overview of modules on statistical and mathematical modeling in the pharmaceutical sciences
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Overview of Modules on Statistical and Mathematical Modeling in the Pharmaceutical Sciences. by Gary Blau, Research Professor E-enterprise Center Discovery Park Purdue University. COURSE BACKGROUND. - PowerPoint PPT PresentationTRANSCRIPT
Nov, 2007Dr. Gary Blau
Overview of Modules on Statistical and
Mathematical Modeling inthe Pharmaceutical Sciences
byGary Blau, Research Professor
E-enterprise CenterDiscovery Park
Purdue University
Nov, 2007Dr. Gary Blau
COURSE BACKGROUND
• Initial ideas developed for Pharmaceutical Scientists at the Dow Chemical Plant in Brindisi, Italy (1975)
• Subsequently evolved into a global course on Process Optimization presented to Dow Scientists and engineers in Europe and North America.
Nov, 2007Dr. Gary Blau
COURSE BACKGROUND
• Morphed into two courses in the chemical engineering department (Module 1: Statistical Model Building and Design of Experiments for undergraduates) and (Module 2: Mathematical Model Building for Process Optimization for Graduate students)
• Reformulated into a Short Course for Practicing Professionals in the Pharmaceutical Sciences
Nov, 2007Dr. Gary Blau
WHAT IS A MODEL?
Model (Noun)• A miniature representation of something• A person who serves as a pattern for an artist.• A type of design of a product (car, airplane) • A description or analogy used to visualize
something that cannot be observed directly (atom)
• A system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs (a system)
Nov, 2007Dr. Gary Blau
WHAT DOES IT MEAN TO “MODEL” SOMETHING?
Model (Verb)
• To produce a mathematical relationship representation or simulation of a problem
Nov, 2007Dr. Gary Blau
WHY BUILD A MATHEMATICAL MODEL?
To Answer Questions:More specifically, to predict the behavior of the system under
various conditions without running a test or experimente.g. Process Operations Process Design and Scale-Up Process Optimization Process Control
One-to-One Relationship Math Model Question
Math Models are “built” to answer specific questionTherefore, never use a math model to try to answer questions
not addressed in its construction.
“Remember”: ALL MODELS ARE WRONG BUT SOME ARE USEFUL (George Box)
Nov, 2007Dr. Gary Blau
TYPE OF MATHEMATICAL MODELS
Empirical Response= Linear Function of Operating
Conditions yield = bo + b1*Temp + b2*Pressure +
b3*Agitation+…..
Semi-Empirical/Mechanistic
lnp = A + B/(C+T) (Vapour Pressure) Q=UA(LMΔT) (Heat Transfer) k=koexp(-E/RT) (Arrhenius Temp)
Mechanistic/Fundamental/First Principles PV=nRT (Gas Laws) Navier Stokes Ficks Law
Nov, 2007Dr. Gary Blau
TYPE OF MATHEMATICAL MODELS
Mass/Energy Balances across “units”
Input –Output + Generation=Accumulation
Generation: Many models can frequently be postulated for this term so that “model building” is associated with the identification of the proper form of the model to ANSWER questions
Nov, 2007Dr. Gary Blau
TAXONOMY OF MATHEMATICAL MODELS
• Black versus White• Empirical(Statistical) versus Mechanistic• Linear(Statistical) versus Nonlinear• Small versus Large• Complex versus Simple• Integer/Discrete versus Continuous• Algebraic versus Differential Equations
Nov, 2007Dr. Gary Blau
MATHEMATICAL MODELS
Reverse Engineering
ProcessOptimization
PlantDesign
Process Debottlenecking
“What” Variables and “How” the work together. Questions
“Why” do processes work the way they do. Questions
Nov, 2007Dr. Gary Blau
STEPS IN MODEL BUILDING
1)Define the problem (the question to be answered by the model)
2)Postulate one or model models that could be used to solve the problem.
3)Design/Analyse a set of experimental data to choose between these models and generate statistically meaningful model parameter estimates.
4)If the resultant model selected is inadequate return to step 2.
5) Use the model to solve the problem.
Nov, 2007Dr. Gary Blau
WHAT IS EXPERIMENTAL DESIGN
• A methodological approach to planning and conducting experiments which ensures:
– Experiments will contain the necessary information content to choose between models, estimate model parameters and test model adequacy
Nov, 2007Dr. Gary Blau
WHEN TO APPLY EXPERIMENTAL DESIGN
• When you know something about the process.
• When you can afford to make at least several runs
Nov, 2007Dr. Gary Blau
PHASE OF AN EXPERIMENTAL PROGRAM
A)EXPERIMENT:1) Statement of the Problem2) Choice of Response or
Dependent Variable3) Selection of Factors
(independent variables) that can be controlled or varied.
4) Determine feasible ranges and choice of levels of these factors.
Nov, 2007Dr. Gary Blau
PHASE OF AN EXPERIMENTAL PROGRAM
B: DESIGN1) Number of Experiments2) Sequential Experimentation
3) Randomization/Blocking/Replication4) Postulated Mathematical Model
PROPER DESIGN AVOIDSExcessive data collectionFutile data analysisHigh GI/GO Ratio
Nov, 2007Dr. Gary Blau
PHASE OF AN EXPERIMENTAL PROGRAM
ANALYSIS
1) Data Collection and processing
2) Computation of Test Statistics to Validate Model and Estimate
Model Parameters
3) Interpretation of Results
Nov, 2007Dr. Gary Blau
TOPICS TO BE COVERED IN THESE MODULES
Module 1:1) Quantification of Uncertainty in Experimental data and impact on model analysis using Probability Theory
2) Review of Statistics for building Statistical Models (Multilinear Regression analysis)
3) Design of Experiments for Building Statistical models Single factor Experiments
Multifactor ExperimentsFactorial ExperimentationFractional Factorial ExperimentationResponse Surface ModelingProcess Optimization
Nov, 2007Dr. Gary Blau
TOPICS TO BE COVERED IN THESE MODULES
Module 2
1) When is it necessary to use nonlinear models. 2) Design and Analysis of Experiments with Nonlinear Models
(1) Liklihood Estimation-Nonlinear Regression Methods
(2) Bayesian Estimation-Markov Chain/Monte Carlo Methods
(3) Discrimination of Rival Nonlinear Models (4) Statistical Properties of Estimators(5) Properties of Predicted Values
Nov, 2007Dr. Gary Blau
HOW WILL THE MATERIAL BE COVERED
• Three Scenarios
• Lecture Examples– Software tutorials
• End of Section Problems
Nov, 2007Dr. Gary Blau
HELPFUL HINTS
• Review Probability and Statistics or have a text available during Module 1 (e.g. Runger and Montgomery, Applied Statistics and Probability for Engineers)
• Work all lecture examples using your own version of the software.
• Work all problems at the end of the lectures.
• Complete Module 1 before starting Module 2.
GOOD LUCK
Nov, 2007Dr. Gary Blau
WHEN SHOULD YOU NOT APPLY EXPERIMENTAL DESIGN
• When you are not trying to predict behavior– Just making a product– Just a demonstration
• When only a “couple” of runs are to be made– We will get answer with “just one more” run.– Can’t afford any more
• When you are not even close to the right operating region– Most runs are infeasible– Your product is just junk
• When you don’t know much about process– Brand new process
BUT DON”T USE THESE EXCUSES TOO LONG!!!