TWO METHODS FOR STABILITY DETERMINATION
Figure 2: CI-based and slope based expiry.
If the parameters are stability indicating (i.e., change over time), regression analysis is a primary method for determination
of stability, as the factor is time and the response(s) are the release drug attributes and any additional attributes for
drug characterization. The two methods are based on a rate of degradation and the confidence interval associated with the
rate of degradation. Rate of degradation is best for early development when sample sizes are small, confidence interval based
expiry is best for long-term studies when the sample sizes, and time intervals have more data. Simple linear regression provides
a rate of degradation (slope), starting value at time 0 (intercept), a confidence interval of the mean estimate at each time
point, and residual error around the regression line (see Figure 2). Nonlinear and other types of special linear models (e.g., sqrt,1/x, log, exponential, polynomials) are generally avoided
unless specifically indicated from the data, historical experience, and/or a careful analysis of the residuals. The extrapolation
of the nonlinear or special fits may produce nonsensical and/or irreproducible estimates of shelf life when extrapolated,
so they must be used carefully.
ICH Q1E, 2.3 regarding extrapolation states, "An extrapolation of stability data assumes that the same change pattern will
continue to apply beyond the period covered by long-term data. The correctness of the assumed change pattern is critical when
extrapolation is considered. When estimating a regression line or curve to fit the long-term data, the data themselves provide
a check on the correctness of the assumed change pattern, and statistical methods can be applied to test the goodness of fit
of the data to the assumed line or curve. No such internal check is possible beyond the period covered by long-term data.
Thus, a retest period or shelf life granted on the basis of extrapolation should always be verified by additional long-term
stability data as soon as these data become available" (4).
The 95% confidence interval is used in determining expiry and takes into account the sample size, variation in the batch data,
and number of time points. In early development, when the sample size is small, it is best to focus on degradation rate. In
Phase III stability, when the number of batches are higher and the sample sizes are greater, it is best of focus on the confidence
interval and the predicted expiry at 95% CI.
STATISTICAL MODELS FOR STABILITY ANALYSIS
Figure 3: ANCOVA full model—individual slopes and intercepts.
The general multivariate analysis for stability and expiry is an analysis of covariance (ANCOVA) or mixed model. Alpha for
all model terms are set at 0.05 except for all batch related terms (main effects and interactions) and they are set per guidance
at alpha=0.25. Setting the batch-related terms to 0.25 will cause the expiry to shorten and favor the consumer/patient with
shortened shelf life. Stability analysis is typically analyzed for each storage condition, and rates of degradation and expiries
are determined. The simplest model where every term is significant per the alpha criteria aforementioned is selected for computing
the expiry. The model type is ANCOVA. The statistical test is an ANOVA (see Figure 3) and should be included in submission reports to make sure the model used is appropriate for the analysis and tests for lot
pooling have been correctly conducted. The ANOVA summarizes the significant model terms and indicates the correct model has
been selected for the data being analyzed. ICH QE discusses the analysis of stability data and the general guidance on analysis,
pooling lots, and submission. There are four models that are most often used in stability analysis (see Table I).
DOE AND STABILITY
Table I: Most often used models in stability analysis.
Design of experiments (DOE) is often used to include additional factors in the analysis and evaluation of stability. This
is particularly true of formulation studies, influence of excipients, and pH. ICH Q1D provides guidance on designing and analysis
of stability studies using DOE (5). In general, when designing stability, DOE time is not included in the matrix generation,
it is typically included as part of the response as there are multiple measurements per time point for each condition in the
matrix. The matrix is stacked, time is crossed with each model term, and then the appropriate analysis is performed with time
as a factor and all other model terms.