 2015).Google Scholar
FDA (2001). Guidance for Industry: Statistical Approaches to Establishing Bioequivalence. Silver Spring, MD, USA: US Department of Health & Human Services, FDA. Available from: http://www.fda.gov/downloads/Drugs/Guidances/ucm070244.pdf (accessed 2 January 2015).Google Scholar
FDA (2003 a). Guidance for Industry: Bioavailability and Bioequivalence Studies for Nasal Aerosols and Nasal Sprays for Local Action. Silver Spring, MD, USA: US Department of Health & Human Services, FDA. Available from: http://www.fda.gov/OHRMS/DOCKETS/98fr/99d-1738-gdl0002.pdf (accessed 2 January 2015).Google Scholar
FDA (2003 b). Guidance for Industry: Bioavailability and Bioequivalence Studies for Orally Administered Drug Products – General Considerations. Silver Spring, MD, USA: US Department of Health & Human Services, FDA. Available from: http://www.fda.gov/downloads/Drugs/.../Guidances/ucm070124.pdf (accessed 2 January 2015).Google Scholar
FDA (2003 c). Statistical Information from the June 1999 Draft Guidance and Statistical Information for in vitro Bioequivalence Data Posted on August 18, 1999 . Silver Spring, MD, USA: US Department of Health & Human Services, FDA. Available from: http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ucm070118.pdf (accessed 2 January 2015).Google Scholar
Freitag, G., Czado, C. & Munk, A. (2007). A nonparametric test for similarity of marginals – with applications to the assessment of population bioequivalence. Journal of Statistical Planning and Inference 137, 697–711.CrossRefGoogle Scholar
Gould, A. L. (2000). A practical approach for evaluating population and individual bioequivalence. Statistics in Medicine 19, 2721–2740.3.0.CO;2-8>CrossRefGoogle ScholarPubMed
Graybill, F. A. & Wang, C. M. (1980). Confidence intervals on nonnegative linear combinations of variances. Journal of the American Statistical Association 75, 869–873.CrossRefGoogle Scholar
Haidar, S. H., Makhlouf, F., Schuirmann, D. J., Hyslop, T., Davit, B., Conner, D. & Yu, L. X. (2008). Evaluation of a scaling approach for the bioequivalence of highly variable drugs. The AAPS Journal 10, 450–454.CrossRefGoogle ScholarPubMed
Harrigan, G. G., Stork, L. G., Riordan, S. G., Reynolds, T. L., Ridley, W. P., Masucci, J. D., MacIsaac, S., Halls, S. C., Orth, R., Smith, R. G., Wen, L., Brown, W. E., Welsch, M., Riley, R., McFarland, D., Pandravada, A. & Glenn, K. C. (2007). Impact of genetics and environment on nutritional and metabolite components of maize grain. Journal of Agricultural and Food Chemistry 55, 6177–6185.CrossRefGoogle ScholarPubMed
Harrigan, G. G., Glenn, K. C. & Ridley, W. P. (2010). Assessing the natural variability in crop composition. Regulatory Toxicology and Pharmacology 58 (Suppl. 1), S13–S20.CrossRefGoogle ScholarPubMed
Harrigan, G. G., Culler, A. H., Culler, M., Breeze, M. L., Berman, K. H., Halls, S. C. & Harrison, J. M. (2013). Investigation of biochemical diversity in a soybean lineage representing 35 years of breeding. Journal of Agricultural and Food Chemistry 61, 10807–10815.CrossRefGoogle Scholar
Harrison, J. M., Howard, D., Malven, M., Halls, S. C., Culler, A. H., Harrigan, G. G. & Wolfinger, R. D. (2013). Principle variance component analysis of crop composition data: a case study on herbicide-tolerant cotton. Journal of Agricultural and Food Chemistry 61, 6412–6422.CrossRefGoogle Scholar
Hauck, W. W. & Anderson, S. (1994). Measuring switchability and prescribability: when is average bioequivalence sufficient? Journal of Pharmacokinetics and Biopharmaceutics 22, 551–564.CrossRefGoogle ScholarPubMed
Hauck, W. W., Chen, M. L., Hyslop, T., Patnaik, R., Schuirmann, D. & Williams, R. (1996). Mean difference vs. variability reduction: tradeoffs in aggregate measures for individual bioequivalence. International Journal of Clinical Pharmacology and Therapeutics 34, 535–541.Google ScholarPubMed
Hauck, W. W., Bois, F. Y., Hyslop, T., Gee, L. & Anderson, S. (1997). A parametric approach to population bioequivalence. Statistics in Medicine 16, 441–454.3.0.CO;2-F>CrossRefGoogle ScholarPubMed
Herman, R. A., Fast, B. J., Johnson, T. Y., Sabbatini, J. & Rudgers, G. W. (2013). Compositional safety of herbicide-tolerant DAS-8191⊘−7 cotton. Journal of Agricultural and Food Chemistry 61, 11683–11692.CrossRefGoogle ScholarPubMed
Hoekenga, O. A., Srinivasan, J., Barry, G. & Bartholomaeus, A. (2013). Compositional analysis of genetically modified (GM) crops: key issues and future needs. Journal of Agricultural and Food Chemistry 61, 8248–8253.CrossRefGoogle ScholarPubMed
Holder, D. J. & Hsuan, F. (1993). Moment-based criteria for determining bioequivalence. Biometrika 80, 835–846.CrossRefGoogle Scholar
Hong, B., Fisher, T. L., Sult, T. S., Maxwell, C. A., Mickelson, J. A., Kishino, H. & Locke, M. E. H. (2014). Model-based tolerance intervals derived from cumulative historical composition data: application for substantial equivalence assessment of a genetically modified crop. Journal of Agricultural and Food Chemistry 62, 9916–9926.CrossRefGoogle ScholarPubMed
Hothorn, L. A. & Oberdoerfer, R. (2006). Statistical analysis used in the nutritional assessment of novel food using the proof of safety. Regulatory Toxicology and Pharmacology 44, 125–135.CrossRefGoogle Scholar
Howe, W. G. (1974). Approximate confidence limits on the mean of X + Y where X and Y are two tabled independent random variables. Journal of the American Statistical Association 69, 789–794.Google Scholar
Hsuan, F. C. (2000). Some statistical considerations on the FDA draft guidance for individual bioequivalence. Statistics in Medicine 19, 2879–2884.3.0.CO;2-9>CrossRefGoogle ScholarPubMed
Hung, H. M. J., Wang, S. J., Tsong, Y., Lawrence, J. & O'Neil, R. T. (2003). Some fundamental issues with non-inferiority testing in active controlled trials. Statistics in Medicine 22, 213–225.CrossRefGoogle Scholar
Hyslop, T., Hsuan, F. & Holder, D. J. (2000). A small sample confidence interval approach to assess individual bioequivalence. Statistics in Medicine 19, 2885–2897.3.0.CO;2-H>CrossRefGoogle ScholarPubMed
Kang, Q. & Vahl, C. I. (2014). Statistical analysis in the safety evaluation of genetically modified crops: equivalence tests. Crop Science 54, 2183–2200.CrossRefGoogle Scholar
Kang, S. H. & Chow, S. C. (2013). Statistical assessment of biosimilarity based on relative distance between follow-on biologics. Statistics in Medicine 32, 382–392.CrossRefGoogle ScholarPubMed
Kimanani, E. K. (2000). Definition of individual bioequivalence: occasion-to-occasion versus mean switchability. Statistics in Medicine 19, 2797–2810.3.0.CO;2-5>CrossRefGoogle ScholarPubMed
König, A., Cockburn, A., Crevel, R. W. R., Debruyne, E., Grafstroem, R., Hammerling, U., Kimber, I., Knudsen, I., Kuiper, H. A., Peijnenburg, A. A. C. M., Penninks, A. H., Poulsen, M., Schauza, M. & Wal, J. M. (2004). Assessment of the safety of foods derived from genetically modified (GM) crops. Food and Chemical Toxicology 42, 1047–1088.CrossRefGoogle ScholarPubMed
Krishnamoorthy, K. & Mathew, T. (2004). One-sided tolerance limits in balanced and unbalanced one-way random models based on generalized confidence intervals. Technometrics 46, 44–52.CrossRefGoogle Scholar
Krishnamoorthy, K. & Mathew, T. (2009). Statistical Tolerance Regions: Theory, Applications, and Computation. New York: Wiley.CrossRefGoogle Scholar
Lee, Y. H., Shao, J. & Chow, S. C. (2004). Modified large-sample confidence intervals for linear combinations of variance components: extension, theory, and application. Journal of the American Statistical Association 99, 467–478.CrossRefGoogle Scholar
Lehmann, E. L. & Romano, J. P. (2005). Testing Statistical Hypotheses, 3rd edn. New York: Springer.Google Scholar
Lepping, M. D., Herman, R. A. & Potts, B. L. (2013). Compositional equivalence of DAS-444⊘6-6 (AAD-12 + 2mEPSPS + PAT) herbicide-tolerant soybean and nontransgenic soybean. Journal of Agricultural and Food Chemistry 61, 11180–11190.CrossRefGoogle ScholarPubMed
Liao, C. T., Lin, T. Y. & Iyer, H. K. (2005). One- and two-sided tolerance intervals for general balanced mixed models and unbalanced one-way random models. Technometrics 47, 323–335.CrossRefGoogle Scholar
Liu, J. P. & Chow, S. C. (1997). A two one-sided tests procedure for assessment of individual bioequivalence. Journal of Biopharmaceutical Statistics 7, 49–61.CrossRefGoogle ScholarPubMed
Lundry, D. R., Burns, J. A., Nemeth, M. A. & Riordan, S. G. (2013). Composition of grain and forage from insect-protected and herbicide-tolerant corn, MON 89034 × TC 1507 × MON 88017 × DAS-59122-7 (SmartStax), is equivalent to that of conventional corn (Zea mays L.). Journal of Agricultural and Food Chemistry 61, 1991–1998.CrossRefGoogle Scholar
McNally, R. J., Iyer, H. & Mathew, T. (2003). Tests for individual and population bioequivalence based on generalized p-values. Statistics in Medicine 22, 31–53.CrossRefGoogle ScholarPubMed
Midha, K. K., Rawson, M. J. & Hubbard, J. W. (1997). Individual and average bioequivalence of highly variable drugs and drug products. Journal of Pharmaceutical Sciences 86, 1193–1197.CrossRefGoogle ScholarPubMed
Monsanto (2011). Petition for the Determination of Nonregulated Status for MON 87712 Soybean. USDA-APHIS Petition No. 11-202-01p. St Louis, MO, USA: Monsanto. Available from: http://www.aphis.usda.gov/brs/aphisdocs/11_20201p.pdf (accessed January 2015).Google Scholar
Monsanto (2012). Petition for Determination of Nonregulated Status for Dicamba and Glufosinate-tolerant Cotton MON 887Æ1. USDA-APHIS Petition No. 12-185-01p. St Louis, MO, USA: Monsanto. Available from: http://www.aphis.usda.gov/brs/aphisdocs/12_18501p.pdf (accessed January 2015).Google Scholar
Monsanto (2013). Petition for Determination of Nonregulated Status for Corn Rootworm Protected and Glyphosate Tolerant MON 87411 Maize. USDA-APHIS Petition No. 13-290-01p. St. Louis, MO, USA: Monsanto. Available from: http://www.aphis.usda.gov/brs/aphisdocs/13_29001p.pdf (accessed 2 January 2015).Google Scholar
Munk, A. (1996). Equivalence and interval testing for Lehmann's alternative. Journal of the American Statistical Association 91, 1187–1196.CrossRefGoogle Scholar
Munk, A. & Pflüger, R. (1999). 1-α equivariant confidence rules for convex alternatives are α/2-level tests – with applications to the multivariate assessment of bioequivalence. Journal of the American Statistical Association 94, 1311–1319.Google Scholar
Oberdoerfer, R. B., Shillito, R. D., Beuckeleer, M. D. & Mitten, D. H. (2005). Rice (Oryza sativa L.) containing the bar gene is compositionally equivalent to the nontransgenic counterpart. Journal of Agricultural and Food Chemistry 53, 1457–1465.CrossRefGoogle Scholar
OECD (1993). Safety Evaluation of Foods Derived by Modern Biotechnology: Concepts and Principles. Paris, France: OECD. Available from: http://dbtbiosafety.nic.in/guideline/OACD/Concepts_and_Principles_1993.pdf (accessed 2 January 2015).Google Scholar
Öfversten, J. (1993). Exact tests for variance components in unbalanced mixed linear models. Biometrics 49, 45–57.CrossRefGoogle Scholar
Patterson, S. (2001). A review of the development of biostatistical design an analysis techniques for assessing in vivo bioequivalence: part two. Indian Journal of Pharmaceutical Sciences 63, 169–186.Google Scholar
Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference Using Likelihood. New York: Oxford University Press.CrossRefGoogle Scholar
Price, W. D. & Underhill, L. (2013). Application of laws, policies, and guidance from the United States and Canada to the regulation of food and feed derived from genetically modified crops: interpretation of composition data. Journal of Agricultural and Food Chemistry 61, 8349–8355.CrossRefGoogle Scholar
Privalle, L. S., Gillikin, N. & Wandelt, C. (2013). Bringing a transgenic crop to market: where compositional analysis fits. Journal of Agricultural and Food Chemistry 61, 8260–8266.CrossRefGoogle ScholarPubMed
Quan, H., Bolognese, J. & Yuan, W. Y. (2001). Assessment of equivalence on multiple endpoints. Statistics in Medicine 20, 3159–3173.CrossRefGoogle ScholarPubMed
Quiroz, J., Ting, N., Wei, G. C. G. & Burdick, R. K. (2002). Alternative confidence intervals for the assessment of bioequivalence in four-period cross-over designs. Statistics in Medicine 21, 1825–1847.CrossRefGoogle ScholarPubMed
Schall, R. (1995 a). A unified view of individual, population and average bioequivalence. In Bio-International 2. Bioavailability, Bioequivalence and Pharmacokinetic Studies (Eds Blume, H. H. & Midha, K. K.), pp. 91–106. Stuttgart, Germany: Medpharm Scientific Publication.Google Scholar
Schall, R. (1995 b). Assessment of individual and population bioequivalence using the probability that bioavailabilities are similar. Biometrics 51, 615–626.CrossRefGoogle ScholarPubMed
Schall, R. & Endrenyi, L. (2010). Bioequivalence: tried and tested. Cardiovascular Journal of Africa 21, 69–71.Google ScholarPubMed
Schall, R. & Luus, H. G. (1993). On population and individual bioequivalence. Statistics in Medicine 12, 1109–1124.CrossRefGoogle ScholarPubMed
Schall, R. & Williams, R. L. (1996). Towards a practical strategy for assessing individual bioequivalence. Journal of Pharmacokinetics and Biopharmaceutics 24, 133–149.CrossRefGoogle ScholarPubMed
Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics 15, 657–680.CrossRefGoogle ScholarPubMed
Shao, J., Chow, S. C. & Wang, B. (2000). The bootstrap procedure in individual bioequivalence. Statistics in Medicine 19, 2741–2754.3.0.CO;2-3>CrossRefGoogle ScholarPubMed
Sheiner, L. B. (1992). Bioequivalence revisited. Statistics in Medicine 11, 1777–1788.CrossRefGoogle ScholarPubMed
Shewry, P. R., Hawkesford, M. J., Piironen, V., Lampi, A. M., Gebruers, K., Boros, D., Andersson, A. A. M., Åman, P., Rakszegi, M., Bedo, Z. & Ward, J. L. (2013). Natural variation in grain composition of wheat and related cereals. Journal of Agricultural and Food Chemistry 61, 8295–8303.CrossRefGoogle ScholarPubMed
Syngenta Seeds & Bayer CropScience AG (2012). Revised Petition for Determination of Nonregulated Status for Herbicide-tolerant Event SYHT0H2 Soybean. USDA-APHIS Petition No. 12-215-01p. Research Triangle Park, NC, USA: Syngenta Seeds, INC. & Bayer CropScience AG. Available from: http://www.aphis.usda.gov/brs/aphisdocs/12_21501p.pdf (accessed 2 January 2015).Google Scholar
Ting, N. T., Burdick, R. K., Graybill, F. A., Jeyaratnam, S. & Lu, T. F. C. (1990). Confidence interval on linear combinations of variance components that are unrestricted in sign. Journal of Statistical Computation and Simulation 35, 135–143.CrossRefGoogle Scholar
Toutain, P. L. & Koritz, G. D. (1997). Veterinary drug bioequivalence determination. Journal of Veterinary Pharmacology and Therapeutics 20, 79–90.CrossRefGoogle ScholarPubMed
Tsui, K. W. & Weerahandi, S. (1989). Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. Journal of the American Statistical Association 84, 602–607.Google Scholar
Van der Voet, H., Perry, J. N., Amzal, B. & Paoletti, C. (2011). A statistical assessment of differences and equivalences between genetically modified and reference plant varieties. BMC Biotechnology 11, 15. doi:10.1186/1472-6750-11-15.CrossRefGoogle ScholarPubMed
Van der Voet, H., Perry, J. N., Amzal, B. & Paoletti, C. (2012). Response to comments on the paper ‘A statistical assessment of differences and equivalences between genetically modified and reference plant varieties’ by van der Voet et al. 2011. BMC Biotechnology 12, 13. doi:10.1186/1472-6750-12-13.Google Scholar
Venkatesh, T. V., Breeze, M. L., Liu, K., Harrigan, G. G. & Culler, A. H. (2014). Compositional analysis of grain and forage from MON87427, an inducible male sterile and tissue selective glyphosate-tolerant maize product for hybrid seed production. Journal of Agricultural and Food Chemistry 62, 1964–1973.CrossRefGoogle Scholar
Vourinen, J. & Turunen, J. (1996). A three-step procedure for assessing bioequivalence in the general mixed model framework. Statistics in Medicine 15, 2635–2655.3.0.CO;2-X>CrossRefGoogle Scholar
Wang, W. Z., Hwang, J. T. G. & Dasgupta, A. (1999). Statistical tests for multivariate bioequivalence. Biometrika 86, 395–402.CrossRefGoogle Scholar
Ward, K. J., Nemeth, M. A., Brownie, C., Hong, B., Herman, R. A. & Oberdoerfer, R. (2012). Comments on the paper ‘A statistical assessment of differences and equivalences between genetically modified and reference plant varieties’ by van der Voet et al. (2011). BMC Biotechnology 12, 13. doi:10.1186/1472-6750-12-13.CrossRefGoogle Scholar
Weerahandi, S. (1991). Testing variance components in mixed models with generalized p values. Journal of the American Statistical Association 86, 151–153.Google Scholar
Weerahandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association 88, 899–905.CrossRefGoogle Scholar
Wellek, S. (1996). A new approach to equivalence assessment in standard comparative bioavailability trials by means of the Mann–Whitney statistic. Biometrical Journal 38, 695–710.CrossRefGoogle Scholar
Wellek, S. (2000). On a reasonable disaggregate criterion of population bioequivalence admitting of resampling-free testing procedures. Statistics in Medicine 19, 2755–2767.3.0.CO;2-O>CrossRefGoogle ScholarPubMed
Wellek, S. (2010). Testing Statistical Hypotheses of Equivalence and Noninferiority, 2nd edn. Boca Raton, FL, USA: Chapman and Hall/CRC.CrossRefGoogle Scholar
Zariffa, N. M. D., Patterson, S. D., Boyle, D. & Hyneck, M. (2000). Case studies, practical issues and observations on population and individual bioequivalence. Statistics in Medicine 19, 2811–2820.3.0.CO;2-P>CrossRefGoogle ScholarPubMed
Zhou, J., Berman, K. H., Breeze, M. L., Nemeth, M. A., Oliveira, W. S., Braga, D. P. V., Berger, G. U. & Harrigan, G. G. (2011). Compositional variability in conventional and glyphosate-tolerant soybean (Glycine max L.) varieties grown in different regions in Brazil. Journal of Agricultural and Food Chemistry 59, 11652–11656.CrossRefGoogle ScholarPubMed