Didier Mathieu

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

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.

Optimisation of the chemical generation of singlet oxygen (1O2, 1Δg) from the hydrogen peroxide–lanthanum(III) catalytic system using an improved NIR spectrometer

A near-IR chemiluminescence spectrometer designed to study chemical sources of singlet oxygen ((1)O(2), (1)Delta(g)), was built by coupling a reactor compartment to a nitrogen-cooled Ge diode through a bundle of optical fibres. This device was used to optimise the generation of (1)O(2) from the hydrogen peroxide-lanthanum(iii) catalytic system. The reaction kinetics were studied with a 2(3)3(3)//12 screening experimental design comprising twelve experiments. The influence of six factors was examined: the nature of the lanthanum salt (hydroxide, oxide or nitrate) and its concentration (0.05 or 0.1 mol L(-1)), the pH value (5, 7 or 9), the concentration of H(2)O(2) (0.5, 1 or 2 mol L(-1)), the temperature (20 or 30 degrees C) and the concentration of EDTA (0 or 5 mmol L(-1)). Two responses were measured: the rate of H(2)O(2) disproportionation and the intensity of the luminescence of (1)O(2) at 1270 nm. The essential factor is the nature of the lanthanum salt since La(NO(3))(3) induces the disproportionation of H(2)O(2) about 60 x faster than La(2)O(3) or La(OH)(3). Other influencing factors are the pH value, the concentration of H(2)O(2), the temperature and the concentration of the lanthanum salt whereas the concentration of EDTA has no effect on the reaction. The catalytic activity of La(NO(3))(3) was then investigated in further detail by studying the influence of two factors (pH and [H(2)O(2)]) thanks to a Doehlert design.

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.