Research Article Received 17 April 2013, Accepted 10 December 2013 Published online 9 January 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/sim.6081 Inference of bioequivalence for log-normal distributed data with unspecified variances Siyan Xu, a * † Steven Y. Hua, b Ronald Menton, b Kerry Barker, b Sandeep Menon a,c and Ralph B. D’Agostino a,d Two drugs are bioequivalent if the ratio of a pharmacokinetic (PK) parameter of two products falls within equivalence margins. The distribution of PK parameters is often assumed to be log-normal, therefore bioequiva- lence (BE) is usually assessed on the difference of logarithmically transformed PK parameters (ı). In the presence of unspecified variances, test procedures such as two one-sided tests (TOST) use sample estimates for those variances; Bayesian models integrate them out in the posterior distribution. These methods limit our knowledge on the extent that inference about BE is affected by the variability of PK parameters. In this paper, we propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components: F -statistic function for variances and t -statistic function for ı. Demonstrated with published real-life data, the proposed method not only produces results that are same as TOST and compa- rable with Bayesian method but also helps identify ranges of variances, which could make the determination of BE more achievable. Our findings manifest the advantages of the proposed method in making inference about the extent that BE is affected by the unspecified variances, which cannot be accomplished either by TOST or Bayesian method. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: bioequivalence; likelihood function; TOST; unspecified variances; Bayesian model 1. Introduction Establishment of bioequivalence (BE) is a regulatory requirement needed prior to claiming that a proposed generic version (test product) of a drug is equivalent to the branded-name drug (reference product). For example, US FDA guidance document [1] recommends that 90% CI values for the ratio of the relative means for AUC0-t, AUC0-1, and Cmax of the new and reference drugs should fall between 0.80 and 1.25. These limits, set by regulations applicable in both US and the European Economic Area, are acceptance criteria to assure that the difference between the test and reference products is no more than clinical relevance. AUC and Cmax are two pharmacokinetic (PK) parameters that represent area under the concentration-time curve and maximum concentration of a drug. The usual BE definition places the focus of statistical inference on whether the parameter of interest falls within the equivalence margins even more rigorously than estimating the parameter itself. Because PK data are assumed to be log-normal, BE is assessed on the difference in a logarithm-transformed PK parameter. Statistical methods in establishing BE are readily available in literature including testing procedures developed by Metzler [2], Kirkwood [3], Westlake [4], Anderson and Hauck [5], Locke [6], Schuirmann [7], Berger and Hsu [8], among others. A comparison of operating characteristics in these testing pro- cedures can be found in a review paper by Choi et al. [9]. The above methods are based on frequentist theory. One short fall of the frequentist theory is it attempts to use the same probabilities to measure a Biostatistics, Boston University School of Public Health, 801 Massachusetts Avenue, Boston, MA 02118, U.S.A. b Biotechnology Clinical Development, Pfizer Inc., 35 Cambridgepark Dr., Cambridge, MA 02140, U.S.A. c Bio-therapeutics Clinical Research, Pfizer Inc., 35 Cambridgepark Dr., Cambridge, MA 02140, U.S.A. d Boston University Mathematics and Statistics Department, 111 Cummington Street, Boston, MA 02215, U.S.A. *Correspondence to: Siyan Xu, Boston University, Biostatistics, 801 Massachusetts Avenue, Boston, MA 02118, U.S.A. † E-mail: siyanxu@bu.edu 2924 Copyright © 2014 John Wiley & Sons, Ltd. Statist. Med. 2014, 33 2924–2938