Keywords: Joint modeling, accelerated stability, quality attribute
Stability study is a critical component for the submission and market authorization of a new drug or biological product. Long-term stability studies should be used to establish the stability profile and shelf life of the drug product. Accelerated stability studies can provide insight into degradation pathways and help expedite the development of formulation and packaging. Accelerated stability studies are also useful to identify the stability-indicating attributes and appropriate assay methods for measuring the degradation. The selection and specifications of critical quality attributes are imperative for ensuring the quality, safety and efficacy of the drug. For each individual attribute, Arrhenius equation can be used to combine accelerated stability data with limited long-term stability data to predict the degradation rates under long-term storage conditions. Usually, multiple stability-indicating critical attributes are intrinsically correlated because they are all indicators of drug quality. We propose a multivariate nonlinear mixed-effects model, which can combine the accelerated and long-term stability data with Arrhenius equation and incorporate the correlation among the attributes with random effects. Simulation studies show that the joint modeling of the multiple correlated attributes may provide more efficient estimates of degradation rates. The proposed model can provide insight on selecting the most relevant set of stability-indicating attributes and to set coherent specifications for multiple attributes. The accelerated stability data for a therapeutic protein was analyzed for illustration.