Testing the Fit of Regression Models Estimated with Extremely Small Samples: Application in Pharmaceutical Stability Studies

Pharmaceutical stability studies are conducted to estimate the shelf life, i.e. the period during which the drug product maintains its identity and stability. In the evaluation of process, regression curve is fitted on the data obtained during the study and the shelf life is determined using the fitted curve. The evaluation process suggested by ICH considers only the case of the true relationship between the measured attribute and time being linear. However, no method is suggested for the practitioner to decide if the linear model is appropriate for their dataset. This is a major problem, as a falsely selected model may distort the estimated shelf life to a great extent, resulting in unreliable quality control. The difficulty of model misspecification detection in stability studies is that very few observations are available. The conventional methods applied for model verification might not be appropriate or efficient due to the small sample size. In this paper, this problem is addressed and some developed methods are proposed to detect model misspecification. The methods can be applied for any process where the regression estimation is performed on independent small samples. Besides stability studies, frequently performed construction of single calibration curves for an analytical measurement is another case where the methods may be applied. It is shown that our methods are statistically appropriate and some of them have high efficiency in the detection of model misspecification when applied in simulated situations which resemble pre-approval and post-approval stability studies.