Prediction bounds for random shelf-lives

Stability models for sequential storage

Some drugs are intended for sequential storage under two different storage conditions. If the data for each condition are analyzed separately, predicting assay and other responses after T1 months at one condition followed by T2 months at the other condition is non-trivial for several reasons. First, the two analyses will give different intercept terms. What should one do about that? Second, how would one calculate the confidence limits for combined storage? Third, what if prior storage at one condition affects the slope at the other condition? This paper proposes a simple ANCOVA model containing two slope terms, one for each storage condition. When multiple batches and/or packages are involved, it is easily generalized to two sets of slope terms. Confidence limits are straightforward and can be calculated using existing commercial software. With properly designed data, one can test whether prior storage at one condition affects the slope at the other condition. If no such effect is significant, very useful extrapolations can be made. Temperature excursions, model reduction and curvilinear dependencies are discussed.

Pooling batches in drug stability study by using constant-width simultaneous confidence bands

One important study objective in drug stability studies is to estimate the shelf-life of a drug. A key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf-life for the drug. In this paper constant-width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches, with a particular view to establish the practical equivalence of different batches. This approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal. It is shown how constant-width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models. In particular, it is shown that constant-width simultaneous confidence bands have a better chance to establish the equivalence than, and so are preferable to, the hyperbola-shaped simultaneous confidence bands considered.

Stability analysis with discrete responses

We consider the estimation of shelf life of a drug product when the stability data are discrete. When there is no batch-to-batch variation, the proposed shelf life estimator is an approximate 95% lower confidence bound of the true shelf life. In the presence of batch-to-batch variation, the proposed shelf life estimator is an approximate 95% lower prediction bound of the shelf life of future batches. As a result, the proposed shelf life is applicable to all future batches of the same drug product. Testing for batch-to-batch variation based on discrete responses is also discussed.

Rank regression in stability analysis

Stability data are often collected to determine the shelf life of certain characteristics of a pharmaceutical product, for example, a drug's potency over time. Statistical approaches such as the linear regression models are considered as appropriate to analyze the stability data. However, most of these regression models in both theory and practice rely heavily on their underlying parametric assumptions, such as normality of the continuous characteristics or their transformations. In this article, we propose and study some rank-based regression procedures for the stability data when the linear regression models are semiparametric with unspecified error structure. Numerical studies including Monte Carlo simulations and practical example are demonstrated with the proposed procedures as well.