Experiences in Batch Trajectory Alignment for Pharmaceutical Process Improvement through Multivariate Latent Variable Modelling

In multivariate analysis of batch data, the step known as trajectory alignment (or synchronization) is not solely intended to homogenize the number of samples across batch data. Its primary objective is to standardize the data according to the evolution of the process, irrespective of the number of samples per run. The use of an indicator variable performs both objectives well. Two examples from the pharmaceutical sector are discussed to illustrate the different ways to deal with uneven samples across batches and across variables in the same batch (multi-rate data). Since trajectory alignment is not necessarily trivial, a simple approach based on the covariance matrix of the scores from a variable-wise unfolded data set is used to assess the need to analyze the dynamics of a given process (and hence perform alignment). The presented examples are representative of a broad variety of batch processes that are operated by recipe in the pharmaceutical sector. In our experience, the variables associated with the automation triggers in these recipes are the best indicator variables to use since the resulting alignment scheme can be performed in real-time for monitoring applications.