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# Where Did the 80-125% Bioequivalence Criteria Come From?

Most people involved in clinical pharmacokinetics are familiar with the 80-125% criterion. This criterion is used to compare two treatments with the purpose of evaluating if the treatments are bioequivalent. But, where did this come from? Why 80-125%? Why not 90-110%? or why not 80-120%?

Before we explain where 80-125% came from, let me explain the specifics of the criterion. When testing two treatments (e.g. 2 formulations, male vs. female, impaired vs non-impaired, etc.) often we would like to know if there is a difference in systemic exposure between the two treatments. The currently accepted test is often called “bioequivalence”.

The bioequivalence test states that we can conclude that two treatments are not different from one another if the 90% confidence interval of the ratio of a log-transformed exposure measure (AUC and/or Cmax) falls completely within the range 80-125%. It is important to note that we only conclude that the two treatments are “not different” from one another. We do not conclude that they are the “same”. However, if the 90% confidence interval falls outside the 80-125% range, we conclude that the two treatments are different from one another.

The basis for the 80-125% range is arbitrary … sort of. The FDA (and other regulatory bodies) “decided” that differences in systemic drug exposure up to 20% are not clinically significant. Now, that may lead you to believe that the appropriate range should be 80-120% (100% ± 20%) … but that isn’t the range. This is because the pharmacokinetic parameters for exposure (AUC and/or Cmax) are log-normally distributed. This means that if you transform these exposure parameters by taking the logarithm, you will get a normal distribution. Normal distributions are generally required for specific statistical tests. Thus, the symmetrical ± 20% has to be in the log-transformed space so that the statistical test of bioequivalence will be valid. The following table illustrates the different ratios, and the log-transformed difference.

Test Reference Ratio Percentage ln(ratio)
0.8 1.0 0.8 80% -0.223
0.9 1.0 0.9 90% -0.105
1.0 1.0 1.0 100% 0
1.1 1.0 1.1 110% 0.095
1.2 1.0 1.2 120% 0.182
1.25 1.0 1.25 125% 0.223

Starting at the lower limit (80%), we calculate the natural log of the ratio as -0.223. We can also see that the natural log of the ratio of 100% is 0. Therefore, a symmetrical distribution around 100% on the natural log transformed ratio would be ± 0.223. As shown in the table above, this corresponds to 125% at the upper limit. That’s how we get 80-125% as the target range that represents ± 20% systemic exposure.

This same principle can be used for other ranges that are commonly used for comparisons between 2 treatments where a wider range is acceptable.

Clinical Range ± ln(ratio) Acceptable Range
± 20% ± 0.223 80 – 125%
± 30% ± 0.357 70 – 143%
± 50% ± 0.693 50 – 200%

When conducting a study to compare two treatments, make sure you pick the correct range for the statistical test. All of these ranges are commonly accepted by regulatory agencies. In addition, if you need a custom range (e.g. ± 25%), you can calculate it by determining the ln(ratio) of the lower limit, then creating the symmetrical ln(ratio) for the upper limit and back-calculating the untransformed upper limit.

Ezetimibe and atorvastatin are both used to treat dyslipidemia—an abnormally high level of lipids in the blood—by lowering levels of low-density-lipoprotein cholesterol (LDL-C). The sponsor wanted to develop a fixed-dose combination (FDC) of two previously approved drugs, ezetimibe and atorvastatin. n bioequivalence (BE) trials conducted across a combined dose range of ezetimibe/atorvastatin, all parameters met traditional BE bounds except atorvastatin Cmax at two intermediate doses. Thus, the agency requested data from clinical equivalence (CE) trials to evaluate the two doses that did not meet atorvastatin BE. Read this case study to learn how Certara Strategic Consulting scientists used model-based meta-analysis to understand the impact of dosing regimen and formulation on low-density-lipoprotein cholesterol (LDL-C) levels, to predict the impact of changes in exposure for ezetimibe+atorvastatin FDC on efficacy, and inform the design of CE trials.

### 筆者について

By: Nathan Teuscher
Dr. Teuscher has been involved in clinical pharmacology and pharmacometrics work since 2002. He holds a PhD in Pharmaceutical Sciences from the University of Michigan and has held leadership roles at biotechnology companies, contract research organizations, and mid-sized pharmaceutical companies. Prior to joining Certara, Dr. Teuscher was an active consultant for companies and authored the Learn PKPD blog for many years. At Certara, Dr. Teuscher developed the software training department, led the software development of Phoenix, and now works as a pharmacometrics consultant. He specializes in developing fit-for-purpose models to support drug development efforts at all stages of clinical development. He has worked in multiple therapeutic areas including immunology, oncology, metabolic disorders, neurology, pulmonary, and more. Dr. Teuscher is passionate about helping scientists leverage data to aid in establishing the safety and efficacy of therapeutics.