Working with bivariate data in R

Contingency tables

• Consider an example of two treatment groups, e.g. Control group and Treatment group
• The patients are also classified according to the grade of disease, with grades I, II, and III
• The count for each of these can be expressed as in the code below using rbind()

# Row form using rbind()
rbind(c(22, 29), c(28, 23), c(27, 24))

##      [,1] [,2]
## [1,]   22   29
## [2,]   28   23
## [3,]   27   24

• In this example there are 77 patients in the control arm (sum of the first column) and 76 in the treatment arm (sum of the second column)
• The rows represent the three disease grades with 51 with grade I disease, 51 with grade II disease, and 51 with grade III disease (sums of the rows)
• The contingency tables expresses the division of the patients in the size possible groups
• The same can be achived with cbind() where each numeric vector will have its values expressed as a column

# Column form using cbind()
cbind(c(22, 28, 27), c(29, 23, 24))

##      [,1] [,2]
## [1,]   22   29
## [2,]   28   23
## [3,]   27   24

• Yet another way to create the same data is through the use of the matrix() command
  • The number of rows is specified
  • Default is to fill in the table column by column

matrix(c(22, 28, 27, 29, 23, 24),
       nrow = 3)

##      [,1] [,2]
## [1,]   22   29
## [2,]   28   23
## [3,]   27   24

• This can also be done row by row
• Note the change in the order of the values needed to achieve this

matrix(c(22, 29, 28, 23, 27, 24),
       byrow = TRUE,
       nrow = 3)

##      [,1] [,2]
## [1,]   22   29
## [2,]   28   23
## [3,]   27   24

• Storing the table as a computer variable allows for the addition of row and column names

contingencyTable <- matrix(c(22, 29, 28, 23, 27, 24),
                           byrow = TRUE,
                           nrow = 3)
rownames(contingencyTable) <- c("Grade I",
                                "Grade II",
                                "Grade III")
colnames(contingencyTable) <- c("Control",
                                "Treatment")
contingencyTable

##           Control Treatment
## Grade I        22        29
## Grade II       28        23
## Grade III      27        24

• Data in a data.frame can also be expressed as a contingency table

set.seed(123)
df <- data.frame(Grade = sample(c("Grade I",
                                  "Grade II",
                                  "Grade III"),
                                size = 153,
                                replace = TRUE),
                 Group = sample(c("Control",
                                  "Treatment"),
                                size = 153,
                                replace = TRUE))
head(df)

##       Grade     Group
## 1   Grade I   Control
## 2 Grade III   Control
## 3  Grade II   Control
## 4 Grade III Treatment
## 5 Grade III   Control
## 6   Grade I   Control

• Using the table() command

table(df$Grade,
      df$Group)

##            
##             Control Treatment
##   Grade I        22        29
##   Grade II       28        23
##   Grade III      27        24

Stacked bar chart

• A stacked bar chart is a simple way of visualizing the data

barplot(table(df$Grade,
             df$Group),
        legend.text = TRUE,
        main = "Number of patients with grade of disease (by treatment group)",
        xlab = "Treatment group",
        ylab = "Grade count",
        col = c("deepskyblue",
                "orange",
                "gray"),
        border = NA,
        las = 1)

• By changing the x and y axis values a transpose of the data can be visualized

barplot(table(df$Group,
              df$Grade),
        legend.text = TRUE,
        main = "Number of patients in each group (by grade of disease)",
        xlab = "Grade of disease",
        ylab = "Treatment group count",
        col = c("deepskyblue",
                "orange"),
        border = NA,
        las = 1)

Visualizing the data

• A scatter plot creates pairs of values for each row (patient)

plot(df$Temp,
     df$WCC,
     main = "Temperature vs white cell count",
     xlab = "Temperature (deg Celcius)",
     ylab = "White cell count",
     las = TRUE)