Table of Contents xi

Watching Out for Special Situations that Arise in Multiple

Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Synergy and anti-synergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

Collinearity and the mystery of the disappearing significance. . . 246

Calculating How Many Participants You Need. . . . . . . . . . . . . . . . . . . 247

CHAPTER 18: A Yes-or-No Proposition: Logistic Regression. . . . . . 249

Using Logistic Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

Understanding the Basics of Logistic Regression. . . . . . . . . . . . . . . . . 251

Fitting a function with an S shape to your data . . . . . . . . . . . . . . . . . . 252

Handling multiple predictors in your logistic model . . . . . . . . . . . 255

Running a Logistic Regression Model with Software. . . . . . . . . . . . . . 256

Interpreting the Output of Logistic Regression. . . . . . . . . . . . . . . . . . . 257

Seeing summary information about the variables. . . . . . . . . . . . . 258

Assessing the adequacy of the model. . . . . . . . . . . . . . . . . . . . . . . 258

Checking out the table of regression coefficients. . . . . . . . . . . . . .259

Predicting probabilities with the fitted logistic formula. . . . . . . . . 260

Making yes or no predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .262

Heads Up: Knowing What Can Go Wrong with

Logistic Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

Don’t misinterpret odds ratios for numerical predictors . . . . . . . 267

Beware of the complete separation problem. . . . . . . . . . . . . . . . . 267

Figuring Out the Sample Size You Need for Logistic Regression. . . . 268

CHAPTER 19: Other Useful Kinds of Regression. . . . . . . . . . . . . . . . . . . . 271

Analyzing Counts and Rates with Poisson Regression. . . . . . . . . . . . . 271

Introducing the generalized linear model. . . . . . . . . . . . . . . . . . . . 272

Running a Poisson regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

Interpreting the Poisson regression output . . . . . . . . . . . . . . . . . . 275

Discovering other uses for Poisson regression. . . . . . . . . . . . . . . . 276

Anything Goes with Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . 279

Distinguishing nonlinear regression from other kinds. . . . . . . . . 279

Checking out an example from drug research. . . . . . . . . . . . . . . . 280

Running a nonlinear regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Interpreting the output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Using equivalent functions to fit the parameters

you really want. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Smoothing Nonparametric Data with LOWESS. . . . . . . . . . . . . . . . . . . 286

Running LOWESS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Adjusting the amount of smoothing. . . . . . . . . . . . . . . . . . . . . . . . . 289

CHAPTER 20: Getting the Hint from Epidemiologic Inference. . . 291

Staying Clearheaded about Confounding. . . . . . . . . . . . . . . . . . . . . . . 292

Avoiding overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Adjusting for confounders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Understanding Interaction (Effect Modification) . . . . . . . . . . . . . . . . . 296