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 C_{max}) 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 C_{max}) 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 C_{max }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.

This explanation help me a lot. Thanks

Tarun- We’re so glad that you found it helpful!

Above article is really helpful for understand the term confidence interval and pharmacokinetic study.

Thank you for your kind comment, Prakash. We aim to be an educational resource for the community.

Its my dream to work with reputed researcher in pharmacokinetic field.

Thank you for giving explanation for logarithmic range from 80% to 125%.

Thank you for this explanation. I was however wondering why the lower limit was taken as the reference: indeed, we find 80%-125% if we take R = 100% – 20%, and then compute the other bound as exp(-ln(R)). But if we take R = 100% + 20%, we can compute the lower bound in the same way, thus obtaining 83%-120%. Why is 80-125 selected, and not 83-120?

Thierry, I don’t know why they chose to use the lower limit as a reference.

Probable so that one should not be under exposed (lower efficacy).

I have a question regarding AUC vs. Cmax when comparing the same drug that’s given through two different routes of administration – if the Cmax is slightly elevated for one administration versus the other, would the elevated Cmax still mean that either administration is safe to use?

The comparison would be deep muscle injection vs. a subcutaneous administration, same drug, same dosage level. The drug would be a once weekly drug taken for a number of weeks in a row, at least 10 weeks before stopping. After comparing, let’s say the AUC is all but identical, both administrations were under the curve and within 95% of each other. However, what if the Cmax for one of them was slightly higher than the other administration? Is the drug still safe to use regardless of administration? For example sake, let’s say that the Cmax goes even higher when a larger dose is administered, and the higher dose is still at an acceptable Cmax level. In other words, even though the lower dosage levels of Cmax were different, both were still under the safe level per FDA precedence. What are your thoughts on this?

Generally the FDA considers drugs that do not have a narrow therapeutic window to be safe if the AUC and Cmax of a new formulation/new route of administration are within 20% of the reference. Thus, if the Cmax you describe is within 20% of the reference, then it is likely that the FDA would consider the new route bioequivalent with the reference route.

Thanks a lot for this awesome explanation.

After reading this article, I understand, “where did the 80-125% bioequivalence criteria come from?”

Great explanation, very clear and informative.

Thank you for your explanation.

It’s so helpful for me.

Regarding:

“Generally the FDA considers drugs that do not have a narrow therapeutic window to be safe if the AUC and Cmax of a new formulation/new route of administration are within 20% of the reference. Thus, if the Cmax you describe is within 20% of the reference, then it is likely that the FDA would consider the new route bioequivalent with the reference route.”

The regulations regarding bioequivalence and bioavailability testing at 21 CFR 320.23 (b) allow for:

(b) …. Some pharmaceutical equivalents or pharmaceutical alternatives may be equivalent in the extent of their absorption but not in their rate of absorption and yet may be considered bioequivalent because such differences in the rate of absorption are intentional and are reflected in the labeling, are not essential to the attainment of effective body drug concentrations on chronic use, and are considered medically insignificant for the particular drug product studied.

Because the differences cited in the example are “designed”, in that they have a different frequency of administration, this would not be an issue and is quite commonly seen at the FDA.

Thank you for the interesting explanation. Another way to look at this is, when you construct a confidence interval for a ratio, say A/B and if the limits are (a, b), then if one constructs a confidence interval for B/A, the limits should be (1/b, 1/a). That’s why we have (80%, 125%); note that 0.8 = 1/1.25, and 1.25 = 1/0.8.

Thank you for giving an explanation for logarithmic range from 80% to 125%. Now I am clear.

Thank you for explaining about this.

Thank for giving a clear explanation.

Dear Nathan,

Thanks for this helpful explanation. Nevertheless, a short question remains:

Results of a BE study:

Parameter, Ratio Test/Ref (Confidence Interval)

AUC(0-t), 97 (91 – 104)

Cmax, 90 (85- 95)

The criteria “lowest limit above 80” and “highest limit below 125” are fulfilled. However, the expected level 100 was not included in the CI of Cmax.

Bioequivalence: yes or no (EMA guidance)?

Thanks for a reply,

Best, Manfred

Dear Nathan,

The explanation is very informative and thank you very much. Can you kindly help me out in the sequential steps for analysis of Bioequivalence of 2 molecules given parenterally (say intramuscularly).

Kindly let me know whether the following steps are correct or not?

Consider a randomized, Parallel bioequivalence trial conducted in 12 patients in each arm (T, R) and

1) We have the analysed the drug levels in the plasma and have the concentration time profiles of the drug (given parenterally).

2) Then we have to calculate AUC (infinity) and then log transformed each AUC infinity value (so we have total 24 AUC last values – 12 of test and 12 reference drug).

3) Then we have to calculate the mean AUC infinity of test and reference. Then we have to calculate T/R ratio of AUC infinity.

4) For the arrived T/R ratio we have to calculate the 90% confidence intervals.

5) If the arrived CIs are within 80 to 125 we can declare that the two molecules are not different (or bioequivalent).

In the similar way we have to calculate the T/R for Cmax also.

Can you kindly let me know, whether the steps are correct of not. If not kindly guide me.