Tmax: An Unconfounded Metric for Rate of Absorption in Single Dose Bioequivalence Studies
Abstract
Purpose While peak drug concentration (Cmax) is recognized to be contaminated by the extent of absorption, it has long served as the indicator of change in absorption rate in bioequivalence studies. This concentration measure per se is a measure of extreme drug exposure, not absorption rate. This paper redirects attention to Tmax as the absorption rate variable.Methods We show that the time to peak measure (Tmax), if obtained from equally spaced sampling times during the suspected absorption phase, defines a count process which encapsulates the rate of absorption. Furthermore such count data appear to follow the single parameter Poisson distribution which characterizes the rate of many a discrete process, and which therefore supplies the proper theoretical basis to compare two or more formulations for differences in the rate of absorption. This paper urges limiting the use of peak height measures based on Cmax to evaluate only for dose-dumping, a legitimate safety concern with any formulation. These principles and techniques are illustrated by a bioequivalence study in which two test suspensions are compared to a reference formulation.Results Appropriate statistical evaluation of absorption rate via Tmax supports bioequivalence, whereas the customary analysis with Cmax leads to rejection of bioequivalence. This suggests that the inappropriate use of Cmax as a surrogate metric for absorption rate contributes to the unpredictable and uncertain outcome in bioequivalence evaluation today.
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The rate of absorption can be profoundly affected by the drug formulation and route of administration.
“The rate of absorption can be profoundly affected by the drug formulation and route of administration [16, 17], which has implications for the onset and duration of action for oral and LAI antipsychotics.”
From Pharmacokinetic Characteristics of Long-Acting Injectable Antipsychotics for Schizophrenia: An Overview (2021) · cites this paper as [17]
Cites
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,620 · see citing works
(2005) · Springer eBooks · doi:10.1007/0-387-27255-0_9 · Cited by 20,333 · see citing works
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836 · see citing works
Schuirmann, D. J. (1987) · Journal of Pharmacokinetics and Biopharmaceutics · doi:10.1007/bf01068419 · Cited by 2,696 · see citing works
An Introduction to Probability Theory and Its Applications
Feller, W., & Morse, P. Μ. (1958) · Physics Today · doi:10.1063/1.3062516 · Cited by 2,040 · see citing works
An Introduction To Probability Theory And Its Applications
Feller, W. 1.-1. (1950) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 1,249 · see citing works
Handbook of the Poisson Distribution.
Bassett, E. E., & Haight, F. A. (1968) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343850 · Cited by 552 · see citing works
An Introduction to Probability Theory and its Applications.
David, F. N., & Feller, W. (1958) · Biometrika · doi:10.2307/2333079 · Cited by 476 · see citing works
Cmax/AUC is a clearer measure than Cmax for absorption rates in investigations of bioequivalence.
Endrényi, L., Fritsch, S. R. S., & Yan, W. (1991) · PubMed · Cited by 137 · see citing works
Handbook of the Poisson Distribution
Katti, S. K., Rao, A. V., & Haight, F. A. (1968) · Technometrics · doi:10.2307/1267063 · Cited by 127 · see citing works
Biopharmaceutical statistics for drug development
Metzler, C. M. (1988) · Journal of Pharmaceutical Sciences · doi:10.1002/jps.2600770822 · Cited by 100 · see citing works
Handbook of the Poisson distribution
Haight, F. A. (1967) · CERN Document Server (European Organization for Nuclear Research) · Cited by 78 · see citing works
Striving for standards in bioequivalence assessment: a review.
Schulz, H. ‐., & Vw, S. (1991) · PubMed · Cited by 50 · see citing works
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Cited by
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Correll, C. U., Kim, E., Sliwa, J. K., Hamm, W., Gopal, S., Mathews, M., Venkatasubramanian, R., & Saklad, S. R. (2021) · CNS Drugs · doi:10.1007/s40263-020-00779-5 · Cited by 205 · see citing works
Measures of Exposure versus Measures of Rate and Extent of Absorption
Chen, M., Lesko, L. J., & Williams, R. L. (2001) · Clinical Pharmacokinetics · doi:10.2165/00003088-200140080-00001 · Cited by 99 · see citing works
Metrics for the Evaluation of Bioequivalence of Modified-Release Formulations
Endrényi, L., & Tóthfalusi, L. (2012) · The AAPS Journal · doi:10.1208/s12248-012-9396-8 · Cited by 50 · see citing works
Stable isotope breath tests for assessing gastric emptying: A comprehensive review
Sanaka, M., & Nakada, K. (2010) · Journal of Smooth Muscle Research · doi:10.1540/jsmr.46.267 · Cited by 48 · see citing works
Innovative Approaches for Demonstration of Bioequivalence: the US FDA Perspective
Zhang, X., Zheng, N., Lionberger, R. A., & Yu, L. X. (2013) · Therapeutic Delivery · doi:10.4155/tde.13.41 · Cited by 46 · see citing works
Karalis, V. D., & Macheras, P. E. (2003) · European Journal of Pharmaceutical Sciences · doi:10.1016/s0928-0987(03)00064-2 · Cited by 26 · see citing works
Novel Direct Curve Comparison Metrics for Bioequivalence
Polli, J. E., & McLean, A. M. (2001) · Pharmaceutical Research · doi:10.1023/a:1011067908500 · Cited by 22 · see citing works
Bridging the Gap Between In Vitro Dissolution and the Time Course of Ibuprofen-Mediating Pain Relief
Cristofoletti, R., & Dressman, J. (2016) · Journal of Pharmaceutical Sciences · doi:10.1016/j.xphs.2016.08.024 · Cited by 18 · see citing works
Finding Tmax and Cmax in Multicompartmental Models
Han, Y. R., Lee, P. I., & Pang, K. S. (2018) · Drug Metabolism and Disposition · doi:10.1124/dmd.118.082636 · Cited by 16 · see citing works
Why Rate of Absorption Inferences in Single Dose Bioequivalence Studies are Often Inappropriate
Basson, R. P., Ghosh, A., Cerimele, B. J., DESANTE, K. A., & Howey, D. C. (1998) · Pharmaceutical Research · doi:10.1023/a:1011974803996 · Cited by 16 · see citing works
Self-citationMachine Learning in Bioequivalence: Towards Identifying an Appropriate Measure of Absorption Rate
Karalis, V. D. (2022) · Applied Sciences · doi:10.3390/app13010418 · Cited by 14 · see citing works
Estimation of C max and T max in Populations After Single and Multiple Drug Administrations
Tóthfalusi, L., & Endrényi, L. (2003) · Journal of Pharmacokinetics and Pharmacodynamics · doi:10.1023/b:jopa.0000008159.97748.09 · Cited by 14 · see citing works
Karalis, V. D. (2023) · Applied Sciences · doi:10.3390/app13042257 · Cited by 13 · see citing works
Mordenti, J. J., Cavagnaro, J. A., & Green, J. D. (1996) · Pharmaceutical Research · doi:10.1023/a:1016002823485 · Cited by 10 · see citing works
Modeling and Simulation in Bioequivalence
Karalis, V. D. (2016) · Interdisciplinary applied mathematics · doi:10.1007/978-3-319-27598-7_10 · Cited by 7 · see citing works
An In Silico Approach toward the Appropriate Absorption Rate Metric in Bioequivalence
Karalis, V. D. (2023) · Pharmaceuticals · doi:10.3390/ph16050725 · Cited by 7 · see citing works
Thompson, G. A., & Toothaker, R. D. (2004) · Pharmaceutical Research · doi:10.1023/b:pham.0000026428.48103.4f · Cited by 5 · see citing works
The Linares Addictive Potential Model
Linares, Ó. (2012) · Journal of Pharmacy and Nutrition Sciences · doi:10.6000/1927-5951.2012.02.02.3 · Cited by 4 · see citing works
A Vector Theory of Assessing Clinical Trials: An Application to Bioequivalence
Karalis, V. D. (2024) · Journal of Cardiovascular Development and Disease · doi:10.3390/jcdd11070185 · Cited by 4 · see citing works
Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
Kokkali, M., & Karalis, V. D. (2024) · Applied Sciences · doi:10.3390/app14146115 · Cited by 3 · see citing works
C max and t max verification using Fibonacci sequence and absorption rate
Grabowski, T., JAROSZEWSKI, J. J., Borucka, B., & Ziółkowski, H. (2012) · European Journal of Drug Metabolism and Pharmacokinetics · doi:10.1007/s13318-012-0101-1 · Cited by 3 · see citing works
Pharmacokinetics of voriconazole in horses and alpacas
Chan, H. M. (2008) · Cited by 1 · see citing works
- Authors
- Basson, R. P., Cerimele, B. J., DeSante, K. A., & Howey, D. C.
- Affiliations
- Eli Lilly (United States) (US)
- Venue
- Pharmaceutical Research
- Published
- 1996-02
- Volume
- 13
- Issue
- 2
- Pages
- 324-328
- ISSN
- 0724-8741 (ISSN-L)
- 1573-904X
- OpenAlex
- W1563687119
- Cited by
- 22
- References
- 13
- Citations by year
- 2024: 2 · 2023: 2 · 2022: 1 · 2021: 1 · 2018: 1 · 2016: 2 · 2013: 1 · 2012: 3
- FWCI
- 0.81
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Pharmaceutical Research (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Health Sciences › Medicine › Pediatrics, Perinatology and Child Health › Pharmaceutical studies and practices
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Pharmaceutical Science › Drug Solubulity and Delivery Systems
- Keywords
- Tmax, time to peak concentration, bioequivalence, Cmax, counting processes, Poisson distribution, dose dumping, pharmacokinetics
- MeSH terms
- Absorption, Adult, Anti-Bacterial Agents, Chemistry, Pharmaceutical, Drug Administration Schedule, Humans, Male, Pharmacokinetics, Therapeutic Equivalency, Cross-Over Studies
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