Contingency analysis: R code for Chapter 9 examples
Download the R code on this page as a single file here (make sure to install the “epitools” package before running).
New methods on this page
Click on a function argument for a short description of its meaning. The variable names are plucked from the examples further below.
Odds ratio using the epitools package:
oddsratio(, )
χ2 contingency test:
chisq.test(, , )
Fisher’s exact test:
fisher.test(, )
Other new methods:
Relative risk.
G-test.
Mosaic plot for a case-control study.
Figure 9.1-1. Sex and survival on the Titanic
Mosaic plot showing association between sex and survival on the shipwrecked Titanic.
Read and inspect the data.
titanic <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter09/chap09f1.1Titanic.csv"))
head(titanic)
Contingency table of the association between sex and survival. The addmargins function includes the row and columns sums with the contingency table.
titanicTable <- table(titanic$survival, titanic$sex) addmargins(titanicTable)
Mosaic plot of the association.
mosaicplot( t(titanicTable), col = c("firebrick", "goldenrod1"), cex.axis = 1,
sub = "Sex", ylab = "Relative frequency", main = "")
Example 9.2. Aspirin and cancer
Odds ratio and relative risk to estimate association between aspirin treatment and cancer incidence in a 2x2 contingency table.
Read and inspect the data.
cancer <- read.csv(url("http://whitlockschluter.zoology.ubc.ca/wp-content/data/chapter09/chap09e2AspirinCancer.csv"))
head(cancer)
2 x 2 contingency table showing association between aspirin treatment and cancer incidence (Table 9.2-1).
cancerTable <- table(cancer$cancer, cancer$aspirinTreatment) cancerTable
Mosaic plot showing the association (Figure 9.2-1).
mosaicplot( t(cancerTable), col = c("firebrick", "goldenrod1"), cex.axis = 1,
sub = "Aspirin treatment", ylab = "Relative frequency", main = "")
Calculate odds ratio using the epitools package. Install the package if you haven't already done so (this needs to be done just once per computer, after you've installed R). To use, load the epitools package (this needs to be done just once per R session).
install.packages("epitools", dependencies = TRUE)
library(epitools)
The formulas for the odds ratio and relative risk in the book assume that the contingency table has a layout exactly like cancerTable, namely
# treatment control # sick a b # healthy c d
This layout works for the oddsratio function.
oddsratio(cancerTable, method = "wald")
The resulting output of oddsratio includes a lot of incidental computations. To get clean output only for the odds ratio, including the 95% confidence interval, use the following instead.
oddsratio(cancerTable, method = "wald")$measure[-1,]
For step-by-step calculations of the odds ratio and confidence interval, see .
Calculate relative risk using the epitools package. The layout expected by the riskratio function is the complete opposite of the layout used in the book. To use the command with a contingency table in book style (such as cancerTable), we need to flip (transpose) the table and reverse the order of the rows. We can do this all at once with the following arguments to the riskratio function.
library(epitools) riskratio(t(cancerTable), rev = "both", method = "wald")
Notice that the result differs slightly from the relative risk value given in the book for these same data (1.007) because rounding error here is reduced.
For clean output only for the relative risk, including the 95% confidence interval, use the following command:
riskratio(t(cancerTable), method = "wald", rev = "both")$measure[-1,]
For step-by-step calculations of the relative risk, see .
Example 9.3. Toxoplasma and driving accidence
Odds ratio to estimate association between Toxoplasma infection and driving accidence in a 2 x 2 case-control study.
Read and inspect the data.
toxoplasma <- read.csv(url("http://whitlockschluter.zoology.ubc.ca/wp-content/data/chapter09/chap09e3ToxoplasmaAndAccidents.csv"))
head(toxoplasma)
2 x 2 contingency table (Table 9.3-1).
toxTable <- table(toxoplasma$accident, toxoplasma$condition) toxTable
Mosaic plot for a case-control study (Figure 9.3-1).
mosaicplot(toxTable, col=c("firebrick", "goldenrod1"), cex.axis = 1.2,
sub = "Condition", dir = c("h","v"), ylab = "Relative frequency")
Odds ratio using epitools.
library(epitools) oddsratio(toxTable, method = "wald") oddsratio(toxTable, method = "wald")$measure[-1,] # clean output
Example 9.4. Worm gets bird
χ2 contingency test to test association between trematode infection status of killifish and their fate (eaten or not eaten) in the presence of predatory birds.
Read and inspect the data.
worm <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter09/chap09e4WormGetsBird.csv"))
head(worm)
Set the preferred order of infection categories in tables and graphs.
worm$infection <- factor(worm$infection,
levels = c("uninfected", "lightly", "highly"))
Contingency table (Table 9.4-1 ). The addmargins function adds the row and column sums to the display of the table.
wormTable <- table(worm$fate, worm$infection) addmargins(wormTable)
Mosaic plot (Figure 9.4-1).
mosaicplot( t(wormTable), col = c("firebrick", "goldenrod1"), cex.axis = 1,
sub = "Infection status", ylab = "Relative frequency")
χ2 contingency test. We include the argument correct = FALSE to avoid Yates' correction. This has no effect except in 2 x 2 tables, but we keep it here for demonstration purposes.
saveChiTest <- chisq.test(worm$fate, worm$infection, correct = FALSE) saveChiTest
The expected frequencies under null hypothesis are included with the results, but aren't normally shown. Type saveChiTest$expected to extract them. Include the addmargins function if you want to see the row and column sums too.
addmargins(saveChiTest$expected)
G-test applied to the worm-gets-bird data (Section 9.6). R has no simple, built-in function to carry out the G-test with goodness-of-fit data. Code for a command g.test by Brent Larget is available here. Below, we source this code, which then allows you to use his function g.test.
source("http://www.stat.wisc.edu/~st571-1/gtest.R")
g.test(wormTable)
Example 9.5. Vampire bat feeding
Fisher's exact test of association between estrous status of cows and whether cows were bitten by vampire bats.
Read and inspect the data.
vampire <- read.csv(url("http://www.zoology.ubc.ca/~schluter/WhitlockSchluter/wp-content/data/chapter09/chap09e5VampireBites.csv"))
Contingency table (Table 9.5-1).
vampireTable <- table(vampire$bitten, vampire$estrous) vampireTable
Expected frequencies under null hypothesis of independence. R complains because of the violation of assumptions. Just in case you hadn't noticed.
saveTest <- chisq.test(vampire$bitten, vampire$estrous, correct = FALSE) saveTest$expected
Fisher's exact test. The output includes an estimate of the odds ratio, but it uses a different method than is used in our book.
fisher.test(vampire$bitten, vampire$estrous)
# First assign the labels a,b,c, and d to the table, as on page 240.
# Then plug the values into the formula for odds ratio
x = as.vector(cancerTable)
names(x) = c("a","c","b","d")
orHat = unname(x["a"] * x["d"]) / (x["b"] * x["c"])
unname(orHat)
# Standard error of log odds ratio
seLnOR = sqrt(1/x["a"] + 1/x["b"]+ 1/x["c"] + 1/x["d"])
unname(seLnOR)
# 95% confidence interval
Z = qnorm(1 - 0.05/2) # when rounded, is 1.96
ciLnOR = c(log(orHat) - Z * seLnOR, log(orHat) + Z * seLnOR)
ciOR = exp(ciLnOR) # transform back to ratio scale
names(ciOR) = c("lower","upper")
ciOR
x = as.vector(cancerTable)
names(x) = c("a","c","b","d")
phat1 = x["a"]/(x["a"] + x["c"])
phat2 = x["b"]/(x["b"] + x["d"])
rrHat = unname(phat1/phat2)
unname(rrHat)
# Standard error
seLnRR = sqrt( 1/x["a"] + 1/x["b"] - 1/(x["a"]+x["c"]) - 1/(x["b"]+x["d"]) )
unname(seLnRR)
# 95% confidence interval
Z = qnorm(1 - 0.05/2) # when rounded, is 1.96
ciLnRR = c(log(rrHat) - Z * seLnRR, log(rrHat) + Z * seLnRR)
ciRR = exp(ciLnRR) # transform back to ratio scale
names(ciRR) = c("lower","upper")
ciRR