Regression control chart with unknown parameters for detection of out-of-trend results in pharmaceutical on-going stability studies

Abstract The main purpose of on-going stability studies in pharmaceutical industry is to test whether the regulatory requirement regarding the shelf-life is fulfilled when the drug is already produced for patients. That is, the estimated shelf-life of the products agrees with the shelf-life claimed during the registration of the drug. The monitored process is the change in certain attributes (e.g. pH) of the drug products over time and the estimated shelf-life for a given batch is determined based on the results of the monitoring. Out–of-trend (OOT) data points in stability study, distorts the estimated trend which results in distorted estimation of shelf-life. Undetected OOT points could lead to overestimated shelf-life which may results in drug products with non-acceptable quality, continuously distributed to patients. In this paper, the regression control chart method is adapted for pharmaceutical stability studies to detect OOT points within stability studies. The challenge is that the sample size is small. Usually in a study the number of data collected is limited to 8-10 points. The parameters (true regression line and residual variance) of the process cannot be taken as known and the uncertainty of the estimated parameters is rather large. Therefore, the generally used regression control chart that utilizes the Shewhart method in which the parameters are known, may not be used. The proposed method in this paper takes the uncertainty of the parameters into account. Also adaptations of the proposed method for different ANCOVA models – such as a) every batch has the same true intercept and slope, b) every batch has the same slope but the intercepts differ, c) batches have different intercepts and slopes as well – are presented. When the proposed method employs the information obtained from the ANCOVA test, the statistical power of OOT detection is increased, i.e. the OOT detection is more effective.