- Introduction (H1) L1
- General methods for multivariable models (H2) L2
- Missing data (H3, L5)
- Multivariable modeling strategy (H4)
- Bootstrap, Validating, Describing, and Simplifying the Model (L9, H5)
- R Multivariable Modeling/Validation/Presentation Software (H6, BBR9)
- Case Study in Longitudinal Data Modeling with Generalized Least Squares (H7, L11)
- Case study in data reduction (H8, L12)
- Maximum Likelihood Estimation (H9, L13) | https://bstt513.class.uic.edu/estimLS.pdf Donald Hedeker's Notes
- Binary Logistic Model (H10, L15)
- Binary Logistic Case Study 1 (H11, L16)
- Binary Logistic Case Study 2 (H12, L17)
- Ordinal Logistic Models (H13, L18)
- Ordinal Logistic Regression Case Study (H14, L19)
- Case Study in Ordinal Regression for Continuous Univariate Y (H15, L21-22)
- Transform-both-sides Nonparametric Additive Regression Models (H16, L22-23)
- Some Components of Survival Analysis and Parametric Survival Models (H17-H18, L24)
- Parametric Survival Model Case Study (H19, L25)
- Cox Model (H20), Cox Model Case Study (H21) (L26)
- Analysis of Covariance in Randomized Trials (BBR Chapter 13, L27)
- Medical Diagnostic Research (BBR Chapter 19, L28)

- Course overview and logistics
- Course philosophy
- Hypothesis testing vs. estimation vs. prediction
- Examples of multivariable prediction problems
- Misunderstandings about classification vs. prediction (read this also)
- Study planning considerations
- Choice of model
- Model uncertainty/data driven model selection/phantom d.f.

- Notation for general regression models
- Model formulations
- Interpreting model parameters
- nominal predictors
- interactions
- Review of chunk tests
- Relaxing linearity assumption for continuous predictors
- avoiding categorization - see also BBR Sections 18.3.2-18.3.3
- nonparametric smoothing
- simple nonlinear terms (L3)
- splines for estimating shape of regression function and determining predictor transformations
- cubic spline functions
- restricted cubic splines
- see interactive demos of spline fitting and continuity here
- nonparametric regression (smoothers)
- advantages of splines over other methods
- recursive partitioning and tree models in a nutshell
- Bayesian spline modeling: watch McElreath's presentation

- New directions in predictive modeling (L4)
- Tests of association
- Grambsch and O'Brien paper

- Assessment of model fit
- regression assumptions
- modeling and testing complex interactions
- interactions to prespecify
- distributional assumptions

- Types of missing data
- Prelude to modeling
- Missing values for different types of response variables
- Problems with alternatives to imputation
- Strategies for developing imputation models
- Single imputation
- Predictive mean matching
- Multiple imputation
- The
`aregImpute`

algorithm (L6) - Diagnostics
- Summary and rough guidelines; effective sample size

- Pre-specification of predictor complexity
- Variable selection
- Sample size, overfitting, and number of predictors (L7); also see this
- Shrinkage
- Collinearity
- Data reduction
- Overly influential observations (L8)
- Comparing two models
- Improving the practice of multivariable prediction
- Overall modeling strategies

- Describing the fitted model
- Bootstrap; see also Section 8.6 of BBR
- Model validation; see also this and this
- Bootstrapping ranks of predictors (L10)
- Simplifying the model by approximating it
- How do we break bad habits?

- Notation and model for mean time-response profile
- Keeping baseline variables as baseline
- Modeling within-subject dependence
- Overview of competing methods for serial data
- Checking model fit
- Software
- Case study from a randomized trial

- How many parameters can be estimated?
- Redundancy analysis
- Variable clustering
- Transformation/scaling of variables using
`transcan`

- Principal components Cox regression
- Sparse principal components
- Nonparametric transform-both-sides regression for transforming/scaling variables

- Three test statistics
- Robust covariance matrix estimator
- Correcting variances for clustered or serial data using sandwich and bootstrap estimators
- Confidence regions
- Wald (large-sample normal approximation)
- Bootstrap
- Simultaneous (normal approx)

- General contrasts through differences in linear predictor
- Further use of the log likelihood
- Weighted MLE
- Penalized MLE
- Effective d.f.

- Model
- Odds ratios, risk ratios, and risk differences
- Detailed example
- Estimation
- Test statistics
- Residuals
- Assessment of model fit
- Quantifying predictive ability
- Validating the model
- Describing fitted models
- R functions

- Ordinality assumption
- PO Model
- Model
- Assumptions, interpretations of parameters, estimation, residuals
- Assessment of fit
- Predictive ability measures
- Describing the model
- Validation
- R functions

- CR Model
- Model
- Assumptions, interpretation of parameters, estimation, residuals
- Assessment of fit
- Extended CR model including penalization
- Validation
- R functions

- No transformation satisfying all linear model assumptions exists for the dataset
- Assumptions of the proportional odds ordinal logistic model (semiparametric model) are not satisfied
- Development and validation of a quantile regression model for median glycohemoglobin
- Failure of linear multiple regression
- Failure of proportional odds model for continuous gh
- Comparison with quantile regression
- Obtaining many types of predicted values

- Generalized additive models
- ACE
- AVAS
- Parametric approach
- Obtaining estimates on the original scale
- Smearing estimator

- R
`areg.boot`

function - Examples

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Topic revision: 04 Feb 2020, FrankHarrell

Topic revision: 04 Feb 2020, FrankHarrell

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