How the prediction works

Each degradant is modelled on its own, with every model choice explained and open to override. This page summarises the methods; the report for each analysis lists the exact settings, parameter estimates and decisions.

Temperature and humidity

The rate of each degradation follows the humidity-corrected Arrhenius equation used in the accelerated stability assessment program (ASAP):

ln k = ln A − E_a / (R·T) + B · RH

E_a is the activation energy and B the humidity sensitivity. With only one humidity level the B term is left out.

Change over time

Several shapes are fitted to all conditions at once (a global fit) and compared:

• Linear: steady growth, typical for degradants at low levels.
• Power law: growth that slows (or speeds up) over time, common for diffusion-limited or surface reactions.
• First order and first order to a plateau: for assay loss, including biologics that level off.
• Isoconversion: the classic ASAP approach, using the time each condition takes to reach the limit.

Choosing the model

The mildest condition is left out and each model predicts it from the rest; the model that predicts it best is preferred, with AICc used when they are close and the simplest model kept when several are equally good, unless another gives a noticeably shorter shelf life. Models with implausible parameters (for example an activation energy outside 40 to 200 kJ/mol) are set aside with the reason shown. In validated mode you can restrict every degradant to the models your procedure allows, or lock any degradant to one model.

Results below the limit

<LOQ and ND results are treated as censored: the model only has to predict a value below the limit there. This keeps early time points informative without inventing a number for them.

Uncertainty

Parameter uncertainty from the fit (scaled by Student's t when there are few degrees of freedom) and the measurement scatter are propagated by Monte Carlo sampling. The shelf life shown is the median time to reach the limit, the lower bound is the 5th percentile, and the probability of staying within the limit is given at the time points you choose. The random seed is fixed, so the same data and settings always give the same answer.

What it is for

Accelerated predictions support decisions such as formulation and packaging choice, setting an initial shelf life and planning studies. They do not replace real-time stability data; see ICH Q1A(R2) and Q1E.

References

• Waterman KC, Carella AJ, Gumkowski MJ, et al. Improved protocol and data analysis for accelerated shelf-life estimation of solid dosage forms. Pharm Res 2007;24:780–790.
• Waterman KC. The application of the Accelerated Stability Assessment Program (ASAP) to quality by design (QbD) for drug product stability. AAPS PharmSciTech 2011;12:932–937.
• ICH Q1A(R2) Stability testing of new drug substances and products; ICH Q1E Evaluation of stability data.