Interpretation of high dimensional definitive screening designs assisted by bootstrapped partial least squares regression

Definitive screening design (DSD) has become a widely used type of Design of Experiments for chemical, pharmaceutical and biopharmaceutical processes and product development due to its optimization properties with an estimation of main, interaction, and squared variable effects with a minimum number of experiments. These high dimensional DOEs with more variables than samples, and with partly correlated variables, make the statistical interpretation frequently challenging. The purpose of the study was to test bootstrap PLSR using a heredity procedure to select the variable subset to be finally evaluated by MLR. The heredity selection was used on bootstrap T values given by original PLSR coefficients (B) divided on the bootstrap estimated standard deviation. The investigated fractional weighted and non-parametric bootstrap PLSR resulted in same variable selection outcome and final models in this study.

A simulation study with 7 main variables and 12 tested literature real data DSDs with 4, 5, 7 and 8 main variables showed improved model performance for small and particularly for large DSDs for the bootstrap PLSR MLR methods compared to two common DSD reference methods; DSD fit definitive screening and AICc forward stepwise regression (AICc FSR). Variable selection accuracy and predictive ability were significantly improved by the investigated method in 6 out of 13 DSDs compared to the best model from either of the two reference methods. The remaining 7 DSDs gave the same model as best reference model. Strong heredity was found to provide the best models for all real data in this study. The use of the heredity procedure on the percent non-zero SVEM FSR variable effects followed by MLR showed promising results. AICc Lasso regression was among other methods partially tested and was found to set almost all variables to zero effect when tested on three large minimum DSDs. While the DSD fit definitive screening method may often be the first choice for DSD, the heredity bootstrap PLSR MLR and heredity SVEM FSR MLR may be alternative methods to improve the variable selection and model precision.