Introduction of Thomas H. Taylor, Jr., PE

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Introduction ofThomas H. Taylor, Jr., PE

• Georgia Institute of Technology, BS Applied
  Mathematics, 1975
• Georgia State University, MS Decision Sciences,
  Statistics Concentration, 1985
• Registered Professional Engineer, Industrial
• 25 years in private-sector energy industry 8
  years in micro-biology and public health, in
  federal government
• Senior Executive in utility consulting industry
• Senior federal employee, well published in
  scientific journals.
• Holder of Methods Patent for new computational
  approach and associated SASTM-based software for
  series-dilution bioassays
• Career conclusions
• Modeling (and much of statistics in general) is
  transferable across sectors, industries, and
  disciplines.
• The jargon varies across sectors, industries, and
  disciplines

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Presentation Outline

• Introduction of T. Taylor
• Regression Modeling Motivation
• Implicit in the development of a real-world model
  is the expectation that it be used for decision
  making.
• The decision-making is the guiding principle for
  model development.
• Modeling Examples
• Course of Disease response decisions
• Epidemiological, Chronic policy and treatment
  decisions
• Epidemiological, Outbreak announcements
  recalls
• Software for modeling SASTM is superior to
  ExcelTM in modeling situations, due to
  documentation, reproducibility, and
  audit-worthiness.
• Regression modeling in the real world is not as
  clean as it is in many textbooks

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Decision-making and Risk

• Implicit in decision making is the minimization
  of risk
• Risk probability (event) X loss function
  (event)
• Loss functions are different in different
  industries and sectors
• Risk is used incorrectly in some sectors and
  industries.
• Government decision criteria are considerably
  different from private sector
• Public welfare is not expected to be
  cost-effective
• Epidemiology
• Objective Reduce burden of disease or rate of
  mortality
• Intervention Vaccine introduction educational
  campaigns, e.g. hand-washing avoidance of
  specific behaviors food and drug recalls
• Energy
• Objective reduce energy use, or re-arrange
  energy use
• Actions green marketing efficiency mandates
  development of alternatives
• Classic Marketing
• Objective increase sales maximize profit
  minimize risk
• Decisions pricing, product/service choice RD

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Decision/Outcome Criterion
yx
Spore eqiuvalent of toxin level
not sick
sick
Individual tolerance
exposure
spores
5
ExposurePersonal Tolerance
Fulminant Stage
Prodromal Stage
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Exposure gtgt Personal Tolerance
Fulminant Stage
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Decision Timepoints (from Model!)
100,000
Not sick
10-11 days to peak toxin level (asymptomatic)
Individual tolerance
10-11 days to prodromal disease
50,000
6-7 days till prodromal
4-5 days till prodromal
2-3 days
600
3 hrs.
600
50,000
100,000
exposure
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Popular Regression Models

• Time series
• Simple Trends, e.g. energy increase per year
• Application-specific functions, e.g. sigmoidal
• ARIMA et al
• Causal not really association ? cause
• Energy
• End-use BTUf(appliance stock, efficiency)
• Econometric BTUf(cost of energy, income,
  inflation)
• Epidemiological
• Case-statusf(age, sex, race, genetic factors)
• Case-statusf(exposure1, exposure2,)
• Survival (Time-to-Event) models

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SASTM Regression Procedures

• General Regression The REG Procedure
• Nonlinear Regression The NLIN Procedure
• Response Surface Regression The RSREG Procedure
• Partial Least Squares Regression The PLS
  Procedure
• Regression for Ill-conditioned Data The ORTHOREG
  Procedure
• Local Regression The LOESS Procedure
• Robust Regression The ROBUSTREG Procedure
• Logistic Regression The LOGISTIC Procedure
• Regression with Transformations The TRANSREG
  Procedure
• Regression Using the GLM, CATMOD, LOGISTIC,
  PROBIT, and LIFEREG Procedures
• Interactive Features in the CATMOD, GLM, and REG
  Procedures
• http//support.sas.com/onlinedoc/913/docMainpage.j
  sp

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SASTM Regression Help (1)

• CATMOD
• analyzes data that can be represented by a
  contingency table. PROC CATMOD fits linear models
  to functions of response frequencies, and it can
  be used for linear and logistic regression. The
  CATMOD procedure is discussed in detail in
  Chapter 5, "Introduction to Categorical Data
  Analysis Procedures."
• GENMOD
• fits generalized linear models. PROC GENMOD is
  especially suited for responses with discrete
  outcomes, and it performs logistic regression and
  Poisson regression as well as fitting Generalized
  Estimating Equations for repeated measures data.
  See Chapter 5, "Introduction to Categorical Data
  Analysis Procedures," and Chapter 29, "The GENMOD
  Procedure," for more information.
• GLM
• uses the method of least squares to fit general
  linear models. In addition to many other
  analyses, PROC GLM can perform simple, multiple,
  polynomial, and weighted regression. PROC GLM has
  many of the same input/output capabilities as
  PROC REG, but it does not provide as many
  diagnostic tools or allow interactive changes in
  the model or data. See Chapter 4, "Introduction
  to Analysis-of-Variance Procedures," for a more
  detailed overview of the GLM procedure.
• LIFEREG
• fits parametric models to failure-time data that
  may be right censored. These types of models are
  commonly used in survival analysis. See Chapter
  10, "Introduction to Survival Analysis
  Procedures," for a more detailed overview of the
  LIFEREG procedure.
• http//v8doc.sas.com/sashtml/

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SASTM Regression Help (2)

• LOGISTIC
• fits logistic models for binomial and ordinal
  outcomes. PROC LOGISTIC provides a wide variety
  of model-building methods and computes numerous
  regression diagnostics. See Chapter 5,
  "Introduction to Categorical Data Analysis
  Procedures," for a brief comparison of PROC
  LOGISTIC with other procedures.
• NLIN
• builds nonlinear regression models. Several
  different iterative methods are available.
• ORTHOREG
• performs regression using the Gentleman-Givens
  computational method. For ill-conditioned data,
  PROC ORTHOREG can produce more accurate parameter
  estimates than other procedures such as PROC GLM
  and PROC REG.
• PLS
• performs partial least squares regression,
  principal components regression, and reduced rank
  regression, with cross validation for the number
  of components.
• http//v8doc.sas.com/sashtml/

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SASTM Regression Help (3)

• PROBIT
• performs probit regression as well as logistic
  regression and ordinal logistic regression. The
  PROBIT procedure is useful when the dependent
  variable is either dichotomous or polychotomous
  and the independent variables are continuous.
• REG
• performs linear regression with many diagnostic
  capabilities, selects models using one of nine
  methods, produces scatter plots of raw data and
  statistics, highlights scatter plots to identify
  particular observations, and allows interactive
  changes in both the regression model and the data
  used to fit the model.
• RSREG
• builds quadratic response-surface regression
  models. PROC RSREG analyzes the fitted response
  surface to determine the factor levels of optimum
  response and performs a ridge analysis to search
  for the region of optimum response.
• TRANSREG
• fits univariate and multivariate linear models,
  optionally with spline and other nonlinear
  transformations. Models include ordinary
  regression and ANOVA, multiple and multivariate
  regression, metric and nonmetric conjoint
  analysis, metric and nonmetric vector and ideal
  point preference mapping, redundancy analysis,
  canonical correlation, and response surface
  regression.
• http//v8doc.sas.com/sashtml/

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SASTM Regression Help (4)

• Several SAS/ETS procedures also perform
  regression. The following procedures are
  documented in the SAS/ETS User's Guide.
• AUTOREG
• implements regression models using time-series
  data where the errors are autocorrelated.
• PDLREG
• performs regression analysis with polynomial
  distributed lags.
• SYSLIN
• handles linear simultaneous systems of equations,
  such as econometric models.
• MODEL
• handles nonlinear simultaneous systems of
  equations, such as econometric models.
• http//v8doc.sas.com/sashtml/

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Point-and-click vs. SASTM code

• SASTM has tremendously more capability
• Use of SASTM procedures provides documentation,
  formally and operationally
• Spreadsheets and point-and-click environments
  cannot withstand audits
• Regulatory agencies FERC, FDA, NRC, USDA (FDA
  21 CFR Part 11)
• Labor intensive point-and-click can be replaced
  with SASTM code to save time and, therefore,
  focus on analysis, not mechanics.

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Specific Models

• Disease A (used as decision/outcome example
  above)
• Course of disease - NOT regression
• Disease P
• Time series
• Simple periodic with exception!

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Seasonal Data with Aberrations
1996
1997
1998
1999
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Sinusoidal Piecewise Regression with Trend
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Specific Models

• Disease A
• Course of disease - NOT regression
• Disease P
• Time series
• Simple periodic with exception!
• Sigmoid
• Laboratory applications

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Plot of Measured Response by Dilution Well-behav
ed Specimen
Measured Response
Measured response can be cell counts, optical
density, luminescence, or other lab-measured
quantity.
100
True Midpoint (LD50, ED50, etc)
0
Observed 50 Titer
True 50 Titer
Dilution
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What about? High-Variance Specimens Robustness
of True 50 Endpoint
Observed Response
Midpoint (50)
Dilution
50
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Specific Models

• Disease A
• Course of disease - NOT regression
• Disease P
• Time series
• Simple periodic with exception!
• Sigmoid
• Laboratory applications
• Investigation of foodborne disease outbreak
• Not a laboratory
• Not a controlled experiment
• Not even a designed experiment
• Observational data

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Foodborne Disease Outbreak

• Associative (not causal) models
• Epidemiological
• Case-statusf(exposure1, exposure2,)

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George Box all models are wrong, but some are
useful.

• George Edward Pelham Box (18 October 1919 ) is
  one of the most influential statisticians of the
  20th century and a pioneer in the areas of
  quality control, time series analysis, design of
  experiments and Bayesian inference.
• He served as President of the American
  Statistical Association in 1978 and of the
  Institute of Mathematical Statistics in 1979. He
  received the Shewhart Medal from the American
  Society for Quality Control in 1968, the Wilks
  Memorial Award from the American Statistical
  Association in 1972, the R. A. Fisher Lectureship
  in 1974, and the Guy Medal in Gold from the Royal
  Statistical Society in 1993. He was elected a
  member of the American Academy of Arts and
  Sciences in 1974 and a Fellow of the Royal
  Society in 1979.