In the event of a temperature excursion, two critical factors are evaluated to assess potential product impact, namely, excursion temperature, and the total duration of the product’s exposure to the excursion. Generally, a greater excursion temperature and/or a longer duration correspond to an increased potential impact on the product. Based on these factors, a tiered approach with pre-determined allowable ranges is developed. By establishing a database of product-specific allowable excursion range, the workflow shown in Fig. 2 can be leveraged upon excursion notification to obtain a quick assessment of potential product impact. The following sections detail the methodology for calculating these allowable ranges. Detailed calculations for Tables II, III and IV can be found in the supplementary materials.

Fig. 2

Impact assessment process workflow using the proposed tier-based approach

Tier 1: Temperature Excursion within the Pre-Determined Allowable Range

The pre-determined allowable excursion range dictates the assessment tiers, with Tier 1 falling within the allowable range. The allowable duration, denoted as ta, is calculated using the equation:

$$_=\frac_-_\right)-\left(__\right)\right]}_}$$

(1)

where, xSLL is the shelf life specification limit of the degradation product at the end of shelf life, xRL is the release specification limit of the degradation product at product release, rl is long-term degradation rate obtained from long-term stability studies under recommended storage conditions, re is the degradation rate obtained from the stress study at elevated temperature conditions (50°C or 60°C), and ts is the shelf life of the product. The stress study temperature is established as the allowable excursion temperature. The calculated allowable duration, ta, is compared against the duration of the stress study at 50°C or 60°C, and the shorter duration is established as the allowable excursion duration. Thus, the established allowable duration is guaranteed not to exceed the duration supported by the generated data. For studies at 50°C or 60°C, it is recommended to conduct at least four time points including time zero (for example, timepoints: 0, 4, 7 and 14 days) to accurately determine re.

The difference between the release and shelf life limits is the minimum allowance for product changes attributable to degradation throughout its shelf life. In the example shown in Fig. 1, the release limit is 4.0% and the shelf life limit is 6.0% for total degradation. This signifies that no product exceeding 4.0% will be released. Thus, the minimum allowance to account for changes (in total degradation) during shelf life is 2.0%. Excursions from recommended storage temperatures can potentially deplete this 2.0% allowance, leading to a reduced allowance for degradation during the product’s intended shelf life. Normal degradation under recommended long-term storage condition is derived using rl from long-term stability studies and shelf life time ts. The allowable duration is calculated by employing the degradation rate obtained from the stress study at the elevated temperature (50°C or 60°C), using Eq. 1. This calculated duration is inherently conservative as the allowance is the minimum by using the release limit and can be applied to all batches, as no batch can be released at a level exceeding the release limit. When the excursion falls within the pre-determined allowable duration and stress study temperature, the product is expected to remain within specification limits throughout shelf life.

Table II presents an assessment for product X with a recommended long-term storage condition at 15–30°C. A stress study was performed at 50°C for 14 days, with all product specification limits being met at every recorded time point. The total degradation products attribute was the shelf life limiting factor for product X. Degradation rates at the long-term condition and excursion temperature were experimentally determined, at 0.0842%/month and 0.0408%/day for total degradation products, respectively. The calculated allowable duration following Eq. 1 is 23 days at 50°C. As the stress study was performed at 50°C for 14 days, a shorter duration than the calculated duration of 23 days, 14 days was assigned as the allowable duration at 50°C. This means that any excursion within these ranges (temperature ≤ 50°C and excursion duration ≤ 14 days) will not require further quality impact assessment. It should be noted that after any change to shelf life or specification limit, additional calculations must be performed to confirm the previously established allowable excursion range.

Table II Allowable Excursion Duration Calculations for Product X at 50ºC

A Tier 1 excursion, defined by Eq. 1 as a conservative allowable temperature and duration for a product across release lots, ensures product quality throughout its shelf life, eliminating the need for further evaluation. A pre-built database of Tier 1 allowable excursion ranges for commercial products can expedite product disposition for pharmaceutical manufacturers upon notice of temperature excursion event. For example, if a temperature excursion is experienced by a Product X lot for a duration of 3 days, with a maximum temperature of 45°C, no further impact assessment would be necessary. This is because the pre-determined allowable range specifies an allowable temperature of 50°C for a duration not exceeding 14 days.

Tier 2: Temperature Excursion Duration Longer than the Pre-Determined Allowable Duration

When a temperature excursion is within the predetermined allowable temperature, but occurs for longer than the predetermined allowable duration, the actual release data from the lot that experienced the excursion (hereinafter referred to as excursion lot) is used to assess the impact using the equation:

$$_=\frac_-_\right)-\left(__\right)\right]}_}$$

(2)

where, ta,i is the allowable excursion duration for the individual excursion lot and xRL,i is the actual degradation content at product release for the excursion lot. Tier 1 assessments are conducted under the assumption that products are released at the established release limits. However, product batches are typically released with values well within these limits. Therefore, a longer allowable excursion duration can be determined using real, lot-specific release data, as calculated using Eq. 2 within the framework of Tier 2 assessments. Under the conditions defined by the calculated allowable excursion duration and the allowable temperature in Tier 2, any excursions observed within the Tier 2 are considered to have no impact on product quality.

The case study from Tier 1 for product X established an allowable excursion duration of 14 days at 50°C. This predetermined limit is not applicable to lot Z of product X, which experienced a temperature excursion at 45°C for 15 days. While the excursion temperature was within 50°C, the duration exceeded the allowable duration of 14 days. Tier 2 assessments, summarized in Table III, indicate an excursion allowable duration of 72 days at 50°C for lot Z with total degradation (shelf life limiting factor) of 1.5% at release following Eq. 2. Since the actual excursion duration of 15 days falls within the calculated allowable time of 72 days, the excursion lot Z is expected to maintain its quality within acceptance limits throughout its shelf life.

Table III Determining Allowable Excursion Duration for a Specific Excursion LotTier 3: Temperature Excursion Above the Pre-Determined Allowable Temperature with a Case Study

When temperature excursion is above the predetermined allowable temperature range, additional analysis using the Arrhenius equation is performed to evaluate impact using the shelf life limiting factor. In addition to the stability data used to establish Tier 1 and Tier 2 ranges (long-term stability and stress study at elevated temperatures), data available from commercial stability lots of the product are used in Tier 3 assessment. To evaluate the impact of the excursion, the final degradation product of the excursion lot at the end of shelf life is calculated using Eq. 3, which is then compared against the specification limit. If the final degradation product is within the shelf life specification limit, the excursion lot in evaluation is predicted to maintain within quality acceptance limits throughout shelf life. The final degradation product, Cfinal, is calculated as,

where, C0 is the adjusted release value of the excursion lot, Δexcursion is the amount of the degradation product induced from excursion, and Chighest is the highest degradation at the end of shelf life for the product under normal storage. Cfinal represents the combination of the highest degradation during long-term storage and predicted amount of degradation during excursion. The C0 component accounts for the elevated amount of degradant at release from the excursion lot if it's observed relative to the stability lots used to build the Arrhenius equation.

The assessment of Tier 3 excursions is exemplified through a case study. The analysis workflow is shown in Fig. 3. In this example, a commercial drug product V for market use experienced an excursion of 69°C for 1 h during shipment. According to the known database, the Tier 1 allowable excursion range established for drug product V is up to 50°C for 7 days. The temperature of 69°C exceeds the predetermined allowable temperature limit of 50°C. This is an event where Tier 3 approach with the Arrhenius equation can be utilized to guide the decision if this material can be released for market use. For drug product V at its commercial phase, real-time stability data at 25°C /60% RH, 30°C /75% RH to shelf life at 36 months and 40°C /75%RH to 6 months are available. This data was used to develop a predictive model using the Arrhenius equation, allowing the estimation of degradation at temperature that product may experience, including those not measured, such as the 69°C excursion scenario. The predictions were tested against real-world data from stress studies at 50°C and 60°C, leading to prediction verification and model validation. These evaluations are expected to demonstrate the model’s capabilities beyond the temperature range of 25–40°C used for its construction. The steps to perform Tier 3 assessment for this case are described below. Goodness-of-fit assessments ensured model viability, but detailed descriptions are beyond the scope of this discussion.

Fig. 3

Tier 3 assessment workflow for excursions exceeding pre-determined allowable temperature range

In this case study for drug product V, linear regression analyses on assay, individual degradation products and total degradation products versus time were constructed using JMP 16.1.0 for all the lots on stability following ICH Q1E. The shelf life analysis resulted in impurity Y, a degradation product, reaching the specification limit first, or giving the shortest predicted shelf life. Therefore, impurity Y is the shelf life limiting factor and was used for subsequent evaluation.

Real time data from product V stability lots were used to determine the degradation rates at 25°C (3 lots), 30°C (9 lots), and 40°C (9 lots). For each temperature, a separate linear regression model with individual intercept and slope parameters was employed for each lot (Fig. 4a-c). The highest upper 95% confidence limit of the slope, estimated from the individual lot models, was used as the degradation rate (k) at that specific temperature. The degradation rates at 25°C, 30°C and 40°C were determined to be 0.061, 0.146, and 0.495 (month −1), respectively, and were then used to model the temperature dependence of degradation rates using the Arrhenius equation.

Fig. 4

Linear regression plots with different intercept and different slope models for degradation data at 25°C (a) and 30°C (b) and 40°C (c)

The degradation rates from three conditions at 25°C, 30°C, and 40°C obtained from step 2 were used to construct the Arrhenius model for impurity Y for product V (Fig. 5), allowing for estimating the degradation rate at the excursion temperature of 69°C. Validation of Tier-3's approach was achieved by comparing Arrhenius-predicted impurity Y % with experimentally determined values from stress studies at 50°C and 60°C (Table IV). The predictions were obtained by adding the calculated degradation from the stress study (at 50°C and 60°C), determined using the degradation rate estimated through Arrhenius exploration, to the experimentally determined impurity Y % level at the initial time point. The model’s predictions were generally observed to be within an acceptable range, although with errors. These errors can be attributed to uncertainty in modeling when using Arrhenius equation to approximate the temperature dependent degradation profiles. Furthermore, analytical variability may also contribute to the observed departures between experimental and predicted outcomes. The errors manifested as over-predictions compared to experimental values, resulting in a conservative estimate of degradation for temperature excursion impact assessement. This overestimation is anticipated as the highest 95% confidence level degradation rates were utilized for construction of the Arrhenius equation. It is noteworthy that the direction of the errors, i.e., predicted values exceeding or falling below experimental data, is not invariably consistent. Under-predictions may be exhibited at extreme temperatures, particularly those further away from the temperatures used for constructing the Arrhenius equation.

Fig. 5

Extrapolation using linear regression model to determine the degradation rate for excursion temperature of 69°C using Arrhenius equation

Table IV Validation of Tier 3 Arrhenius Law-Based Model

The Arrhenius plot yielded a linear fit of ln(k) = 40.39 – 12.85 * 1/T(K) * 1000. At 69°C, the Arrhenius model predicted a degradation rate of k (69°C) = 16.93% (month−1). In this case study for product V, the excursion at 69°C lasted for only one hour. Therefore, the impurity Y content induced by this excursion is, Δexcursion = 0.024%, calculated as 16.93 (%/month) / (30 days/month) / (24 h/day) * 1 h.

The Chighest value, representing the maximum predicted degradation at the end of shelf life at 30°C, was determined using an Analysis of Covariance (ANCOVA)-based predictive model developed per ICH Q1E guidelines. This model analyzed data at 30°C for stability lots and evaluated three linear degradation models: individual intercepts and slopes for each lot, common slope but individual intercepts for each lot, and a unified model with common slope and intercept for all lots. The ANCOVA test in JMP assessed lot poolability and guided the selection of most appropriate model. In the case study of product V excursion, stability data for lots stored at 30°C necessitated different slope and different intercept regression models based on poolability results. The predicted impurity Y (%) level at 36 months with corresponding 95% confidence intervals was calculated for each individual lot. The highest value among these predictions, evaluated at 5.26%, was then adopted as the Chighest value (Fig. 6).

Fig. 6

Impurity Y (%) with 95% confidence intervals at 36 months estimated using a different slope different intercept regression model for stability lots stored at 30°C

The C0 value was calculated to account for any observed elevation in the degradant level at release from the excursion lot, relative to the stability lots. If the excursion lot release value fell within the range observed in the stability lots, then it was expected to be contained within the degradation under recommended storage. If the release value of the excursion lot was higher than the highest value observed in stability lots, then the difference was accounted for by the C0 value. The C0 value was determined by comparing the degradant at lot release of the excursion lot, Crelease, to the highest initial amount of degradant observed in any stability lots used in the predictive model for the product, Cmax, using the following conditions:

a.

when Crelease less than Cmax, C0 = 0

b.

when Crelease greater than Cmax, C0 = Crelease – Cmax

In this case study for product V, impurity Y (%) was 0.2% for the excursion lot at release. The range of impurity Y (%) at release from the stability lots (25°C, 30°C and 40°C) used to establish the shelf life model (steps 2 and 3) was 0.1% to 0.4%. Since 0.2% of impurity Y for the excursion lot was less than the maximum of 0.4%, C0 was determined as 0% and no adjustment was needed for the release value of the excursion lot.

Tier 3 analysis, incorporating a one-hour excursion at 69°C, predicted an impurity Y level of 5.28% at the end of the 36-month shelf life, calculated as Cfinal = 0% (C0) + 0.024% (Δexcursion) + 5.26% (Chighest at 36 months) = 5.284%, satisfying the specification limit of NMT 6.0%. Therefore, this lot of product V is predicted to maintain its quality throughout its shelf life after being exposed to the one-hour excursion at 69°C.