Prasanth Sambaraju is an independent researcher based in Hyderabad, India. 

Prasanth Sambaraju

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Submitted: June 29, 2022
Accepted: July 5, 2023

Stability studies are carried out to study the impact on the quality of drug substance or drug product over a period of time under the combined influence of environmental factors like temperature, humidity, and exposure to light. One of the main purposes of stability testing is to establish shelf life for these drug products. The goal of this paper is to create an Excel spreadsheet, which can be used for statistical testing of more than three stability batches for poolability. The spreadsheet is designed to meet the poolability criteria as per International Council for Harmonisation Harmonised Tripartite guideline for evaluation of stability data, Q1E.

Stability studies in the pharmaceutical industry are intended to measure the degradation of drug product over time. These studies are conducted by taking random samples from a batch that is stored under specified conditions. By using data from these studies, degradation rate as a function of time is calculated. The shelf life is the point in time where the lower 95% confidence interval from the linear fitted regression line crosses the 90% labeled amount (1). The shelf-life estimation for a hypothetical single batch is shown in 

Figure 1. Shelf-life estimation for a single hypothetical batch. Where CI means confidence interval. (Figure courtesy of the author)

The International Council for Harmonisation (ICH) Tripartite Guideline, Q1E 

, describes the procedure for shelf-life estimation. The objective of statistical analysis outlined in the guideline is to determine variability among these batches and then estimate the shelf life accordingly (2).

When multiple batches are manufactured, data from these batches can be pooled for shelf-life calculation. According to ICH’s guideline (2), analysis of covariance (ANCOVA) is used to test statistical difference between both slopes and intercepts of regression lines generated from these multiple batches, using time as a covariate. A significance level of 0.25 is used as the criterion for pooling (3).

In a previous paper (4), the use of Microsoft Excel to test the equality of slopes and intercepts using ANCOVA for three batches was described. The goal of this paper is to test for equality of slope and intercepts using Microsoft Excel, when the number of test batches is greater than three. Two reported datasets each containing data from six batches will be used to demonstrate this approach.

Two stability data datasets each involving six batches from Ruberg and Stegeman’s research (1) were tested separately using the aforementioned approach. The procedure involved regression analysis of stability data using in-built Excel functions and then creating an ANCOVA table using these values. For multi-batch stability data

 shows the possible scenarios for drug product degradation. The common intercept separate slope (CISS) model is used only in special circumstances (5). The other models used to describe stability studies are listed below:

Figure 2. Different models to explain stability studies.

*CISS model is only used in special circumstances. (Figure courtesy of the author)

Common intercept common slope (CICS) model.

 This model indicates that all the batches have a common intercept and slope. The values for common slope and intercept for dataset 1 are obtained by using regression analysis in Excel.

Separate intercept separate slope (SISS) model. 

This model indicates that different batches have different slopes and different intercepts. These values can be obtained by regression analysis from individual batches separately. Residual sum of squares is obtained by adding squared differences between observed and expected value. The expected value is calculated using slope and intercept from individual batches.

Separate intercept common slope (SICS) model.

 This model indicates that different batches have common slope and separate intercept. These values can be obtained by regression analysis using dummy dependent variables containing ones and zeros.

ANCOVA calculations for comparing the intercepts and slopes of stability batches were calculated as described (4) and are shown in 

. These tests make a comparison between two models, simple (reduced) vs. complicated (full) model (5). The P-value obtained for row C in ANCOVA table (

) was less than 0.25, due to which null hypothesis was rejected (SICS model) and alternate hypothesis (SISS model) was used for shelf-life estimation.

Table I. Slope and intercept for different models. Where CICS means common intercept common slope; SISS means separate intercept separate slope; SICS means separate intercept common slope.

Table II. ANCOVA calculations for dataset 1. Where CICS means common intercept common slope; SISS means separate intercept separate slope; SICS means separate intercept common slope; SSE means sum of squared errors; SS is the difference between the sum of squared errors of null and alternate hypothesis and df is the difference between degrees of freedom of null and alternate hypothesis.

The calculations comparing intercepts and slopes of stability batches are shown in 

) obtained for dataset 2, the P-value for row C was greater than 0.25, thereby failed to reject the null hypothesis (SICS model). In row B, the P-value was less than 0.25, due to which null hypothesis was rejected (CICS model) and alternate hypothesis (SICS model) was used for shelf‑life estimation.

Table III. Slope and intercept for different models. Where CICS means common intercept common slope; SISS means separate intercept separate slope; SICS means separate intercept common slope.

Table IV. ANCOVA calculations for dataset 2. Where CICS means common intercept common slope; SISS means separate intercept separate slope; SICS means separate intercept common slope; SSE means sum of squared errors; SS is the difference between the sum of squared errors of null and alternate hypothesis and df is the difference between degrees of freedom of null and alternate hypothesis.

The stability model selected at the end of analysis for both datasets matches with the model used for shelf-life estimation (1). The advantage of this Excel spreadsheet approach is that it gives the users an easy and convenient way to test for poolability of stability data. The procedure doesn’t involve any programming and can be used when the number of batches is greater than three. The limitation of this method is that it can be used only to evaluate data from one factor, batches.

Ruberg, S.J.; Stegeman, J.W. Pooling Data for Stability Studies: Testing the Equality of Batch Degradation Slopes. 

Lee, H.-y.; Wu, P.-c.; Lee; Y.-j. stab: An R Package for Drug Stability Data Analysis. 

LeBlond, D. Hypothesis Testing: Examples in Pharmaceutical Process and Analytical Development. 

LeBlond, D.; Griffith, D.; Aubuchon, K. Linear Regression 102: Stability Shelf Life Estimation Using Analysis of Covariance. 

Prasanth Sambaraju is an independent researcher based in Hyderabad, India.

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Vol. 47, No. 11
November 2023
Pages: 24-27

When referring to this article, please cite it as Sambaraju, P. Pooling of Batches for Stability Data Analysis. 

Articles

One of the main purposes of stability testing is to establish shelf life for these drug products. The goal of this paper is to create an Excel spreadsheet, which can be used for statistical testing of more than three stability batches for poolability. 