How to calcuate drug shelf life

 Shelf life, or the expiration dating period, is defined as the interval that a drug product is expected to remain within the approved specifications after manufacture. The calculation of the shelf life is the primary objective of a stability study.

The general method for determining the shelf life, as recommended by the FDA and ICH guidelines, involves statistical analysis of stability data:

Primary Calculation Method (Long-Term Stability)

The shelf life is determined as the time point at which the 95% one-sided lower confidence limit for the mean degradation curve intersects the acceptable lower specification limit ($\tau_{\eta}$).

1. Modeling Degradation: The stability data, typically using percent of label claim as the primary variable, are fitted to a mathematical relationship.

   • The degradation relationship can usually be represented by a linear, quadratic, or cubic function on an arithmetic or logarithmic scale.
   • For characteristics expected to decrease (e.g., strength), the 95% one-sided lower confidence limit is used.
   • For characteristics expected to increase (e.g., degradation products), the 95% one-sided upper confidence limit is used.

2. Statistical Calculation (Linear Model): Assuming the strength decreases linearly over time (a zero-order reaction), the expected degradation is modeled by linear regression, $E(Y_{j}) = \alpha + \beta\lambda_{j}$.

   • The shelf life ($x_{L}$) is calculated by solving the quadratic equation that results from setting the 95% lower confidence limit for the mean degradation line, $L(x)$, equal to the lower specification limit, $\tau_{\eta}$. $x_{L}$ is the smaller root of this equation.
   • It is not acceptable to determine the expiration dating period by simply finding where the fitted least-squares line intersects the specification limit (which would only provide a 50% confidence level).

Handling Multiple Batches

When multiple batches (a minimum of three) are tested, the approach depends on batch-to-batch variability:

• Pooling Data: If analysis shows that the batch-to-batch variability is small (e.g., slopes and intercepts are sufficiently similar, sometimes assessed using a significance level of 0.25), the data from different batches may be combined into one overall estimate to establish a single, more precise shelf life.
• Minimum Approach (Fixed Effects): If it is inappropriate to combine data due to significant batch-to-batch variability, the overall expiration dating period may be based on the minimum of the individual shelf lives estimated from each batch. This is considered a conservative estimate.
• Random Batch Effects (Advanced Methods): For establishing a shelf life applicable to all future production batches, statistical methods incorporating random batch effects are used (e.g., Chow and Shao's approach or the HLC method). These methods include the between-batch variability when constructing the confidence limit for the mean degradation curve.

Tentative Shelf Life (Accelerated Testing)

Accelerated stability testing (or stress testing) is used primarily to predict a tentative expiration dating period in a shorter timeframe by increasing the rate of chemical or physical degradation under exaggerated conditions.

The prediction relies on kinetic models:

1. Reaction Order: The analysis involves empirically determining the order of the reaction (e.g., zero-order for linear degradation or first-order for logarithmic degradation).
2. Arrhenius Equation: The relationship between the degradation rate and temperature is characterized using the Arrhenius equation.
3. Extrapolation: The tentative shelf life is obtained by extrapolating the relationship to ambient (marketing) storage conditions.