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tables for discussion within your work-group, but not for publication.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:
## [1] "id" "bweight" "lowbw" "gestwks" "preterm" "matage" "hyp"
## [8] "sex"## id bweight lowbw gestwks preterm matage hyp sex
## 1 1 2974 0 38.52 0 34 0 2
## 2 2 3270 0 NA NA 30 0 1
## 3 3 2620 0 38.15 0 35 0 2
## 4 4 3751 0 39.80 0 31 0 1
## 5 5 3200 0 38.89 0 33 1 1
## 6 6 3673 0 40.97 0 33 0 2In 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
## --------------
## sex count()
## --------------
## M 264
## F 236
## --------------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:
## ---------------------------
## sex count() percent(sex)
## ---------------------------
## M 264 52.8
## F 236 47.2
## ---------------------------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.
## -----------------------------
## sex count() percent(sex)
## -----------------------------
## M 264 52.8
## F 236 47.2
##
## Total 500 100.0
## -----------------------------To see how the mean birth weight changes with sex, try
## --------------------
## sex mean(bweight)
## --------------------
## M 3229.90
## F 3032.83
## --------------------Add the count to this table. Add also the margin with margin=TRUE.
## ------------------------------
## sex count() mean(bweight)
## ------------------------------
## M 264 3229.90
## F 236 3032.83
##
## Total 500 3136.88
## ------------------------------As an alternative to bweight we can look at lowbw with
## ---------------------
## sex percent(lowbw)
## ---------------------
## M 100.0
## F 100.0
## ---------------------All the percentages are 100! To use the percent function the variable lowbw must also be in the index, as in
## ----------------------
## ------lowbw------
## sex 0 1
## ----------------------
## M 89.8 10.2
## F 86.0 14.0
## ----------------------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.
## ------------------
## gest4 count()
## ------------------
## [20,35) 31
## [35,37) 32
## [37,39) 167
## [39,45) 260
## ------------------## ------------------------
## gest4 mean(bweight)
## ------------------------
## [20,35) 1733.74
## [35,37) 2590.31
## [37,39) 3093.77
## [39,45) 3401.26
## ------------------------## ----------------------------------------
## --------------gest4--------------
## lowbw [20,35) [35,37) [37,39) [39,45)
## ----------------------------------------
## 0 19.4 59.4 89.2 98.8
## 1 80.6 40.6 10.8 1.2
## ----------------------------------------Another way of obtaining the percentage of low birth weight babies by gestation is to use the ratio function:
## -----------------------
## gest4 ratio(lowbw,
## 1, 100)
## -----------------------
## [20,35) 80.65
## [35,37) 40.62
## [37,39) 10.78
## [39,45) 1.15
## -----------------------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:
## --------------------------
## gest4 N (%)
## --------------------------
## [20,35) 31 6.3
## [35,37) 32 6.5
## [37,39) 167 34.1
## [39,45) 260 53.1
## --------------------------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:
## --------------------
## Gestation count()
## time
## --------------------
## [20,35) 31
## [35,37) 32
## [37,39) 167
## [39,45) 260
## --------------------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.
## ----------------------
## -------hyp-------
## sex normal hyper
## ----------------------
## M 3310.75 2814.40
## F 3079.50 2699.72
## ----------------------Add the count to this table and repeat the function call using margin = TRUE to calculate the
marginal tables.
## --------------------------------
## -----------hyp-----------
## sex normal hyper Total
## --------------------------------
## M 221 43 264
## 3310.75 2814.40 3229.90
##
## F 207 29 236
## 3079.50 2699.72 3032.83
##
##
## Total 428 72 500
## 3198.90 2768.21 3136.88
## --------------------------------Use stat.table with the ratio function to obtain a \(2\times 2\) table of percent low birth weight by sex and hyp.
## --------------------------------
## -----------hyp-----------
## sex normal hyper Total
## --------------------------------
## M 221 43 264
## 3310.75 2814.40 3229.90
##
## F 207 29 236
## 3079.50 2699.72 3032.83
##
##
## Total 428 72 500
## 3198.90 2768.21 3136.88
## --------------------------------## --------------------------------
## -----------hyp-----------
## sex normal hyper Total
## --------------------------------
## M 221 43 264
## 6.79 27.91 10.23
##
## F 207 29 236
## 12.08 27.59 13.98
##
##
## Total 428 72 500
## 9.35 27.78 12.00
## --------------------------------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)## ------------------
## gest4 odds of
## low bw
## ------------------
## [20,35) 4.17
## [35,37) 0.68
## [37,39) 0.12
## [39,45) 0.01
## ------------------shows a table of odds that the baby has low birth weight. Use
width=15 and digits=3 and see the difference.
## --------------------------
## gest4 odds of low bw
## --------------------------
## [20,35) 4.167
## [35,37) 0.684
## [37,39) 0.121
## [39,45) 0.012
## --------------------------