Roger Phan-Tan-Luu

Pharmaceutical Experimental Design

OverviewScreeningFactor Influence StudiesStatistical and Mathematical ToolsResponse Surface MethodologyOptimizationVariability and QualityExchange AlgorithmsMixturesMixtures in a Constrained Region of InterestAppendix I. A Summary of Matrix AlgebraAppendix II. Experimental Designs and Models for ScreeningAppendix III. Designs for Response Surface ModelingAppendix IV. Choice of Computer SoftwareAppendix V. Symbols

Genetic algorithm as a tool for selection of D-optimal design

Abstract Asymmetrical designs are now widely used in the industrial world. However, the traditional methods to construct them are very poor and difficult to handle. To construct experimental design in ‘non-standard’ occurrences, algorithmic methods, such as Fedorovs or Mitchells algorithms, are broadly used. But in case of high dimensionality, this class of algorithms cannot be used. In this paper, a new technique based on the genetic algorithm for constructing experimental designs is described.

Mixture design applied to the formulation of hydrotropes for liquid detergents

Abstract In a previous study, we presented a new method for preparing a mixture of sodium toluenesulfonates (STS), sodium xylenesulfonates (SXS), sodium benzenesulfonate (SBS) and Na 2 SO 4 by sulfonating the BTX fraction of a Tunisian natural gas. Such mixtures can be used as a hydrotrope agent for concentrated liquid detergents. In the present work, we performed a mixture design in order to study the effect of each of these four components on the clear point and the viscosity of a liquid detergent, and therefore, to determine the conditions allowing to improve the effectiveness of the hydrotrope. Twenty-eight combinations of the 4 components out of 51 candidate points are selected by the Nemrod-W software according to the D-optimal criterion to fit two polynomial models. The statistical study shows that the fitted models were adequate to describe the clear point and the viscosity responses. Optimal conditions allowing to lower the two responses are then looking for by examining the response surface both as a contour plot, and as three-dimensional surface plot and the response trace. We prove that Na 2 SO 4 exhibits a harmful negative effect, while SXS and STS exhibit, respectively, a strong and moderate positive effect on both clear point and viscosity responses. As expected, SBS has a harmful effect on the two responses but the magnitude of this effect is lesser than that predicted by the preliminary experiments carried out with SBS alone. This phenomenon is explained by the formation of heteroassociation between SBS, STS and SXS similar to what is found in surfactants. The effectiveness of the hydrotrope, obtained by sulfonation of the BTX fraction of the Tunisian natural gas, is really improved by removing sulfates either by adding lime to precipitate gypsum, or isopropanol to reduce the solubility of Na 2 SO 4 .

Correct and incorrect use of multilinear regression

Abstract Multilinear regression is applied when experimenters wish to investigate the relationship between a block of predictor variables ( X ), whose values are fixed by the experimenter, and one or more responses ( Y ), measured at each experiment. The objective is to find a mathematical equation relating X and Y , by means of regression coefficients. Regression analysis is said to give good results when a squared multiple regression coefficient R 2 close to 1 is obtained and when the sum of squares of residuals (differences between experimental value of the response and computed value) is small. However, it must be noted that a bad choice of the experiments renders the obtained regression equation meaningless. In this paper an example of correct and incorrect use of multilinear regression is presented in detail the quality of the coefficients and the goodness of the prediction depend on the experimental design, and the value of R 2 gives no information at all about them. A set of criteria useful to judge the quality of an experimental plan, before carrying out any experiment, is proposed.

Experimental research methodology applied to the development of a formulation for use with textiles

Abstract Chardon, J., Nony, J., Sergent, M., Mathieu, D. and Phan-Tan-Luu, R., 1989. Experimental research methodology applied to the development of a formulation for use with textiles. Chemometrics and Intelligent Laboratory Systems, 6: 313-321. The development of a finishing product formula for polyester/cotton cloth for use as bed linen for the hotel trade required four criteria to be taken into consideration: the fabrics feel, hydrophilicity, wash and wear quality, and soil release after treatment. The finishing product formula was based on the use of a resin (and its catalyst) and from 1 to 3 fabric softeners. The problem lay in detertmining the nature of the fabric softeners and the relevant quantities of resin and softener needed to obtain the best characteristics. A two-phase experimental strategy was drawn up: one phase for the quantities of resin and softeners, and the other phase for the types of softeners used. The quantities phase was studied using a Doehlert experimental matrix and the softener type phase was assessed using a Scheffe simplex-centroid design for the three products. The experiments carried out allowed the definition of a zone of two phases in which the objectives were attained: two softeners were selected and the appropriate quantities of resin and softeners were determined.

Fractions of Rechtschaffner matrices as supersaturated designs in screening experiments aimed at evaluating main and two-factor interaction effects

Optimal fractions of resolution V design matrices proposed by Rechtschaffner in 1967 are developed and applied as supersaturated designs in screening experiments. Rechtschaffner matrices allow evaluation of all main factors and two-factor interactions, which in many real-world studies are of practical significance. However, the number of experimental runs increases rapidly with the number of factors in the matrices, which are therefore impractical for more than 5-6 factors. On the contrary, saturated fractions based on Hadamard matrices, which are commonly applied in screening studies, cannot evaluate the interaction effects. Here, a procedure for selecting the optimum fractions of Rechtschaffner matrices is presented and provides supersaturated matrices that are well adapted to a variety of problems, thus allowing the development of screening studies with a relatively small number of experiments. The procedures developed to derive the size-reduced matrices and to evaluate the active factors are discussed and compared in terms of efficiency and reliability, by means of simulation studies and application to a real problem. These fractions are the first supersaturated design matrices capable of estimating interaction effects. Additionally, one important advantage of these supersaturated matrices is that they enable development of follow-up procedures in cases of inconclusive results, by enlarging the matrix and eventually resolving the full Rechtschaffner matrix of departure when it is necessary to evaluate the active factors and their interactions.

Methodological Approach of the Experimental Research

Abstract Many preliminary studies contain a large number of potentially relevant factors, but often only a few are believed to have actual effects. To isolate influential factors ( screening ) in an efficient way, special experimental strategies are needed, such as the supersaturated designs or the techniques of group screenin. For investigating k factors, these supersatured designs are composed of n observations where n ≪ k + 1. They are useful in situations in which the number of active factors is very small compared to the total number of factors being considered; more specifically, in practice experiments with simulated systems.