Chapter 4 Tabulation

4.1 Introduction

R and its add-on packages provide several different tabulation functions with different capabilities. The appropriate function to use depends on your goal. There are at least three different uses for tables.

The first use is to create simple summary statistics that will be used for further calculations in R. For example, a two-by-two table created by the table function can be passed to fisher.test, which will calculate odds ratios and confidence intervals. The appearance of these tables may, however, be quite basic, as their principal goal is to create new objects for future calculations.

A quite different use of tabulation is to make production quality tables for publication. You may want to generate reports from for publication in paper form, or on the World Wide Web. The package xtable provides this capability, but it is not covered by this course.

An intermediate use of tabulation functions is to create human-readable tables for discussion within your work-group, but not for publication. The Epi package provides a function stat.table for this purpose, and this practical is designed to introduce this function.

4.2 The births data

We shall use the births data which concern 500 mothers who had singleton births in a large London hospital. The outcome of interest is the birth weight of the baby, also dichotomised as normal or low birth weight. These data are available in the Epi package:

library(Epi)
data(births)
names(births)
head(births)

In order to work with this data set we need to transform some of the variables into factors. This is done with the following commands:

births$hyp <- factor(births$hyp, labels = c("normal", "hyper"))
births$sex <- factor(births$sex, labels = c("M", "F"))
births$agegrp <- 
  cut(
    births$matage, 
    breaks = c(20, 25, 30, 35, 40, 45), 
    right = FALSE
  )
births$gest4 <- 
  cut(
    births$gestwks, 
    breaks = c(20, 35, 37, 39, 45), 
    right = FALSE
  )

Now use str(births) to examine the modified data frame. We have transformed the binary variables hyp and sex into factors with informative labels. This will help when displaying the tables. We have also created grouped variables agegrp and gest4 from the continuous variables matage and gestwks so that they can be tabulated.

4.3 One-way tables

The simplest table one-way table is created by

stat.table(index = sex, data = births)

This creates a count of individuals, classified by levels of the factor sex. Compare this table with the equivalent one produced by the table function. Note that stat.table has a data argument that allows you to use variables in a data frame without specifying the frame.

You can display several summary statistics in the same table by giving a list of expressions to the contents argument:

stat.table(
  index = sex, 
  contents = list(count(), percent(sex)), 
  data = births
)

Only a limited set of expressions are allowed: see the help page for stat.table for details.

You can also calculate marginal tables by specifying margin=TRUE in your call to stat.table. Do this for the above table. Check that the percentages add up to 100 and the total for count() is the same as the number of rows of the data frame births.

To see how the mean birth weight changes with sex, try

stat.table(index = sex, contents = mean(bweight), data = births)

Add the count to this table. Add also the margin with margin=TRUE.

As an alternative to bweight we can look at lowbw with

stat.table(index = sex, contents = percent(lowbw), data = births)

All the percentages are 100! To use the percent function the variable lowbw must also be in the index, as in

stat.table(
  index = list(sex, lowbw), 
  contents = percent(lowbw), 
  data = births
)

The final column is the percentage of babies with low birth weight by different categories of gestation.

  • Obtain a table showing the frequency distribution of gest4.
  • Show how the mean birth weight changes with gest4.
  • Show how the percentage of low birth weight babies changes with gest4.

Another way of obtaining the percentage of low birth weight babies by gestation is to use the ratio function:

stat.table(gest4, ratio(lowbw, 1, 100), data = births)

This only works because lowbw is coded 0/1, with 1 for low birth weight.

Tables of odds can be produced in the same way by using ratio(lowbw, 1-lowbw). The ratio function is also very useful for making tables of rates with (say) ratio(D,Y,1000) where D is the number of failures, and Y is the follow-up time. We shall return to rates in a later practical.

4.4 Improving the Presentation of Tables

The stat.table function provides default column headings based on the contents argument, but these are not always very informative. Supply your own column headings using tagged lists as the value of the contents argument, within a stat.table call:

stat.table(gest4, contents = list(
  N = count(),
  "(%)" = percent(gest4)
), data = births)

This improves the readability of the table. It remains to give an informative title to the index variable. You can do this in the same way: instead of giving gest4 as the index argument to stat.table, use a named list:

stat.table(index = list("Gestation time" = gest4), data = births)

4.5 Two-way Tables

The following call gives a \(2\times 2\) table showing the mean birth weight cross-classified by sex and hyp.

stat.table(
  list(sex, hyp), 
  contents = mean(bweight), 
  data = births
)

Add the count to this table and repeat the function call using margin = TRUE to calculate the marginal tables.

Use stat.table with the ratio function to obtain a \(2\times 2\) table of percent low birth weight by sex and hyp.

You can have fine-grained control over which margins to calculate by giving a logical vector to the margin argument. Use margin=c(FALSE, TRUE) to calculate margins over sex but not hyp. This might not be what you expect, but the margin argument indicates which of the index variables are to be marginalized out, not which index variables are to remain.

4.6 Printing

Just like every other R function, stat.table produces an object that can be saved and printed later, or used for further calculation. You can control the appearance of a table with an explicit call to print()

There are two arguments to the print method for stat.table. The width argument which specifies the minimum column width, and the digits argument which controls the number of digits printed after the decimal point. This table

odds.tab <- 
  stat.table(
    gest4, 
    list("odds of low bw" = ratio(lowbw, 1 - lowbw)),
    data = births
)
print(odds.tab)

shows a table of odds that the baby has low birth weight. Use width=15 and digits=3 and see the difference.