Regression Methods for Public Health using R
Welcome
Thanks for visiting!
Use
Preface
Software information and conventions
Acknowledgments
About the Author
1
Introduction
1.1
R and R Studio
1.2
Datasets
2
Overview of Regression Methods
2.1
Why use regression?
2.2
Basic statistical concepts
2.3
To Do
3
Data summarization
3.1
Examining the data
3.2
Missing data options
3.2.1
Complete case analysis
3.2.2
Multiple imputation
3.3
Creating a “Table 1”
3.3.1
Function for summarizing a continuous variable
3.3.2
Function for summarizing a categorical variable
3.3.3
Overall
3.3.4
By outcome or exposure
3.3.5
Formatting
3.4
To Do
4
Example of each type of regression
4.1
Continuous outcome – Linear regression
4.2
Yes/No outcome – Binary logistic regression
4.3
Time-to-event outcome – Survival analysis
5
Simple linear regression
5.1
Introduction
5.2
Notation and interpretation
5.3
Visualizing the relationship
5.4
Fitting the SLR model
5.4.1
Continuous predictor
5.4.2
Categorical predictor
5.5
Fitting curves using polynomials
5.6
Predictions from the model
5.7
Confidence intervals, confidence bands, prediction intervals
5.7.1
CI for regression coefficients
5.7.2
CI for mean outcome
5.7.3
CI for individual observations
5.8
Assumptions
5.9
Exercises
6
Multiple linear regression
6.1
Introduction
6.2
Notation and interpretation
6.3
Examine the data
6.4
Visualize the unadjusted relationships
6.5
Fitting the MLR model
6.6
Visualizing the adjusted relationships
6.7
Interactions
6.7.1
Types of interactions
6.7.2
When to include an interaction
6.7.3
Test of interaction
6.7.4
Overall test of a predictor involved in an interaction
6.8
Predictions
6.9
Confidence intervals, confidence bands, prediction intervals
6.10
Diagnostics
6.10.1
Residuals
6.10.2
Computing residuals
6.10.3
Checking assumptions
6.10.4
Collinearity
6.10.5
Outliers
6.10.6
Influential observations
6.11
Model selection
6.11.1
Confounders, mediators, and moderators
6.11.2
Confirmatory analysis
6.11.3
Exploratory analysis
6.12
Multiple testing
6.13
Writing it up
6.14
Steps of linear regression
7
Binary logistic regression
7.1
Introduction
7.2
Odds and odds ratios
7.3
Fitting the binary LR model
7.4
Interactions
7.5
Prediction
7.6
Separation
7.7
Assumptions
7.8
Diagnostics
7.9
Conditional logistic regression for matched data
7.10
Log-binomial regression to estimate a risk ratio
7.11
Writing it up
7.12
Steps of binary logistic regression
8
Survival analysis
8.1
Introduction
8.2
Censoring
8.3
Survival and hazard functions
8.4
Setting up the dataset
8.5
Kaplan-Meier estimate of the survival function
8.6
Cox regression
8.6.1
Fitting the Cox regression model
8.6.2
Estimating the survival function
8.6.3
Interactions
8.6.4
Prediction
8.6.5
Separation
8.6.6
Time dependent covariates
8.6.7
Proportional hazards assumption
8.6.8
Diagnostics
8.6.9
Writing it up
8.7
Steps of survival analysis
9
Sensitivity analyses
9.1
Introduction
9.2
What happens if I remove outliers and influential observations?
9.3
Bootstrap to check impact of assumption violations
9.4
Writing it up
10
Complex survey data
10.1
Descriptive statistics
10.2
Weighted linear regression
10.3
Weighted logistic regression
10.4
Weighted Cox regression
11
Multiple imputation of missing data
11.1
Introduction
11.2
Linear regression with MI
11.3
Logistic regression with MI
11.4
Cox regression with MI
Appendix
A
Datasets
B
R and RStudio
B.1
Installation
B.2
R Basics
B.3
Resources for learning R
C
Selected SAS code
References
Published with bookdown
Regression Methods for Public Health using R
Chapter 11
Multiple imputation of missing data
11.1
Introduction
11.2
Linear regression with MI
11.3
Logistic regression with MI
11.4
Cox regression with MI