Skip to main content

Main menu

  • Home
  • Content
    • Current Issue
    • Past Issues
    • Accepted Articles
    • Email Alerts
    • RSS
    • Terms of Use
  • About PDA JPST
    • JPST Editors and Editorial Board
    • About/Vision/Mission
    • Paper of the Year
  • Author & Reviewer Resources
    • Author Resources / Submit
    • Reviewer Resources
  • JPST Access and Subscriptions
    • PDA Members
    • Institutional Subscriptions
    • Nonmember Access
  • Support
    • Join PDA
    • Contact
    • Feedback
    • Advertising
    • CiteTrack
  • .
    • Visit PDA
    • PDA Letter
    • Technical Reports
    • news uPDATe
    • Bookstore

User menu

  • Register
  • Subscribe
  • My alerts
  • Log in
  • My Cart

Search

  • Advanced search
PDA Journal of Pharmaceutical Science and Technology
  • .
    • Visit PDA
    • PDA Letter
    • Technical Reports
    • news uPDATe
    • Bookstore
  • Register
  • Subscribe
  • My alerts
  • Log in
  • My Cart
PDA Journal of Pharmaceutical Science and Technology

Advanced Search

  • Home
  • Content
    • Current Issue
    • Past Issues
    • Accepted Articles
    • Email Alerts
    • RSS
    • Terms of Use
  • About PDA JPST
    • JPST Editors and Editorial Board
    • About/Vision/Mission
    • Paper of the Year
  • Author & Reviewer Resources
    • Author Resources / Submit
    • Reviewer Resources
  • JPST Access and Subscriptions
    • PDA Members
    • Institutional Subscriptions
    • Nonmember Access
  • Support
    • Join PDA
    • Contact
    • Feedback
    • Advertising
    • CiteTrack
  • Follow pda on Twitter
  • Visit PDA on LinkedIn
  • Visit pda on Facebook
Research ArticleResearch

Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products

Richard O. Montes, Richard K. Burdick and David J. Leblond
PDA Journal of Pharmaceutical Science and Technology January 2019, 73 (1) 39-59; DOI: https://doi.org/10.5731/pdajpst.2018.008839
Richard O. Montes
1Pfizer, Lake Forest, Illinois, USA;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: richard.montes@pfizer.com
Richard K. Burdick
2Burdick Statistical Consulting, Louisville, Colorado, USA; and
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
David J. Leblond
3CMCStats, Wadsworth, Illinois, USA
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • Article
  • Figures & Data
  • References
  • Info & Metrics
  • PDF
Loading

Abstract

Tolerance intervals are used to statistically derive the acceptance limits to which drugs must conform upon manufacture (release) and throughout shelf-life. The single measurement per lot in release data and repeated measurements per lot longitudinally for stability data have to be considered in the calculation. Methods for the one-way random effects model by Hoffman and Kringle (HK) for two-sided intervals and Hoffman (H) for one-sided limits are extended to a random-intercept, fixed-slope model in this paper. The performance of HK and H was evaluated via simulation by varying the following factors: (a) magnitude of stability trend over time, (b) sample size, (c) percentage of lot-to-lot contribution to total variation, (d) targeted proportion, and (e) data inclusion. The performance metrics are average width (for two-sided) or average limit (for one-sided) and attained confidence level. HK and H maintained nominal confidence levels as originally developed, but H is too conservative (i.e., achieved confidence level exceeds the nominal level) in some situations. The HK method adapted for an attribute that changes over time performed comparably to the more computationally intensive generalized pivotal quantity and Bayesian posterior predictive methods. Mathematical formulas and example calculations as implemented using R statistical software functions are provided to assist practitioners in implementing the methods. The calculations for the proposed approach can also be easily performed in a spreadsheet given basic regression output from a statistical software package. Microsoft Excel spreadsheets are available from the authors upon request.

LAY ABSTRACT: Tolerance intervals (a measure of what can be expected from the manufacturing process) calculated from attribute measurements of drug product lots are one of the factors considered when establishing acceptance limits to ensure drug product quality. The methods often used to calculate tolerance intervals when there are multiple measurements per lot and the attribute changes over time are either lacking in statistical rigor or statistically rigorous but computationally intensive to implement. The latter type requires simulations that have to be programmed using specialized statistical software, because closed-form mathematical formulas are not available. As a consequence, some quality practitioners and applied statisticians involved in setting acceptance limits may be hindered in using such computationally intensive methods. This paper aims to address this need by proposing an approach that is statistically rigorous yet simple enough to implement using spreadsheets. The approach builds upon previously published works developed for attributes that do not change over time and adapts the cited works for attributes that change over time. The proposed approach is demonstrated to have good statistical properties and compares favorably against the more computationally intensive alternative methods. The paper provides closed-form mathematical formulas, example data, and illustrative calculations as implemented in programmed R functions to facilitate implementation by practitioners. Alternatively, the calculations can be performed without requiring complex programming/simulation using Microsoft Excel spreadsheets that can be requested from the authors.

  • Bayesian posterior predictive
  • Generalized pivotal quantity
  • Random effects model
  • Release and shelf-life specification limits
  • Tolerance interval
  • © PDA, Inc. 2019
View Full Text

PDA members receive access to all articles published in the current year and previous volume year. Institutional subscribers received access to all content. Log in below to receive access to this article if you are either of these.  

If you are neither or you are a PDA member trying to access an article outside of your membership license, then you must purchase access to this article (below). If you do not have a username or password for JPST, you will be required to create an account prior to purchasing. 

Full issue PDFs are for PDA members only.

Note to pda.org users

The PDA and PDA bookstore websites (www.pda.org and www.pda.org/bookstore) are separate websites from the PDA JPST website. When you first join PDA, your initial UserID and Password are sent to HighWirePress to create your PDA JPST account. Subsequent UserrID and Password changes required at the PDA websites will not pass on to PDA JPST and vice versa. If you forget your PDA JPST UserID and/or Password, you can request help to retrieve UserID and reset Password below.

Log in using your username and password

Forgot your user name or password?

Log in through your institution

You may be able to gain access using your login credentials for your institution. Contact your library if you do not have a username and password.
If your organization uses OpenAthens, you can log in using your OpenAthens username and password. To check if your institution is supported, please see this list. Contact your library for more details.

Purchase access

You may purchase access to this article. This will require you to create an account if you don't already have one.

patientACCESS

patientACCESS - Patients desiring access to articles

Full issue PDFs are for PDA members only. You can join PDA at www.pda.org. 

PreviousNext
Back to top

In This Issue

PDA Journal of Pharmaceutical Science and Technology: 73 (1)
PDA Journal of Pharmaceutical Science and Technology
Vol. 73, Issue 1
January/February 2019
  • Table of Contents
  • Index by Author
Print
Download PDF
Article Alerts
Sign In to Email Alerts with your Email Address
Email Article

Thank you for your interest in spreading the word on PDA Journal of Pharmaceutical Science and Technology.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products
(Your Name) has sent you a message from PDA Journal of Pharmaceutical Science and Technology
(Your Name) thought you would like to see the PDA Journal of Pharmaceutical Science and Technology web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
1 + 1 =
Solve this simple math problem and enter the result. E.g. for 1+3, enter 4.
Citation Tools
Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products
Richard O. Montes, Richard K. Burdick, David J. Leblond
PDA Journal of Pharmaceutical Science and Technology Jan 2019, 73 (1) 39-59; DOI: 10.5731/pdajpst.2018.008839

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Share
Simple Approach to Calculate Random Effects Model Tolerance Intervals to Set Release and Shelf-Life Specification Limits of Pharmaceutical Products
Richard O. Montes, Richard K. Burdick, David J. Leblond
PDA Journal of Pharmaceutical Science and Technology Jan 2019, 73 (1) 39-59; DOI: 10.5731/pdajpst.2018.008839
Reddit logo Twitter logo Facebook logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Google Plus One

Jump to section

  • Article
    • Abstract
    • 1. Introduction
    • 2. Methodology
    • 3. Results and Discussion
    • 4. Summary and Recommendation
    • Conflict of Interest Declaration
    • Acknowledgments
    • Appendix: A
    • Appendix: B
    • References
  • Figures & Data
  • Info & Metrics
  • References
  • PDF

Related Articles

  • No related articles found.
  • PubMed
  • Google Scholar

Cited By...

  • Statistically Significant versus Practically Relevant Trend in Stability Data
  • Google Scholar

More in this TOC Section

  • Container Closure Integrity of Vial Primary Packaging Systems under Frozen Storage Conditions: A Case Study
  • Advances in Large Volume Subcutaneous Injections: A Pilot Tolerability Study of an Innovative Needle-Free Injection Platform
  • Quantification and Stability Impact Assessment of Drop Stresses in Biologic Drug Products
Show more Research

Similar Articles

Keywords

  • Bayesian posterior predictive
  • generalized pivotal quantity
  • random effects model
  • release and shelf-life specification limits
  • tolerance interval

Readers

  • About
  • Table of Content Alerts/Other Alerts
  • Subscriptions
  • Terms of Use
  • Contact Editors

Author/Reviewer Information

  • Author Resources
  • Submit Manuscript
  • Reviewers
  • Contact Editors

Parenteral Drug Association, Inc.

  • About
  • Advertising/Sponsorships
  • Events
  • PDA Bookstore
  • Press Releases

© 2023 PDA Journal of Pharmaceutical Science and Technology ISSN: 1079-7440

Powered by HighWire