Pooling data for stability studies: testing the equality of batch degradation slopes

Pharmaceutical products are routinely monitored for their stability over time. Stability studies generally consist of a random sample of dosage units (e.g., tablets, capsules, vials) from a batch or several batches placed in a storage room and periodically assayed for their drug content. The degradation of the drug product is modeled, and according to the Guideline for Submitting Documentation for Stability Studies of Human Drugs and Biologics (Food and Drug Administration, 1987), the shelf-life is calculated as the time point at which the lower 95% confidence limit about the fitted regression line crosses the lowest acceptable limit for drug content (frequently 90% of the labeled amount). When multiple batches are manufactured, preliminary testing for any batch differences (both slope and intercept) should precede pooling stability data from all batches in the analysis. The Guideline recommends a level of significance of .25 for such preliminary testing based on the work described by Bancroft (1964, Biometrics 20, 427-442). Using such a large significance level helps ensure that the power of the test for the batch differences is sufficiently high. This paper presents an approach whereby the power of the test is fixed and the significance level of the test needed to obtain this power is calculated from the data. If the observed significance level does not achieve the calculated significance level, then the data can be pooled. Examples will illustrate the relative performance of the FDA guideline and the proposed procedure.