Common Mistakes

Published

Last modified: 2026-11-12: 8:46:54 (UTC)

Configuring R

Functions from these packages will be used throughout this document:

Show R code

library(conflicted) # check for conflicting function definitions
# printr is not loaded here: it inserts help-file output into markdown output
library(rmarkdown) # Convert R Markdown documents into a variety of formats.
library(pander) # format tables for markdown
library(ggplot2) # graphics
library(ggfortify) # help with graphics
library(dplyr) # manipulate data
library(tibble) # `tibble`s extend `data.frame`s
library(magrittr) # `%>%` and other additional piping tools
library(haven) # import Stata files
library(knitr) # format R output for markdown
library(tidyr) # Tools to help to create tidy data
library(plotly) # interactive graphics
library(dobson) # datasets from Dobson and Barnett 2018
library(parameters) # format model output tables for markdown
library(haven) # import Stata files
library(latex2exp) # use LaTeX in R code (for figures and tables)
library(fs) # filesystem path manipulations
library(survival) # survival analysis
library(survminer) # survival analysis graphics
library(KMsurv) # datasets from Klein and Moeschberger
library(parameters) # format model output tables for
library(webshot2) # convert interactive content to static for pdf
library(forcats) # functions for categorical variables ("factors")
library(stringr) # functions for dealing with strings
library(lubridate) # functions for dealing with dates and times
# Summarizes key information about statistical objects in tidy tibbles
library(broom)
# Provides suite of functions to work with regression model
# `broom::tidy()` tibbles
library(broom.helpers)

Here are some R settings I use in this document:

Show R code

rm(list = ls()) # delete any data that's already loaded into R

conflicts_prefer(dplyr::filter)
ggplot2::theme_set(
  ggplot2::theme_bw() +
    # ggplot2::labs(col = "") +
    ggplot2::theme(
      legend.position = "bottom",
      text = ggplot2::element_text(size = 12, family = "serif")
    )
)

knitr::opts_chunk$set(message = FALSE)
options(digits = 6)

panderOptions("big.mark", ",")
pander::panderOptions("table.emphasize.rownames", FALSE)
pander::panderOptions("table.split.table", Inf)
# use the `filter()` function from dplyr() by default
conflicts_prefer(dplyr::filter)
legend_text_size <- 9
run_graphs <- TRUE

1 Parameters versus random variables

The parameters of a probability distribution shouldn’t involve the random variables being modeled:

Incorrect parameter dependency on random variables

\[X \sim Pois(\lambda)\] \[\hat{\lambda}_{ML} \rightarrow_D N(\bar{X}, \lambda/n)\]

Solution

Solution. \[\hat{\lambda}_{ML} \rightarrow_D N(\lambda, \lambda/n)\]

Expectations are means, not sums, despite the similarity of $\Sigma$ and $\text{E}$. Really, we should use $\mu$ instead of $\text{E}$.

2 Regression modeling

Each mistake in this section is shown in a warning callout, followed by a corrected version.

2.1 Logistic-regression coefficients are log odds ratios

In a logistic regression model, a coefficient $\beta_j$ is a difference in log-odds, so ${\operatorname{exp}\mathopen{}\left\{\beta_j\right\}\mathclose{}}$ is an odds ratio (see the odds ratio theorem for logistic regression), not a risk ratio:

Interpreting ${\operatorname{exp}\mathopen{}\left\{\beta_1\right\}\mathclose{}}$ as a risk ratio

“${\operatorname{exp}\mathopen{}\left\{\beta_1\right\}\mathclose{}} = 1.5$, so a one-unit increase in $x_1$ makes the outcome 50% more likely.”

Solution

Solution. “${\operatorname{exp}\mathopen{}\left\{\beta_1\right\}\mathclose{}} = 1.5$, so a one-unit increase in $x_1$ multiplies the odds of the outcome by 1.5, holding the other covariates fixed: $\text{ϙ}_{\omega}(\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}},\mathord{{\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}^*}}) = 1.5$ when $\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}$ and $\mathord{{\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}^*}}$ differ by one unit in $x_1$ only.”

2.2 Odds ratios approximate risk ratios only for rare outcomes

The odds ratio equals the risk ratio times the correction factor $\frac{1-\pi_2}{1-\pi_1}$ (see the odds ratio correction-factor theorem). That correction factor is close to 1 only when both risks are small.

Reporting an odds ratio as a risk ratio for a common outcome

$\pi_1 = 0.4$, $\pi_2 = 0.2$, odds ratio $= 2.67$: “exposed participants had 2.67 times the risk of unexposed participants.”

Solution

Solution. The risk ratio is $\frac{\pi_1}{\pi_2} = \frac{0.4}{0.2} = 2$. The odds ratio is $\frac{0.4/0.6}{0.2/0.8} = \frac{0.667}{0.25} = 2.67$, which equals $2 \cdot \frac{0.8}{0.6}$. Report “2.67 times the odds”, or estimate the risk ratio directly.

2.3 Poisson rate models need an offset

When subjects have different amounts of follow-up time $t$, a Poisson model for an event rate includes ${\operatorname{log}\mathopen{}\left\{t\right\}\mathclose{}}$ as an offset (see the Poisson rate model’s mean). Without the offset term, the model describes expected counts, not rates, and ${\operatorname{exp}\mathopen{}\left\{\beta_j\right\}\mathclose{}}$ is a ratio of expected counts rather than a rate ratio.

Omitting the offset

Group A: 10 events in 1000 person-years; group B: 10 events in 500 person-years. A Poisson model fit to the counts alone gives ${\operatorname{exp}\mathopen{}\left\{\hat{\beta}_1\right\}\mathclose{}} = 10/10 = 1$: “the groups have the same event rate.”

Solution

Solution. Include ${\operatorname{log}\mathopen{}\left\{t\right\}\mathclose{}}$ as an offset (in R, offset(log(t)) in the model formula). The incidence rates are $10/1000 = 0.01$ and $10/500 = 0.02$ events per person-year, so the rate ratio for A versus B is $0.01/0.02 = 0.5$.

2.4 Hazard ratios are not ratios of survival probabilities

A hazard ratio compares hazards, which are instantaneous event rates, not survival probabilities. Under proportional hazards, $\operatorname{S}(t|\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}) = \mathopen{}\left[\operatorname{S}_0(t)\right]\mathclose{}^{\theta_{{\lambda}}(\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}})}$ (see the proportional hazards survival theorem), so the hazard ratio enters the survival function as an exponent, not as a multiplier.

Interpreting a hazard ratio as a survival-probability ratio

$\text{ϙ}_{{\lambda}}(t| \mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}: \mathord{{\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}^*}}) = 2$ and $\operatorname{S}(t|\mathord{{\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}^*}}) = 0.8$: “the exposed group has half the probability of surviving to $t$, $\operatorname{S}(t|\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}) = 0.4$.”

Solution

Solution. $\operatorname{S}(t|\mathord{\smash[b]{\underset{\raise.3ex\hbox{$\scriptstyle\sim$}}{x}}\vphantom{x}}) = 0.8^2 = 0.64$, so the ratio of survival probabilities is $0.64/0.8 = 0.8$, and the ratio of cumulative risks is $\frac{1-0.64}{1-0.8} = \frac{0.36}{0.2} = 1.8$. Neither ratio equals the hazard ratio of 2.

2.5 Censored observations are not event-free

A right-censored observation tells us only that the event had not occurred by the end of that subject’s follow-up; the subject might have had the event later.

Treating censored observations as event-free

Of 100 participants, 20 had the event and 30 were censored before 5 years: “the 5-year risk is $20/100 = 0.2$, since the censored participants did not have the event.”

Solution

Solution. Counting censored participants as event-free for the whole period biases the estimated risk downward. Use a survival-analysis method that keeps each censored participant in the risk set only until their censoring time, such as the Kaplan-Meier estimator or a proportional hazards model, under the assumption of non-informative censoring.

3 R

3.1 Don’t copy-paste code

Successful programmers don’t use copy-paste! Write functions instead.

4 Quarto

4.1 Separate divs and slide breaks

Make sure not to put a div ::: on the next line after a slide break ---:

---
::: notes
:::

There needs to be an empty line between them:

---

::: notes
:::

4.2 `library(printr)` currently breaks `df-print: paged`

See https://github.com/yihui/printr/issues/41

5 LaTeX

don’t use align* or align* in quarto; only aligned

Double superscript issues: https://www.overleaf.com/learn/latex/Errors/Double_superscript

Configuring R

1 Parameters versus random variables

2 Regression modeling

2.1 Logistic-regression coefficients are log odds ratios

2.2 Odds ratios approximate risk ratios only for rare outcomes

2.3 Poisson rate models need an offset

2.4 Hazard ratios are not ratios of survival probabilities

2.5 Censored observations are not event-free

3 R

3.1 Don’t copy-paste code

4 Quarto

4.1 Separate divs and slide breaks

4.2 library(printr) currently breaks df-print: paged

5 LaTeX

4.2 `library(printr)` currently breaks `df-print: paged`