Fitting Bioassay Models to Data Course Outline

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Who Should Attend: This course is designed for anyone who works in the biopharmaceutical industry. Although it is useful for the “troops in the trenches” who use mathematical models in their everyday duties, it is intended also for their supervisors all the way up the company structure who must understand the concepts to make proper managerial decisions, especially when dealing with regulatory agencies or when improvements in processes are required.

Click on the titles below to learn more about each session. When live sessions are available, sign up anytime for individual sessions or the entire 11-session live course in Spring 2025! You will receive invitations to join upcoming live sessions. Or sign up to receive links to recordings of any or all sessions as soon as they are available.

Although designed to be taken in a series, you may pick and choose individual sessions, as they are designed to be stand-alone units. When you are ready, click on the “Register Now” button to sign up for individual sessions or the full course. Each live session is interactive: Login, listen, learn and ask questions!

Session 1 is FREE! Each 60-minute session is just $339 per session or $3390 for all 11 sessions! Great group discounts are available.

Session 1: Linear Models

Linear Models

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Relationships among data, information, and models
    • The popular (and incomplete) view of “linear models” (e.g., a calibration line)
    • The mathematical definition of linear models (e.g., a parabola)
    • The mathematical definition of non-linear models (e.g., a 4PL model … maybe)
    • Practice identifying linear and non-linear models
    • Some non-linear models can be “linearized”
    • An application of a common non-linear model to stability studies

Session 2: Terminology

Terminology

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • The definition of a parameter; consideration of multiple factors
    • The definition of a factor; consideration of multiple factors
    • The definition of a response; consideration of multiple responses
    • Subscripts on symbols
    • The difference between probabilistic (or stochastic) and deterministic models
    • The definition of an experimental design point (treatment)
    • Replication
    • The importance of unique design points
    • False replication
    • Purely experimental uncertainty (pure error)
    • Lack of fit of the model to the data

Session 3: Matrices

Matrices

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • The experimental design matrix D (e.g., for a 96-well plate)
    • The response matrix Y
    • The difference between mechanistic models and empirical models
    • Contrasting the statistician’s point of view with the researcher’s point of view
    • We fit models to data, not data to models (or you can go to jail)
    • The matrix of parameter coefficients X
    • The matrix of errors E
    • The matrix of parameters B
    • The matrix representation of all linear models: Y = XB + E

Session 4: Fitting Linear Models to Data Using Least Squares

Fitting Linear Models to Data Using Least Squares

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Constraining the system to obtain only one of an infinite number of solutions
    • The “matrix least squares solution”
    • Limitations of what is meant by “best least squares solution”
    • A caution about algebraic misinterpretation of geometric representations of models
    • Examples of least squares computer program outputs
    • Applications to bioassay models

Session 5: Principles of Model Comparisons

Principles of Model Comparisons

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • A model containing only an intercept term fitted to one set of data
    • A model containing only one factor fitted to the same set of data
    • A model containing a single factor and an intercept term fitted to the same set of data
    • Which model fits best? Why? An introduction to the extra-sum-of-squares principle
    • Applications to bioassay models

Session 6: How Statisticians Partition Our Data

How Statisticians Partition Our Data

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Degrees of freedom
    • The raw data
    • The mean of the raw data
    • Correcting (adjusting) the raw data with reference to their mean
    • Definition of factor effects
    • Definition of residuals or deviations
    • Estimating lack of fit of the model to the data
    • Estimating purely experimental uncertainty (pure error)
    • Applications to bioassay models

Session 7: The Sums of Squares and Degrees of Freedom Tree (ANOVA for Linear Models)

The Sums of Squares and Degrees of Freedom Tree (ANOVA for Linear Models)

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Estimated responses
    • Residuals
    • Sum of squares of residuals calculated with a matrix and its transpose; easy peasy
    • The major difference between linear and non-linear models
    • Why residuals exist: Splitting residuals into lack of fit and purely experimental uncertainty
    • Other sums of squares
    • Pairwise additivity of distances, matrices, degrees of freedom, and sums of squares
    • ANOVA (analysis of variance) for linear models
    • Where non-linear models are different

Session 8: Models without an Intercept

Models without an Intercept

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Adjusting degrees of freedom and ignoring some matrices when an intercept is absent
    • Awareness that some older software does it wrong
    • The Pearson product-moment correlation coefficient from a new perspective
    • Why R2 for a model without an intercept is different in kind than with an intercept
    • Why R2 isn’t necessarily a measure of how well a model fits the data
    • Understanding why small values of R2 are what you want for stability studies
    • Applications to bioassays

Session 9: Using the Sums of Squares and Degrees of Freedom Tree

Using the Sums of Squares and Degrees of Freedom Tree

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    ● An overview of SPC
    • Fisher F test to see if any factors in the model are explaining the variation in the data
    • Fisher F test for lack of fit of a model to the data
    • Transformation of factors or responses to attempt improved fit of model
    • The extra sums of squares principle
    • Applications of the extra sums of squares principle to testing for similarity (parallelism)
    • Confidence intervals for parameter estimates
    • Confidence intervals for fitted models
    • Intuition about experimental design (calibration example)

Session 10: Pre-Averaging and Model-Based Outliers

Pre-Averaging and Model-Based Outliers

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Loss of degrees of freedom when data are pre-averaged or when outliers are removed
    • Effect of loss of degrees of freedom on confidence intervals and statistical tests
    • Gaussian distributions and the frequency of extreme values
    • Model-based outliers
    • Statistical outliers vs. practical outliers
    • Outliers vs. blunders
    • Commonsense thresholds for outlier rejection and retention
    • Patterns in outliers
    • Applications to bioassays

Session 11: The Four-Parameter Logistic (4PL) Model and Alternatives

The Four-Parameter Logistic (4PL) Model and Alternatives

  • Instructor: Dr. Stanley Deming
  • Format: Live session in Spring 2025. Recording available within two weeks after live session.
  • Content:
    • Historical development from challenge assays
    • Historical development from chemical equilibrium
    • Explanation of parameter interpretation (asymptotes, “Hill slope,” and C values)
    • Insensitivity of relative potency estimates to values of asymptotes
    • Probit models
    • Logit models
    • Parallel-line analysis
    • Titration models
    • Exponential models
    • Final topics

COPYRIGHT: U.S. Copyright Law protects the program you are about to attend from unauthorized duplication. Multiple participants are not authorized to share access provided to a single registrant.  For each individual who attends, a single dedicated seat license must be purchased, or a group rate must have been previously arranged with FasTrain. FasTrain reserves the right, at its discretion, to cancel or interrupt access to a web-based training class without notice, or to invoice and collect the group rate payment for the class from the single registrant if this requirement has been violated.