Objective: Random effects are often neglected when defining the control strategy for a biopharmaceutical process. In this article, we present a case study that highlights the importance of considering the variance introduced by random effects in the calculation of proven acceptable ranges (PAR), which form the basis of the control strategy. Methods: Linear mixed models were used to model relations between process parameters and critical quality attributes in a set of unit operations that comprises a typical biopharmaceutical manufacturing process. Fitting such models yields estimates of fixed and random effect sizes as well as random and residual variance components. To form PARs, tolerance intervals specific to mixed models were applied that incorporate the random effect contribution to variance. Results: We compared standardized fixed and random effect sizes for each unit operation and CQA. The results show that the investigated random effect is not only significant but in some unit operations even larger than the average fixed effect. A comparison between ordinary least squares and mixed models tolerance intervals shows that neglecting the contribution of the random effect can result in PARs that are too optimistic. Conclusions: Uncontrollable effects such as week-to-week variability play a major role in process variability and can be modelled as a random effect. Following a workflow such as the one suggested in this article, random effects can be incorporated into a statistically sound control strategy, leading to lowered out of specification results and reduced patient risk.

Global gridded crop models (GGCMs) are simulation tools designed for global, spatially explicit estimation of crop productivity and associated externalities. Key areas for their application are climate impact and adaptation studies. As GGCMs are typically computationally costly and require comprehensive data pre- and post-processing, GGCM emulators are gaining increasing popularity. Earlier emulators have typically been published pre-trained on synthetic weather and management combinations. Here, we present a novel computational pipeline CROp Model Emulator Suite (CROMES) v1.0 that serves for flexibly training GGCM emulators on data commonly available from GGCM simulations. Essentially, CROMES consists of modules to (1) process climate data from daily resolution netCDF files to (sub-)growing season aggregates as climate features, (2) combine various feature types (climate, soil, crop management), (3) train emulators using machine-learning algorithms, and (4) produce predictions. Exemplary, we apply CROMES to train emulators on simulations for rainfed maize from the GGCM EPIC-IIASA and climate projections from a single GCM to subsequently test their skill in predicting crop yields for unseen climate projections from other GCMs. Depending on the training and target data, the regression statistics between GGCM simulations and predictions across all points in time and space are in the ranges R² = 0.97 to 0.98, slope = 0.99 to 1.01, and intercept = −0.06 to +0.06. The RMSE ranges between 0.49 and 0.65 t ha⁻¹. Spatially, patterns are evident with lowest performance in (semi-)arid regions where aggregation of weather data may result in higher information loss while permanent crop growth limitations may hamper evaluation statistics as well. The gain in computational speed for predictions is at more than an order of magnitude with time required to produce target features and subsequent predictions at about 30min on common hardware. We expect CROMES to be of utility in covering more comprehensively uncertainty in climate impact projections, evaluations of adaptation options, and spatio-temporal assessments of crop productivity.

Statistical experimental designs such as factorial, optimal, or definitive screening designs represent the state of the art in biopharmaceutical process characterization. However, such methods alone do not leverage the fact that processes operate as a mutual interplay of multiple steps. Instead, they aim to investigate only one process step at a time. Here, we want to develop a new experimental design method that seeks to gain information about final product quality, placing the right type of run at the right unit operation. This is done by minimizing the simulated out-of-specification rate of an integrated process model comprised of a chain of regression models that map process parameters to critical quality attributes for each unit operation. Unit operation models are connected by passing their response to the next unit operation model as a load parameter, as is done in real-world manufacturing processes. The proposed holistic DoE (hDoE) method is benchmarked against standard process characterization approaches in a set of in silico simulation studies where data are generated by different ground truth processes to illustrate the validity over a range of scenarios. Results show that the hDoE approach leads to a >50% decrease in experiments, even for simple cases, and, at the same time, achieves the main goal of process development, validation, and manufacturing to consistently deliver product quality.

Global gridded crop models (GGCMs) are simulation tools designed for global, spatially explicit estimation of crop productivity and associated externalities. Key areas for their application are climate impact and adaptation studies. As GGCMs are typically computationally costly and require comprehensive data pre- and post-processing, GGCM emulators are gaining increasing popularity. Earlier emulators have typically been published pre-trained on synthetic weather and management combinations. Here, we present a novel computational pipeline CROp Model Emulator Suite (CROMES) v1.0 that serves for flexibly training GGCM emulators on data commonly available from GGCM simulations. Essentially, CROMES consists of modules to (1) process climate data from daily resolution netCDF files to (sub-)growing season aggregates as climate features, (2) combine various feature types (climate, soil, crop management), (3) train emulators using machine-learning algorithms, and (4) produce predictions. Exemplary, we apply CROMES to train emulators on simulations for rainfed maize from the GGCM EPIC-IIASA and climate projections from a single GCM to subsequently test their skill in predicting crop yields for unseen climate projections from other GCMs. Depending on the training and target data, the regression statistics between GGCM simulations and predictions across all points in time and space are in the ranges R2=0.97 to 0.98, slope=0.99 to 1.01, and intercept=-0.06 to +0.06. The RMSE ranges between 0.49 and 0.65 t ha^-1. Spatially, patterns are evident with lowest performance in (semi-)arid regions where aggregation of weather data may result in higher information loss while permanent crop growth limitations may hamper evaluation statistics as well. The gain in computational speed for predictions is at more than an order of magnitude with time required to produce target features and subsequent predictions at about 30min on common hardware. We expect CROMES to be of utility in covering more comprehensively uncertainty in climate impact projections, evaluations of adaptation options, and spatio-temporal assessments of crop productivity.