A Course on Bioequivalence: Unit 15 - Conclusion and Further Topics
This is Unit 15 of a complete bioequivalence analysis course using Pumas. It is the final unit in the course as there are 15 units in the course in total. In this unit we present an outline of the topics touched on the course and point to further directions.
1 A summary of the course
Our focus in this course was on core statistical aspects of bioequivlance analysis for PK endpoints, often using the Pumas pumas_be function, as well as other supporting functions and packages. We studied the basic statistical methodology together with bioequivalence specific aspects of the analysis. Key highlights include:
- Ideas of the analysis, including endpoints and log transformations were in Unit 1 and Unit 2.
- Ideas of the underlying hypothesis test (TOST) and the relationship to the confidence interval bounds, as well as consumer risk protection and power analysis were in Unit 3 and Unit 8.
- Ideas of designs, were in Unit 4.
- Ideas of linear models, and linear mixed models were in Unit 5, Unit 10 and also appeared in other units such as Unit 7 in the context of marginal means and Unit 14 in the context of ANOVA p-values.
- A discussion of nonparameteric approaches was in Unit 9.
- Specific issues dealing with NTID, and HVD were in Unit 11, Unit 12, and Unit 13.
- Finally tooling using Pumas (command line) and PumasCP (in Unit 6) was emphasized throughout.
Studying the content of these 15 units empowers students and professionals with a deep understanding of the interface of statistics and bioequivalence.
Importantly, an understanding of these concepts empowers professionals to report bioequivalence statistical results reliably, and conversely to have a better understanding of planning of bioequivalence trials.
2 Where to from here
There are a few avenues that can be taken to extend beyond the course, with the specific avenue depending on the goal of the student. These avenues include:
- Diving deeper into the statistical concepts to deepen such understanding.
- Improving proficiency in using Julia, Pumas, and other tools.
- Reinforcing pharmacometric concepts underlying bioequivalence, such as non-compartmental analysis (NCA).
- Understanding the many procedural and regulatory details of bioequivalance trials and analysis.
- Exploring and studying the related area of bioequivalence analysis based on pharmacodynamic PD endpoints.
- Exploring and understanding studies related to bioequivalence such as bridging studies.
- Exploring modern approaches based on model-based bioequivalence.
We now comment on each of these avenues.
Deeper into the statistical concepts
As we visited the various statistical concepts, our focus in this course was directed at bioequivalence. With this, one may want to deepen their understanding on the following topics.
- Maximum likelihood estimation
- Linear models
- Linear mixed models
- Analysis of variance
- Various alternatives for nonparameteric models and their analysis
Each of these topics may require substantial reading and investigation. See for example Nazarathy and Klok (2021) as a starting point, or references there-in.
Proficiency in using Julia, Pumas, and other tools
To express the ideas and deal with specific situations, understanding Julia and Pumas code to a deeper level may be of use. See for example other Pumas tutorials introducing Julia as a starting point.
Pharmacometric concepts including NCA
The underlying PK endpoints, such as AUC and Cmax were mostly taken as a given in this course. Having a deeper understanding of non-compartmental analysis (NCA) may be helpful for a deeper understanding of bioequvialence. As a starting point, see Pumas tutorials.
Procedural and regulatory details
While the focus in this course was on statistics, there are several other considerations that go into the planning, execution, and analysis of bioequivalence trials. See other resources, including resources from SOPHAS as a starting point.
Bioequivalence analysis based on pharmacodynamic PD endpoints
Bioequivalence analysis of PD endpoints typically differs from the PK approach. See some regulatory guidelines as a starting point. The FDA (2022) document can be a starting point.
Bridging studies
See other resources, including resources from SOPHAS as a starting point.
Modern approaches based on model-based bioequivalence
Tools such as Pumas support compartmental analysis which can be used for model based bioequivalence (sometimes called virtual bioequivalence). See other resources, including resources from PumasAI as a starting point.
3 Conclusion
In conclusion, this course has provided a comprehensive overview of the statistical foundations and practical applications of bioequivalence analysis, equipping learners with the essential tools needed to confidently plan, conduct, and interpret BE studies. By mastering both the theoretical underpinnings and the implementation using Pumas, students and professionals are now better prepared to address regulatory requirements, make informed decisions in study design, and accurately communicate results, while also laying the groundwork for further exploration into more advanced pharmacometric and statistical methodologies.