Regression Models for Epidemiology

Author

Affiliation

Ezra Morrison

Department of Public Health Sciences, School of Medicine, University of California, Davis

Preface

This web-book is derived from my lecture slides for Epidemiology 204: “Quantitative Epidemiology III: Statistical Models”, at UC Davis.

I have drawn these materials from many sources, including but not limited to:

• David Rocke’s materials from the 2021 edition of this course

• Hua Zhou’s materials from the 2020 edition of Biostat 200C at UCLA

• Vittinghoff et al. (2012)

• Dobson and Barnett (2018)

• Harrell (2015)

Using these lecture notes

These lecture notes are available online at https://d-morrison.github.io/rme/. The online notes are searchable and are currently being iteratively updated¹. A pdf version of the notes is also downloadable from https://d-morrison.github.io/rme/Regression-Models-for-Epidemiology.pdf, and the source files are available at https://github.com/d-morrison/rme.

Compiling chapters as lecture slide decks

Each chapter’s source file can also be compiled as a lecture slide deck, using the _quarto-revealjs.yml Quarto profile included in the git repository on Github.

For example, to compile Chapter 3  Models for Binary Outcomes as a slide deck:

1. install quarto

2. clone the project repository from Github

3. Install the project dependencies using devtools:

library(devtools) # install from CRAN if needed
devtools::install_deps()

4. Render the chapter using the revealjs profile using the following terminal shell command:

quarto render logistic-regression.qmd --profile=revealjs

You can also render all the chapters listed in the _quarto-revealjs.yml Quarto profile as slide decks simultaneously:

quarto render --profile=revealjs

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Extracting LaTeX commands from the online version of the notes

If you want to extract the LaTeX commands for any math expressions in the online lecture notes, you should be able to right-click and get this pop-up menu:

Pop-up menu

If you select “TeX commands”, you will get a window with MathJax code, which is more or less a dialect of LaTeX:

MathJax code window

You can also grab the TeX commands from the quarto source files on github, but those files use custom macros (defined in https://github.com/d-morrison/rme/blob/main/macros.qmd), so it’s a little harder to reuse code from the source files.

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Dark Mode

The online notes have two color palette themes: light and dark. You can toggle between them using the oval button near the top-left corner:

Palette toggle

Other resources

These notes represent my still-developing perspective on regression models in epidemiology. Many other statisticians and epidemiologists have published their own perspectives, and I encourage you to explore your many options and find ones that resonate with you. I have attempted to cite my sources throughout these notes.

Here are some additional resources:

• Dunn, Smyth, et al. (2018) is a recent textbook on GLMs. It doesn’t cover time-to-event models, and it doesn’t use the modern tidyverse packages (ggplot2, dplyr, etc.), but otherwise it seems great.

• Moore (2016) is a recent textbook on survival analysis. It also doesn’t use the tidyverse, but otherwise seems great.

• Harrell (2015) is another popular textbook. It uses ggplot2 but not dplyr, and covers GLMs and survival analysis. An abbreviated but continuously updated version with audio clips is available at https://hbiostat.org/rmsc/.

• Fox (2015) is another standard text.

• McCullagh and Nelder (1989) is a classic, theoretical textbook on GLMs

• Dalgaard (2008) covers GLMs and survival analysis at an applied level, using base R

• Vittinghoff et al. (2012) covers GLMs, survival analysis, and causal inference, using Stata

• Faraway (2016) has GLMs but not survival analysis

• Selvin (2001) provides worked-out examples of applications for a wide range of statistical analysis techniques.

• https://ucla-biostat-200c-2020spring.github.io/schedule/schedule.html provides course notes for “Biostat 200C - Methods in Biostatistics C” at UCLA, which is at the Biostatistics MS level.

• https://online.stat.psu.edu/stat504/book/ provides course notes for “STAT 504 - Analysis of Discrete Data” at Penn State University. It includes logistic regression and Poisson regression, as well as 2-way tables and other related topics, and includes SAS code.

• Nahhas (n.d.) is currently in-development

License

This book is licensed to you under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The code samples in this book are licensed under Creative Commons CC0 1.0 Universal (CC0 1.0), i.e. public domain.

Dalgaard, Peter. 2008. Introductory Statistics with r. New York, NY: Springer New York. https://link.springer.com/book/10.1007/978-0-387-79054-1.

Dobson, Annette J, and Adrian G Barnett. 2018. An Introduction to Generalized Linear Models. 4th ed. CRC press. https://doi.org/10.1201/9781315182780.

Dunn, Peter K, Gordon K Smyth, et al. 2018. Generalized Linear Models with Examples in r. Vol. 53. Springer. https://link.springer.com/book/10.1007/978-1-4419-0118-7.

Faraway, Julian J. 2016. Extending the Linear Model with r: Generalized Linear, Mixed Effects and Nonparametric Regression Models. 2nd ed. Chapman; Hall/CRC. https://doi.org/10.1201/9781315382722.

Fox, John. 2015. Applied Regression Analysis and Generalized Linear Models. Sage publications.

Harrell, Frank E. 2015. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. 2nd ed. Springer. https://doi.org/10.1007/978-3-319-19425-7.

McCullagh, Peter, and J. A. Nelder. 1989. Generalized Linear Models. 2nd ed. Routledge. https://www.utstat.toronto.edu/~brunner/oldclass/2201s11/readings/glmbook.pdf.

Moore, Dirk F. 2016. Applied Survival Analysis Using r. Vol. 473. Springer.

Nahhas, Ramzi W. n.d. Introduction to Regression Methods for Public Health Using r. CRC Press. https://www.bookdown.org/rwnahhas/RMPH/.

Selvin, Steve. 2001. Epidemiologic Analysis: A Case-Oriented Approach. Oxford University Press.

Vittinghoff, Eric, David V Glidden, Stephen C Shiboski, and Charles E McCulloch. 2012. Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models. 2nd ed. Springer. https://doi.org/10.1007/978-1-4614-1353-0.

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1. see the source file repository for recent changes: https://github.com/d-morrison/rme