Definitive Screening Designs Research Articles

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.

New approaches on composite designs for Response Surface Methodology.

Recent attention has increasingly focused on the significance of Definitive Screening Designs (DSDs), originally introduced by Jones and Nachtsheim (2011), as a compelling alternative to traditional designs bib Response Surface Methodology (RSM). This paper introduces two novel composite techniques aimed at enhancing design efficiency and elevating D-values. By utilizing orthogonal matrices and integrating axial components from either simple orthogonal designs or the block orthogonal designs detailed in the work of Alrweili et al. (2020), new design matrices are constructed based on established composite design principles. Notably, the novel designs presented in this manuscript surpass previously documented designs in the existing literature in terms of design efficiency and robustness.

Custom and definitive screening designs for evaluating multiple adsorbents: bisphenol-A adsorption onto villi-structured polyaniline/carboxymethyl cellulose composites

ABSTRACT Polyaniline composites consisting of carboxymethyl cellulose (CMC) have enhanced adsorption properties, but recent studies indicate that the oxidised species – dialdehyde carboxymethyl cellulose (DCMC) – outperforms CMC-based composites. However, these studies fail to study the effect of DCMC's aldehyde content and compare the composites with CMC-based composites; numerous experiments required to investigate each adsorbent for each factor limit such studies. We explored a way to study whether villi-structured polyaniline (VSPANI), its CMC composite (CMC/PANI), and its DCMC composites with 35% (DCMC(A)/PANI) and 77% (DCMC(B)/PANI) aldehyde content would be great adsorbents for removing bisphenol-A (BPA). We first customised a D-optimal screening design to alleviate the pitfalls of definitive screening design (DSD), hence estimating all the main effects: initial concentration, pH, flow rate, adsorbent amount, sample volume and type of adsorbent. We excluded CMC/PANI and DCMC(A)/PANI composites, both with low adsorption capacities of 56.57 and 57.27 mg/g from further investigation. The DSD followed to estimate all second-order effects through which we projected a response surface method (RSM) to optimise and model the active factors. Increasing the aldehyde content on the composites favoured adsorption, but there lacked evidence to suggest VSPANI and DCMC(B)/PANI differed significantly in performance. The models were numerically and graphically proven adequate, explaining 80% and 99% of the variation when predicting removal efficiency and adsorption capacity. VSPANI showed potential as an adsorbent for BPA removal with 85% removal efficiency and 129 mg/g adsorption capacity. This comprehensive approach, combining both designs, allows for sustainable investigation of multiple adsorbents and factors, minimising experimental waste.

RNA crystal improvement with definitive screening designs

RNA crystal improvement with definitive screening designs

Exogenous Auxin and Gibberellin on Fluoride Phytoremediation by Eichhornia crassipes.

High rates of fluorosis were reported worldwide as a result of human consumption of water with fluoride contents. Adjusting fluoride concentration in water as recommended by the World Health Organization (<1.5 mg L-1) is a concern and it needs to be conducted through inexpensive, but efficient techniques, such as phytoremediation. The application of phytohormones was investigated as a strategy to improve this process. Thus, the main goal of this research was to evaluate the effect of exogenous auxin and gibberellin on the tropical duckweed Eichhornia crassipes performance for fluoride phytoremediation. Definitive screening and central composite rotatable designs were used for experiments where fluoride concentration (5~15 mg L-1), phosphorus concentration (1~10 mg L-1), and pH (5~9) were assessed as well throughout 10 days. Fluoride contents were determined in solution and plant tissues by potentiometry. Higher concentrations of fluoride reflected on greater absorptions by plants, though in relative terms removal efficiencies were quite similar for all treatments (~60%). Auxin and acidic conditions favored fluoride removals per mass of plant. Fluoride accumulated mostly in leaves and auxin probably alleviated toxic effects on E. crassipes while gibberellin showed no effect. Therefore, E. crassipes could be employed as a fluoride accumulator plant for water treatment and exogenous auxin may be used to improve the process.

Blocking OMARS designs and definitive screening designs

The family of orthogonal minimally aliased response surface or OMARS designs comprises traditional response surface designs, such as central composite designs and Box-Behnken designs, as well as definitive screening designs. Key features of OMARS designs are the facts that they are orthogonal for the main effects and that the main effects are not at all aliased with any two-factor interaction effect or with any quadratic effect. In this article, we present a method to arrange the runs of an OMARS design in blocks of equal size, so that the main effects can be estimated independently from the blocks, and the interaction effects and the quadratic effects are confounded as little as possible with the blocks. We show that our new method for blocking OMARS designs offers much flexibility when it comes to choosing the number of runs, the number of blocks and the block sizes, and that it often outperforms the blocking arrangements of definitive screening designs available in the literature and in commercial software.

Definitive Screening Designs to Optimize Library-Free DIA-MS Identification and Quantification of Neuropeptides.

Method optimization is crucial for successful mass spectrometry (MS) analysis. However, extensive method assessments, altering various parameters individually, are rarely performed due to practical limitations regarding time and sample quantity. To maximize sample space for optimization while maintaining reasonable instrumentation requirements, a definitive screening design (DSD) is leveraged for systematic optimization of data-independent acquisition (DIA) parameters to maximize crustacean neuropeptide identifications. While DSDs require several injections, a library-free methodology enables surrogate sample usage for comprehensive optimization of MS parameters to assess biomolecules from limited samples. We identified several parameters contributing significant first- or second-order effects to method performance, and the DSD model predicted ideal values to implement. These increased reproducibility and detection capabilities enabled the identification of 461 peptides, compared to 375 and 262 peptides identified through data-dependent acquisition (DDA) and a published DIA method for crustacean neuropeptides, respectively. Herein, we demonstrate a DSD optimization workflow, using standard material, not reliant on spectral libraries for the analysis of any low abundance molecules from previous samples of limited availability. This extends the DIA method to low abundance isoforms dysregulated or only detectable in disease samples, thus improving characterization of previously inaccessible biomolecules, such as neuropeptides. Data are available via ProteomeXchange with identifier PXD038520.

Analysis of data from orthogonal minimally aliased response surface designs

Experimental data are often highly structured due to the use of experimental designs. This does not only simplify the analysis, but it allows for tailored methods of analysis that extract more information from the data than generic methods. One group of three-level experimental designs that are suitable for such tailored methods are orthogonal minimally aliased response surface (OMARS) designs (Núñez Ares and Goos 2020), where all main effects are orthogonal to each other and to all second-order effects. The design based analysis method of Jones and Nachtsheim (2017) has shown significant improvement over existing methods in terms of powers to detect active effects. However, the application of their method is limited to only a small subgroup of OMARS designs known as definitive screening designs (DSDs). In our work, we not only improve upon the Jones and Nachtsheim method for DSDs, but we also generalize their analysis framework to the entire family of OMARS designs. Using extensive simulations, we show that our customized method for analyzing data from OMARS designs is highly effective in identifying active effects when compared to other modern (non-design based) analysis methods, especially in cases where the true model is complex and involves many second-order effects.

Systematic enumeration of definitive screening designs

Systematic enumeration of definitive screening designs

Holistic Design of Experiments Using an Integrated Process Model.

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 &gt;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.

Augmenting definitive screening designs: Going outside the box

Definitive screening designs (DSDs) have grown rapidly in popularity since their introduction by Jones and Nachtsheim (2011). Their appeal is that the second-order response surface (RS) model can be estimated in any subset of three factors, without having to perform a follow-up experiment. However, their usefulness as a one-step RS modeling strategy depends heavily on the sparsity of second-order effects and the dominance of first-order terms over pure quadratic terms. To address these limitations, we show how viewing a projection of the design region as spherical and augmenting the DSD with axial points in factors found to involve second-order effects remedies the deficiencies of a stand-alone DSD. We show that augmentation with a second design consisting of axial points is often the D s -optimal augmentation, as well as minimizing the average prediction variance. Supplemented by this strategy, DSDs are highly effective initial screening designs that support estimation of the second-order RS model in three or four factors.

Photocatalytic Degradation of Orange G Dye by Using Bismuth Molybdate: Photocatalysis Optimization and Modeling via Definitive Screening Designs.

In the current study, Bismuth molybdate was synthesized using simple co-precipitation procedure, and their characterization was carried out by various methods such as FT-IR, SEM, and P-XRD. Furthermore, the photocatalytic degradation of Orange G (ORG) dye using synthesized catalyst under visible light irradiation was studied. Response surface Method was used for the optimization of process variables and degradation kinetics evaluated by modeling of experimental data. Based on the experimental design outcomes, the first-order model was proven as a practical correlation between selected factors and response. Further ANOVA analysis has revealed that only two out of six factors have a significant effect on ORG degradation, however ORG concentration and irradiation time indicated the significant effects sequentially. Maximum ORG degradation of approximately 96% was achieved by keeping process parameters in range, such as 1 g L−1 loading of catalyst, 50 mg L−1 concentration of ORG, 1.4 mol L−1 concentration of H2O2 at pH 7 and a temperature of 30 °C. Kinetics of ORG degradation followed the pseudo first order, and almost complete degradation was achieved within 8 h. The effectiveness of the Bi2MoO6/H2O2 photo-Fenton system in degradation reactions is due to the higher number of photo-generated e- available on the catalyst surface as a result of their ability to inhibit recombination of e- and h+ pair.

Self-validated ensemble models for design of experiments

One of the possible objectives when designing experiments is to build or formulate a model for predicting future observations. When the primary objective is prediction, some typical approaches in the planning phase are to use well-established small-sample experimental designs in the design phase (e.g., Definitive Screening Designs) and to construct predictive models using widely used model selection algorithms such as LASSO. These design and analytic strategies, however, do not guarantee high prediction performance, partly due to the small sample sizes that prevent partitioning the data into training and validation sets, a strategy that is commonly used in machine learning models to improve out-of-sample prediction. In this work, we propose a novel framework for building high-performance predictive models from experimental data that capitalizes on the advantage of having both training and validation sets. However, instead of partitioning the data into two mutually exclusive subsets, we propose a weighting scheme based on the fractional random weight bootstrap that emulates data partitioning by assigning anti-correlated training and validation weights to each observation. The proposed methodology, called Self-Validated Ensemble Modeling (SVEM), proceeds in the spirit of bagging so that it iterates through bootstraps of anti-correlated weights and fitted models, with the final SVEM model being the average of the bootstrapped models. We investigate the performance of the SVEM algorithm with several model-building approaches such as stepwise regression, Lasso, and the Dantzig selector. Finally, through simulation and case studies, we show that SVEM generally generates models with better prediction performance in comparison to one-shot model selection approaches.

On definitive screening designs using Paley’s conference matrices

Definitive screening designs (DSDs) are widely used for studying quantitative factors. However, DSDs constructed from different conference matrices are not equally good. We show DSDs using Paley’s conference matrices guarantee desirable performance (either optimal or near-optimal) under several important criteria.

Three-level designs under second order models

In this paper, the properties of three-level screening designs are studied. A variety of designs are included, such as the definitive screening designs and designs from weighing matrices. These are compared with designs with 13 to 18 runs from Tsai et al., Schoen, Evangelaras et al. and Núñez Ares and Goos. Where possible, new designs were generated with four to six factors by studying and selecting the corresponding projections as needed. Based on the weight given on the model terms, the designs are evaluated, and their performance is presented in tables.

An integrative framework for geometric and hidden projections in three-level fractional factorial designs

Geometric and hidden projection are two important properties to consider for three-level fractional factorials. The effective development of methods that can address tasks involving both these properties requires a unified design framework that integrates them. We highlight one integrative framework that is based on indicator functions for three-level designs under the linear-quadratic parameterization system. We demonstrate the broad scope and utility of this framework by using it to develop a new procedure for addressing a task comprised of three serial problems in geometric and hidden projection. The first in the series is to construct the sets of smallest follow-up runs to a projection of a three-level design that yield specified aliasing relations. Second is to immediately characterize the partial aliasing relations among factorial effects in the resulting augmented designs. The final problem is to identify the augmented designs that maximize popular optimality criteria with respect to the second-order model among all of the candidate augmentations. The application of our procedure is illustrated with sample projections of definitive screening designs onto four, five, and six factors. The integrative framework that we present can ultimately facilitate the systematic development of methods that advance comprehensive understanding of multiple properties for general three-level designs.

Performance of displaced fin heatsink in natural convection subject to upward and downward arrangement

In this study, a heat sink with a displaced fin arrangement is proposed to enhance the thermal performance in natural convection. To demonstrate the competence of the proposed heat sink design, an experimental investigation was carried out for the upward and downward configurations for the heat flux range of 30–470 Wm-2. The experimental results suggest that the proposed heat sink with the fin displacement distance of 20 mm can reduce the total thermal resistance by 11% and 14% for the upward and downward configurations, respectively. The parametric study was conducted with the Definitive Screening Designs (DSDs) method, and it suggested thirteen optimized test conditions. The outcome of the parametric study implies that the fin spacing plays a vital role in determining the heat sink performance, followed by the fin height and fin length; and the effect of heat flux is insignificant. For the thirteen test conditions suggested by the DSDs method, the numerical investigation was conducted. The numerical results show that for the same volume, when compared to the regular rectangular heat sink the proposed heat sink can provide an 11% performance enhancement with a 28.7% reduction in mass.

Projection properties of three‐level screening designs

SummaryScreening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three‐level rather than two‐level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, Journal of Quality Technology43, 1–15, proposed a new class of designs called definitive screening designs. Definitive screening designs have more favourable properties than classical screening designs. In this paper, we study the projection properties of three‐level screening designs. The comparison is based on several criteria such as D‐efficiency, G‐efficiency, A‐efficiency and average of variance over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller factor dimensional space. The best projections and their properties are presented in a tabular form.

An addendum on “Three‐level designs: Evaluation and comparison for screening purposes”

AbstractIn our recent paper “Three‐Level Designs: Evaluation and Comparison for Screening Purposes”, by the same authors, we investigated and compared the original definitive screening designs and the designs that were constructed from weighing matrices. For this purpose, we used the generalized resolution and minimum aberration criteria as well as the projection estimation capacity criterion from the literature to perform the comparison. After our paper was accepted, it came to our attention that there were four significant papers, published by a number of authors, having related content and these were not mentioned in our paper. With this short addendum, we would like to kindly acknowledge the important contributions from those authors in those newly discovered papers in recent literature and also to include them in the related reference list.

An application of definitive screening designs (DSDs) to a food product optimization and adaptations to jones & nachtsheim methodology for fitting DSD models

This paper describes a practical application of a DSD – Definitive Screening Design, in which its powerful properties were used to successfully obtain optimized cost while maintaining Overall Liking scores of a food product with a single screening experiment with six (6) ingredients, as allowed by DSDs projectivity property. The algorithm for model fitting, recently introduced by the creators of DSD, Jones & Nachtsheim, was adapted for a higher flexibility in considering researcher’s previous knowledge. Simulation work is conducted to evaluate such adaptations in a broader range of scenarios.