1.1 Rationale for the package

There has been a long relationship between Epidemiology / Public Health and Biostatistics. Students frequently find introductory textbooks explaining statistical methods and the math behind them, but how to implement those techniques on a computer is rarely explained.

One of the most popular statistical software’s in public health settings is Stata. Stata has the advantage of offering a solid interface with functions that can be accessed via the use of commands or by selecting the proper input in the graphical unit interface (GUI). Furthermore, Stata offers “Grad Plans” to postgraduate students, making it relatively affordable from an economic point of view.

R is a free alternative to Stata. Its use keeps growing, and its popularity is also increasing due to the relatively high number of packages and textbooks available.

In epidemiology, some good packages are already available for R, including: Epi, epibasix, epiDisplay, epiR and epitools. The pubh package does not intend to replace any of them, but to only provide a standard syntax for the most frequent statistical analysis in epidemiology.

1.2 Syntax: the use of formulas

Most students and professionals from the disciplines of Epidemiology and Public Health analyse variables in terms of outcome, exposure and confounders. The following table shows the most common names used in the literature to characterise variables in a cause-effect relationships:

In R, formulas declare relationships between variables. Formulas are also common in classic statistical tests and regression methods.

Formulas have the following standard syntax:

y ~ x, data = my_data

Where y is the outcome or response variable, x is the exposure or predictor of interest, and my_data specifies the data frame’s name where x and y can be found.

The symbol ~ is used in R for formulas. It can be interpreted as depends on. In the most typical scenario, y ~ x means y depends on x or y is a function of x:

y = f(x)

Using epidemiology friendly terms:

Outcome = f(Exposure)

It is worth noting that Stata requires variables to be given in the same order as in formulas: outcome first, predictors next.

The pubh package integrates well with other packages of the tidyverse which use formulas and the pipe operator |> to add layers over functions. In particular, pubh uses ggformula as a graphical interface for plotting and takes advantage of variable labels from sjlabelled. This versatility allows it to interact also with tables from crosstable.

y ~ x|z, data = my_data

1.3 Pipes and the tidyverse

The tidyverse has become now the standard in data manipulation in R. The use of the pipe function |> allows for cleaner code. The principle of pipes is to change the paradigm in coding. In standard codding, when many functions are used, one goes from inner parenthesis to outer ones.

For example if we have three functions, a common syntax would look like:

f3(f2(f1(..., data), ...), ...)

With pipes, however, the code reads top to bottom and left to right:

data |>
  f1(...) |> 
  f2(...) |> 
  f3(...)

Most of the functions from pubh are compatible with pipes and the tidyverse.

1.4 Contributions of the pubh package

The main contributions of the pubh package to students and professionals from the disciplines of Epidemiology and Public Health are:

1. Use of a common syntax for the most used analysis.
2. A function, glm_coef that displays coefficients from most common regression analysis in a way that can be easy interpreted and used for publications.

2.1 Inferential statistics

From the descriptive statistics of Ratio, we know that the relative dispersion in the Hodgkin group is almost as high as the relative dispersion in the non-Hodgkin group.

For new users of R, it helps to have a standard syntax in most of the commands, as R could sometimes be challenging and even intimidating. We can test if the difference in variance is statistically significant with the var.test command, which uses can use a formula syntax:

var.test(Ratio ~ Group, data = Hodgkin)

## 
##  F test to compare two variances
## 
## data:  Ratio by Group
## F = 0.6294, num df = 19, denom df = 19, p-value = 0.3214
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2491238 1.5901459
## sample estimates:
## ratio of variances 
##          0.6293991

What about normality? We can look at the QQ-plots against the standard Normal distribution.

Hodgkin |>
  qq_plot(~ Ratio|Group) 

Let’s say we choose a non-parametric test to compare the groups:

wilcox.test(Ratio ~ Group, data = Hodgkin)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Ratio by Group
## W = 298, p-value = 0.007331
## alternative hypothesis: true location shift is not equal to 0

2.2 Graphical output

For relatively small samples (for example, less than 30 observations per group), it is a standard practice to show the actual data in dot plots with error bars. The pubh package offers two options to show graphically differences in continuous outcomes among groups:

• For small samples: strip_error
• For medium to large samples: bar_error

For our current example:

Hodgkin |>
  strip_error(Ratio ~ Group)

The error bars represent 95% confidence intervals around mean values.

Adding a line on top is relatively easy to show that the two groups are significantly different. The function gf_star needs the reference point on how to draw an horizontal line to display statistical differences or to annotate a plot; in summary, gf_star:

• Draws an horizontal line from \((x1, y2)\) to \((x2, y2)\).
• Draws a vertical line from \((x1, y1)\) to \((x1, y1)\).
• Draws a vertical line from \((x2, y1)\) to \((x2, y1)\).
• Writes a character (the legend or “star”) at the mid point between \(x1\) and \(x2\) at high \(y3\).

Thus:

\[ y1 < y2 < y3 \]

In our current example:

Hodgkin |>
  strip_error(Ratio ~ Group) |>
  gf_star(x1 = 1, y1 = 4, x2 = 2, y2 = 4.05, y3 = 4.1, "**")

For larger samples we could use bar charts with error bars. For example:

data(birthwt, package = "MASS")
birthwt <- birthwt |>
  mutate(
    smoke = factor(smoke, labels = c("Non-smoker", "Smoker")),
    Race = factor(race > 1, labels = c("White", "Non-white")),
    race = factor(race, labels = c("White", "Afican American", "Other"))
    ) |>
  var_labels(
    bwt = 'Birth weight (g)',
    smoke = 'Smoking status',
    race = 'Race',
  )

birthwt |>
  bar_error(bwt ~ smoke)

Quick normality check:

birthwt |>
  qq_plot(~ bwt|smoke)

The (unadjusted) \(t\)-test:

birthwt |> 
  t_test(bwt ~ smoke, detailed = TRUE) |> 
  as.data.frame()

##   estimate estimate1 estimate2 .y.     group1 group2  n1 n2 statistic     p
## 1 283.7767  3055.696  2771.919 bwt Non-smoker Smoker 115 74  2.729886 0.007
##         df conf.low conf.high method alternative
## 1 170.1002 78.57486  488.9786 T-test   two.sided

The final plot with annotation to highlight statistical difference (unadjusted):

birthwt |>
  bar_error(bwt ~ smoke) |>
  gf_star(x1 = 1, x2 = 2, y1 = 3400, y2 = 3500, y3 = 3550, "**")

Both strip_error and bar_error can generate plots stratified by a third variable, for example:

birthwt |>
  bar_error(bwt ~ smoke, fill = ~ Race) 

birthwt |>
  bar_error(bwt ~ smoke|Race)

birthwt |>
  strip_error(bwt ~ smoke, pch = ~ Race, col = ~ Race)