Raphael Bar, PhD, rbar@netvision.net.il, is a consultant at BR Consulting in Ness Ziona, Israel.

Raphael Bar

Stability data of samples of pharmaceuticals are often generated as replicate test results, typically as duplicates. A statistical analysis for determination of an expiration date can then be applied on either the replicates or their corresponding averages in line with the methodology suggested in International Council for Harmonisation (ICH) Q1A(R2) and Q1E guides. This paper aims at clarifying when a shelf-life derived from all replicates or averages is justified and correct. When replicate stability data represent preparations of the same sample, this is a case of pseudoreplication, and, therefore, the statistically derived shelf-life should be based on the averages of the replicates. However, when these replicate data represent independently and randomly selected and tested samples at each time point, a statistically derived shelf-life based on all replicate data is justifiable.

ICH Q1A (R2) and Q1E are often followed in the pharma industry for the evaluation of stability data of drug substances and products and for a statistical extrapolation of a shelf-life of a drug product or a retest period for a drug substance. The length of derived shelf-life or retest period is based heavily on whether data exhibit a change-over-time and/or variability. The outcome of the statistical evaluation depends on the number of the stability data points analyzed. Usually, a new product submission file is expected to include stability data collected during at least the first year (0, 3, 6, 9, and 12-month time intervals) along with a projected shelf-life (or retest period) statistically derived from these five time points. This shelf-life is subsequently updated as more data are generated. Stability samples are usually each tested in several replicates (duplicates or triplicates) while an average result is recorded as a representative test result. For instance, in the case of a solid dosage form such as tablets, not fewer than 20 tablets are randomly selected from the original stability sampling units (e.g., bottle), weighed to determine a tablet average weight, and ground to make a uniform composite from which several portions (typically two) are tested to yield assay results of the mean content of the active ingredient in an average tablet. Thus, the final test results to be subsequently employed for a statistical analysis consist of either these individual replicates or of a single average result of these replicates.

Often, the drug characteristic that is being tested changes linearly over time, and, therefore, a simple linear regression analysis is first performed on the stability data. The shelf-life/retest period is then determined as the time at which the 95% one-sided confidence limit for the mean curve intersects either the lower (e.g., assay of the pharmaceutical active ingredient) or the upper (e.g., impurity content) specification. While the suitability of the linear model is also expected to be evaluated and justified, this paper concentrates solely on how the stability data are used to derive a shelf-life/retest period from a fitted linear model. Should the shelf-life be derived from a linear model fitted to either all individual replicates (duplicates or triplicates) results or to their arithmetic average results?

Submitted: Jan. 1, 2024
Accepted: Feb. 20, 2024

Raphael Bar, PhD, rbar@netvision.net.il, is a pharmaceutical consultant at BR Consulting.

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Vol. 48, No. 6
June 2024
Pages: 24–29

When referring to this article, please cite it has Bar, R. Determination of Shelf-Life from Stability Data: From Replicates or from Averages? 

Articles

A statistical analysis for determining an expiration date can be applied to replicates or their corresponding averages as suggested in industry guidelines.

Determination of Shelf-Life from Stability Data: From Replicates or from Averages?

This paper demonstrates how assay data sets of a formulated liquid product, drug substance, and an impurity, obtained from combined accuracy-precision studies, are evaluated to calculate statistical intervals (prediction and tolerance intervals) and to graphically display the total analytical error (TAE) to account for the systematic and random errors. Inclusion of either the statistical intervals or the TAE within the allowed accuracy limits is an indication of a successful validation of the accuracy and precision method characteristics. This paper subsequently evaluates the capability of common procedures of pharmaceutical analysis to accommodate acceptable TAE and statistical intervals. While considering typical values of standard deviations (0.5–2.5% relative standard deviation) of chromatographic tests and typical specifications (±2, ±5, or ±10%) of pharmaceuticals, it is shown that a substantial portion of specification tolerance is taken up by either the statistical intervals or by the TAE, particularly in cases of narrow specifications and imprecise procedures.

Raphael Bar, is a Consultant at BR Consulting, Israel, 


Vol. 47, No. 5
May 2023
Pages: 32–41, 45

When referring to this article, please cite it as Bar, R. Total Analytical Error in Validation of Analytical Procedures of Pharmaceuticals. 

This paper demonstrates how assay data sets of a formulated liquid product, drug substance, and an impurity, obtained from combined accuracy-precision studies, are evaluated to calculate statistical intervals (prediction and tolerance intervals) and to graphically display the total analytical error (TAE) to account for the systematic and random errors. 

Total Analytical Error in Validation of Analytical Procedures of Pharmaceuticals

Part two of this article series shows how traditional statistical process control rules can be relaxed or adjusted to allow charting and evaluation of real-life data of pharmaceutical processes with a reduced number of false alarms. Ten practical tools or measures are suggested for minimizing false alarms among process data plotted as is on charts, provided concurrent process performance and product quality are demonstrated. This pragmatic approach reduces the number of futile investigations of apparent innocuous process deviations and streamlines the implementation of the third process validation stage of continued process verification or ongoing process verification.

Submitted: March 3, 2021
Accepted: May 3, 2021


Volume 45, Number 11
November 2021
Pages: 46–53

When referring to this article, please cite it as R. Bar, “Practical SPC Rules in the Real World of an Ongoing Process Verification Plan: Part 2. Practical SPC Rules to Apply on Pharmaceutical Process,” 

Part two of this article series shows how traditional statistical process control rules can be relaxed or adjusted to allow charting and evaluation of real-life data of pharmaceutical processes with a reduced number of false alarms. 

Practical SPC Rules in the Real World of an Ongoing Process Verification Plan: Part 2. Practical SPC Rules to Apply on Pharmaceutical Process Data

The European Union (EU) good manufacturing practice (GMP) and FDA regulatory documents require manufacturers to monitor pharmaceutical and biopharmaceutical product quality to ensure that a “state of control” is maintained throughout the lifecycle of new and legacy products during the third process validation stage called “continued process verification (CPV)” or “ongoing process verification (OPV)”. Indeed, EU GMP Annex 15 clearly states that, “Manufacturers should monitor product quality to ensure that a state of control is maintained throughout the product lifecycle with the relevant process trends evaluated”. Thus, regulatory agencies expect manufacturers to implement a CPV/OPV plan.

The implementation of Stage 3 of the manufacturing process validation is translated into establishing an ongoing CPV/OPV program, which allows identification of CPV signals and defining types of responses to these signals. These CPV signals can in theory be detected by evaluating process data plotted on Shewhart charts, also called process-behavior charts, and scrutinizing them with Nelson rules, also referred to as detection rules or runs tests in StatGraphics software (Stagraphics Technologies Inc., USA) program. However, the validity of these rules holds when the fundamental assumptions underlying the classical Shewhart control charts are met. Otherwise, applying traditional statistical process control (SPC) rules on real-world process data would lead to excessive false signal alarms, which in turn would lead to futile investigations aimed supposedly at assigning causes to these apparent process deviations.

This series of papers will review and demonstrate examples of pharmaceutical process data that the SPC fundamental conditions are often not met; explain the regulatory expectations regarding “state of control”; and suggest practical SPC tools that minimize false alarm signals.

It is shown that collecting, charting, and evaluating product and process data under relaxed and adjusted SPC rules allow a practical and streamlined implementation of the CPV/OPV program.


Vol. 45, No. 10
October 2021
Pages: 40–47

When referring to this article, please cite it as R. Bar, “Practical SPC Rules in the Real World of an Ongoing Process Verification Plan: Part 1. Conventional SPC Rules and Pharmaceutical Process Data,” 

Part 1 of this article series demonstrates, using real-world process data, that the four fundamental assumptions underlying the classical Shewhart control charts—randomness, independence, constant average, and constant variation—are often not met.