Modeling and Data Treatment in the Pharmaceutical Sciences by J. T. Carstensen, PhD

Professional Pharmaceutical Book from C.H.I.P.S.

Modeling and Data Treatment in the Pharmaceutical Sciences

by J. T. Carstensen, PhD

The ultimate aim of the book is the ability to use data to model a situation, a phenomenon, or a process and to logically decide on further experimentation.

Modeling and Data Treatment in the Pharmaceutical Sciences concentrates on how to derive a model from existing data, how to plan further to shore up the model and what statistical, mathematical and programming data is associated with it. The emphasis is on modeling, the application of correct statistics and on common errors in published material. The procedures for modeling are outlined.

Features:

Practical guide to modeling in pharmaceutical experimentation
How to derive a model from existing data and apply correct statistics in analyzing situations, phenomena and processes
Valuable resource for preformulation, product development, process improvement, clinical evaluation, and regulatory affairs
Useful reference information provided in extensive tables, graphs and figures

Contents

Purposes of Pharmaceutical Research
- Literature Searches
- Research Motivation
- Levels of Modeling
- Hypothetical Models
- Strict Modeling
- Pseudo-Modeling
- Curve-Fitting
- One Point Modeling
- References
The Single Experiment
- Data in Tables
- Correlation
- Formula Considerations
- Specifications
Representation of Numbers and Data
- Tabular Presentations
- Means
- The Dispersion
- Measures of Dispersion
- Degrees of Freedom
- Special Cases of Standard Deviation
- Populations and Samples
- The Pooled Standard Deviation
- Problems (Chapter 3)
- Answers (Chapter 3)
Computer Programs
- Data Generation from Equations; Basic
- Statworks™
- Sigmaplot®
- Graphical Program (Cricket\Graph TM)
Curve-Fitting and Phenomenology
- Curve-Fitting of Continuous Curves
- Curve-Fitting
- Curve-Fitting by Computer Graphing Programs
- Domains
- Selection of Ordinate and Abscissa
- Common Considerations
- General Curve Forms
- Second Order Curve, First Order Curve with Equilibrium
- The Sigma-Minus Plot
- The Logarithmic Plot
- Polynomial Plots
- Inverse Plots
- Deduction and Curve-Fitting
- Are the Data Monophasic or Biphasic?
- Curve-Fitting the Normalized Frequency Function
- Probability Plots
- Weibull Plotting
- References
- Problems (Chapter 5)
- Answers (Chapter 5)
Normalized Frequency Distributions
- Histograms
- Making Frequency Distributions Comparable
- Normal (Gaussian) Distribution
- Probability Calculations from the Normal Distribution
- Construction of Probability Paper
- Calculation of Probabilities
- Statistical Moments
Other Distributions
- Populations
- The χ²-Distribution, Confidence Intervals
- Outliers
- The Square Distribution. Random Numbers
- The Student t-Distribution
- Confidence Limits
- The Binomial Distribution
- Problems (Chapter 7)
- Answers (Chapter 7)
Significance Testing
- Null Hypothesis
- Testing by Comparing Variances
- The F-Test
- Factorials
- Differences between Estimates of S The Unpaired t-Test. Samples at Hand Only Source of Variance
- Checking the Meaning of Parameters in Programs. Program Validation
- Unequal Variances
- Paired t-Test
- χ²-Test; Contingency Tables; Test for Curvature
- The Wilcoxon/Friedman Test
- Equivalence Testing
- The Power of a Test
- Test of Normality
- Problems (Chapter 8)
- Answers (Chapter 8)
Sampling
- Sampling by Variance
- Sampling by Attributes
- A Pharmaceutical Example
- Blending Validation
- Control Charts
- Arbitrary and Tabulated Sample Sizes
- Problems
- Answers
Least Squares Fitting
- Equation for a Straight Line
- Concept of Least Squares Filling
- Derivation of the Least Squares Fit Equation
- A Long Hand Example
- The Slope
- The Intercept and Extrapolated Estimations
- Prediction Intervals
- The Correlation Coefficient, R
- Upper and Lower Confidence Bounds Programming the Least Squares Fit
- Expiration Periods
- Programs for Regression with Confidence Bounds
- Weighted Least Squares
- ANOVA of Least Squares Fit
- Assumptions Made in the Least Squares
- Nonlinearity and Weighted Least Squares
- The Problem With Normality
- Significance of Correlation and Curvature
- The Significance of the Correlation Coefficient
- Durbin-Watson Statistics
- Multiple Regression
- Transformations
- Non-Linear Regression
- Polynomials
- Least Square Fits of Distribution Functions
Iteration
- One Iterant
- Non-Linear Fitting
- Curvature
- Multiple Parameter Curve Fitting
- A Pharmaceutical Example (Shear Cell)
- Multiple Iterants
- Deconvolution
- The Least Squares Wrist
- Modeling by Comparison and Statistics
- Zero-Point Problems and Other Iterations
- An Example of Multiple Iterants
- Appendix to Chapter 11
Factorials and Phenomenology
- The Simple Factorial
- Screening for Variables
- Multiple Specifications
- Dimensionless Analysis
- The Differentiation Approach
- Examples of Differential Fitting
- Monophasic versus Biphasic Profiles
- Optimization
Monte Carlo Method and Simulation
- Description of the Steps of the Process
- The Initial Thought Process
- Monte Carlo Method
- Simulation
Pseudomodeling
- Relying on Previous Models
- Pseudomodeling
- Going Backwards
- General Equations Imitated in Reverse Deduction
- A Pharmaceutical Example. Auto-Oxidation
- Curves with Extrema
- Models with Functional Assumptions: A Pharmaceutical Example
- Arriving at Differential or other Equations Not Solvable in Closed Form
Modeling
- Definition of Modeling
- Getting Started
- Literature Search
- The Basic Data
- Graphing
- The Saturday Afternoon Experiment. The Quick and Dirty
- Initial Conclusions from the Graph
- The Initial Modeling Thoughts: The Doodle
- Stressing the Model
- The Finishing Touches
- Scrutinizing the Short-Cuts Taken
- It Never Ends

Index

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Modeling and Data Treatment
in the Pharmaceutical Sciences
by J. T. Carstensen, PhD
270 pages • $228.95 + shipping

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