Pharmaceutical Experimental Design and Interpretation, Second Edition

by Armstrong; N. Anthony

• ISBN13: 9780415299015
• ISBN10: 0415299012
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-01-20
• Publisher: CRC Press

Summary

Completely revised and updated, Pharmaceutical Experimental Design and Interpretation, Second Edition explains the major methods of experimental design and evaluation such as multivariate, sequential, and principal components analysis. With new sections on neural networks, artificial intelligence, fractional designs, and optimization techniques, this source will prove invaluable to anyone involved in the design and execution of pharmaceutical research studies and the interpretation of study data.

Author Biography

N. Anthony Armstrong is Senior Lecturer in Pharmaceutics, Welsh School of Pharmacy, University of Wales, United Kingdom

Table of Contents

Chapter 1 Introduction to Experimental Design
1.1 The Experimental Process	1	(1)
1.2 Computers and Experimental Design	2	(2)
1.3 Overview of Experimental Design and Interpretation	4	(5)
Chapter 2 Comparison of Mean Values
2.1 Introduction	9	(1)
2.2 Comparison of Means when the Variance of the Whole Population is Known	10	(2)
2.3 Comparison of Two Means when the Variance of the Whole Population is Not Known	12	(6)
2.3.1 Treatment of Outlying Data Points	15	(3)
2.4 Comparison of Means between More Than Two Groups of Data	18	(7)
2.4.1 Analysis of Variance (ANOVA)	19	(2)
2.4.2 The Least Significant Difference	21	(1)
2.4.3 Two-Way Analysis of Variance	22	(3)
Chapter 3 Nonparametric Methods
3.1 Introduction	25	(1)
3.2 Nonparametric Tests for Paired Data	25	(4)
3.2.1 The Sign Test	25	(2)
3.2.2 The Wilcoxon Signed Rank Test	27	(2)
3.3 Nonparametric Tests for Unpaired Data	29	(4)
3.3.1 The Wilcoxon Two-Sample Test	29	(4)
Chapter 4 Regression and Correlation
4.1 Introduction	33	(1)
4.2 Linear Regression	33	(8)
4.2.1 The Number of Degrees of Freedom (Cell B11 in Table 4.4)	37	(1)
4.2.2 The Coefficient of Determination (r²) (Cell A10 in Table 4.4)	38	(2)
4.2.3 The Standard Errors of the Coefficients (Cells A9 and B9 in Table 4.4)	40	(1)
4.2.4 The F Value or Variance Ratio (Cell All in Table 4.4)	40	(1)
4.2.5 The Two Regression Lines	41	(1)
4.3 Curve Fitting of Nonlinear Relationships	41	(3)
4.3.1 The Power Series	42	(1)
4.3.2 Quadratic Relationships	42	(1)
4.3.3 Cubic Equations	43	(1)
4.3.4 Transformations	44	(1)
4.4 Multiple Regression Analysis	44	(4)
4.4.1 Correlation Coefficients	47	(1)
4.4.2 Standard Error of the Coefficients and the Intercept	48	(1)
4.4.3 F Value	48	(1)
4.5 Interaction between Independent Variables	48	(1)
4.6 Stepwise Regression	49	(1)
4.7 Rank Correlation	50	(2)
4.8 Comments on the Correlation Coefficient	52	(3)
Chapter 5 Multivariate Methods
5.1 Introduction	55	(1)
5.2 Multivariate Distances	55	(4)
5.2.1 Distance Matrices	55	(4)
5.3 Covariance Matrices	59	(3)
5.4 Correlation Matrices	62	(1)
5.5 Cluster Analysis	63	(4)
5.5.1 Cartesian Plots	63	(2)
5.5.2 Dendrograms	65	(2)
5.6 Discrimination Analysis	67	(3)
5.7 Principal Components Analysis	70	(5)
5.8 Factor Analysis	75	(8)
Chapter 6 Factorial Design of Experiments
6.1 Introduction	83	(1)
6.2 Two-Factor, Two-Level Factorial Designs	84	(5)
6.2.1 Two-Factor, Two-Level Factorial Designs with Interaction between the Factors	86	(3)
6.3 Notation in Factorially Designed Experiments	89	(2)
6.4 Factorial Designs with Three Factors and Two Levels	91	(3)
6.5 Factorial Design and Analysis of Variance	94	(6)
6.5.1 Yates's Treatment	95	(3)
6.5.2 Factorial Design and Linear Regression	98	(2)
6.6 Replication in Factorial Designs	100	(3)
6.7 The Sequence of Experiments	103	(1)
6.8 Factorial Designs with Three Levels	104	(6)
6.9 Three-Factor, Three-Level Factorial Designs	110	(5)
6.9.1 Mixed or Asymmetric Designs	114	(1)
6.10 Blocked Factorial Designs	115	(3)
6.11 Fractional Factorial Designs	118	(3)
6.12 Plackett–Burman Designs	121	(1)
6.13 Central Composite Designs	122	(4)
6.14 Box–Behnken Designs	126	(1)
6.15 Doehlert Designs	127	(2)
6.16 The Efficiency of Experimental Designs	129	(6)
Chapter 7 Response-Surface Methodology
7.1 Introduction	135	(1)
7.2 Constraints, Boundaries, and the Experimental Domain	136	(1)
7.3 Response Surfaces Generated from First-Order Models	137	(6)
7.4 Response Surfaces Generated by Models of a Higher Order	143	(7)
7.5 Response-Surface Methodology with Three or More Factors	150	(7)
Chapter 8 Model-Dependent Optimization
8.1 Introduction	157	(1)
8.2 Model-Dependent Optimization	158	(5)
8.2.1 Extension of the Design Space	161	(2)
8.3 Optimization by Combining Contour Plots	163	(2)
8.4 Location of the Optimum of Multiple Responses by the Desirability Function	165	(3)
8.5 Optimization Using Pareto-Optimality	168	(5)
Chapter 9 Sequential Methods and Model-Independent Optimization
9.1 Introduction	173	(1)
9.2 Sequential Analysis	173	(4)
9.2.1 Wald Diagrams	173	(4)
9.3 Model-Independent Optimization	177	(7)
9.3.1 Optimization by Simplex Search	177	(7)
9.4 Comparison of Model-Independent and Model-Dependent Methods	184	(5)
Chapter 10 Experimental Designs for Mixtures
10.1 Introduction	189	(1)
10.2 Three-Component Systems and Ternary Diagrams	190	(3)
10.3 Mixtures with More Than Three Components	193	(2)
10.4 Response-Surface Methodology in Experiments with Mixtures	195	(7)
10.4.1 Rectilinear Relationships between Composition and Response	195	(2)
10.4.2 Derivation of Contour Plots from Rectilinear Models	197	(1)
10.4.3 Higher-Order Relationships between Composition and Response	198	(2)
10.4.4 Contour Plots Derived from Higher-Order Equations	200	(2)
10.5 The Optimization of Mixtures	202	(1)
10.6 Pareto-Optimality and Mixtures	203	(2)
10.7 Process Variables in Mixture Experiments	205	(4)
Chapter 11 Artificial Neural Networks and Experimental Design
11.1 Introduction	209	(10)
11.1.1 Pharmaceutical Applications of ANNs	212	(7)
Appendix 1 Statistical Tables
A1.1 The Cumulative Normal Distribution (Gaussian Distribution)	219	(1)
A1.2 Student's t Distribution	219	(2)
A1.3 Analysis of Variance	221	(2)
Appendix 2 Matrices
A2.1 Introduction	223	(2)
A2.2 Addition and Subtraction of Matrices	225	(1)
A2.3 Multiplication of Matrices	226	(3)
A2.3.1 Multiplying a Matrix by a Constant	226	(1)
A2.3.2 Multiplication of One Matrix by Another	226	(1)
A2.3.3 Multiplication by a Unit Matrix	227	(1)
A2.3.4 Multiplication by a Null Matrix	228	(1)
A2.3.5 Transposition of Matrices	228	(1)
A2.3.6 Inversion of Matrices	229	(1)
A2.4 Determinants	229	(4)
Index	233