Basic Usage

Overview

twoxtwo provides a collection of utilities for data analysis with two-by-two contingency tables. The functions in the package allow users to conveniently aggregate and summarize observation-level data as counts.

The two-by-two table is used in epidemiology to summarize count data by combinations of binary exposure and outcome variables as follows:

OUTCOME + OUTCOME -
EXPOSURE + A B
EXPOSURE - C D

The notation in the table above corresponds to:

• A = Exposed (Exposure “+”) and health indicator present (Outcome “+”)
• B = Exposed (Exposure “+”) and health indicator absent (Outcome “-”)
• C = Unexposed (Exposure “-”) and health indicator present (Outcome “+”)
• D = Unexposed (Exposure “-”) and health indicator absent (Outcome “-”)

The package allows for construction of two-by-two tables, as well as direct calculation of measures of effect and hypothesis testing to assess the relationship between the epidemiological exposure and outcome variables.

Creating a twoxtwo

The usage demonstration below requires that the twoxtwo and dplyr packages are loaded:

library(twoxtwo)
library(dplyr)

The data set used to illustrate the twoxtwo functions will be observation-level data describing smoking status (exposure) and high blood pressure (outcome). For this example, there will be 100 smokers and 200 non-smokers. Of the smokers, 40 will have high blood pressure. 50 of the non-smokers will have high blood pressure:

sh <-
tibble(
smoke = c(rep(TRUE, 100), rep(FALSE,200)),
hbp = c(rep(1,40),rep(0,60),rep(1,50),rep(0,150))
)
sh
# # A tibble: 300 x 2
#    smoke   hbp
#    <lgl> <dbl>
#  1 TRUE      1
#  2 TRUE      1
#  3 TRUE      1
#  4 TRUE      1
#  5 TRUE      1
#  6 TRUE      1
#  7 TRUE      1
#  8 TRUE      1
#  9 TRUE      1
# 10 TRUE      1
# # … with 290 more rows

The twoxtwo() constructor function will aggregate the observations to counts by exposure and outcome:

sh_2x2 <-
sh %>%
twoxtwo(., exposure = smoke, outcome = hbp)

The twoxtwo object is an S3 class. When printed to the console it will display the counts in the contingency table:

sh_2x2
# |         |            |OUTCOME |OUTCOME |
# |:--------|:-----------|:-------|:-------|
# |         |            |hbp=1   |hbp=0   |
# |EXPOSURE |smoke=TRUE  |40      |60      |
# |EXPOSURE |smoke=FALSE |50      |150     |

The object is a list with multiple elements, each of which can be extracted by name if needed.

For example, to view the aggregated counts as a tibble:

sh_2x2$tbl # # A tibble: 2 x 4 # hbp_1 hbp_0 exposure outcome # <dbl> <dbl> <chr> <chr> # 1 40 60 smoke::TRUE/FALSE hbp::1/0 # 2 50 150 smoke::TRUE/FALSE hbp::1/0 To view counts of each cell per the two-by-two notation: sh_2x2$cells
# $A #  40 # #$B
#  60
#
# $C #  50 # #$D
#  150

To view the exposure variable and its levels:

sh_2x2$exposure #$variable
#  "smoke"
#
# $levels #  "TRUE" "FALSE" To view the outcome variable and its levels: sh_2x2$outcome
# $variable #  "hbp" # #$levels
#  "1" "0"

To view the number of observations missing either exposure or outcome:

sh_2x2$n_missing #  0 And to view the original data (stored in the twoxtwo object by default1): sh_2x2$data
# # A tibble: 300 x 2
#    smoke   hbp
#    <lgl> <dbl>
#  1 TRUE      1
#  2 TRUE      1
#  3 TRUE      1
#  4 TRUE      1
#  5 TRUE      1
#  6 TRUE      1
#  7 TRUE      1
#  8 TRUE      1
#  9 TRUE      1
# 10 TRUE      1
# # … with 290 more rows

The S3 class has a summary method, which summarizes the count data and computes measures of effect (odds ratio, risk ratio, and risk difference). When the summary is printed it displays the count data, information about the twoxtwo object (missing data and exposure/outcome), as well as effect measures:

sh_2x2 %>%
summary(.)
#
# |         |            |OUTCOME |OUTCOME |
# |:--------|:-----------|:-------|:-------|
# |         |            |hbp=1   |hbp=0   |
# |EXPOSURE |smoke=TRUE  |40      |60      |
# |EXPOSURE |smoke=FALSE |50      |150     |
#
#
# Outcome: hbp
# Outcome + : 1
# Outcome - : 0
#
# Exposure: smoke
# Exposure + : TRUE
# Exposure - : FALSE
#
# Number of missing observations: 0
#
# Odds Ratio: 2 (1.198,3.338)
# Risk Ratio: 1.6 (1.139,2.247)
# Risk Difference: 0.15 (0.037,0.263)

When the summary is assigned to an object, it stores a named list with the effect measures:

sh_2x2_sum <-
sh_2x2 %>%
summary(.)
#
# |         |            |OUTCOME |OUTCOME |
# |:--------|:-----------|:-------|:-------|
# |         |            |hbp=1   |hbp=0   |
# |EXPOSURE |smoke=TRUE  |40      |60      |
# |EXPOSURE |smoke=FALSE |50      |150     |
#
#
# Outcome: hbp
# Outcome + : 1
# Outcome - : 0
#
# Exposure: smoke
# Exposure + : TRUE
# Exposure - : FALSE
#
# Number of missing observations: 0
#
# Odds Ratio: 2 (1.198,3.338)
# Risk Ratio: 1.6 (1.139,2.247)
# Risk Difference: 0.15 (0.037,0.263)
sh_2x2_sum
# $odds_ratio # # A tibble: 1 x 6 # measure estimate ci_lower ci_upper exposure outcome # <chr> <dbl> <dbl> <dbl> <chr> <chr> # 1 Odds Ratio 2 1.20 3.34 smoke::TRUE/FALSE hbp::1/0 # #$risk_ratio
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Ratio      1.6     1.14     2.25 smoke::TRUE/FALSE hbp::1/0
#
# \$risk_difference
# # A tibble: 1 x 6
#   measure         estimate ci_lower ci_upper exposure          outcome
#   <chr>              <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Difference     0.15   0.0368    0.263 smoke::TRUE/FALSE hbp::1/0
do.call("rbind", sh_2x2_sum)
# # A tibble: 3 x 6
#   measure         estimate ci_lower ci_upper exposure          outcome
# * <chr>              <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Odds Ratio          2      1.20      3.34  smoke::TRUE/FALSE hbp::1/0
# 2 Risk Ratio          1.6    1.14      2.25  smoke::TRUE/FALSE hbp::1/0
# 3 Risk Difference     0.15   0.0368    0.263 smoke::TRUE/FALSE hbp::1/0

Note that the measures of effect are only computed in the twoxtwo() summary if the “retain” argument is set to TRUE.

Calculating measures of effect

Individual measures of effect (odds ratio, risk ratio, and risk difference) can be calculated directly. Each measure includes the point estimate and confidence interval based on the $$\alpha$$ specified and standard error around the estimate. If the user passes a twoxtwo object into a data analysis function, the exposure and outcome will be inherited:

sh_2x2 %>%
odds_ratio()
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Odds Ratio        2     1.20     3.34 smoke::TRUE/FALSE hbp::1/0
sh_2x2 %>%
risk_ratio()
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Ratio      1.6     1.14     2.25 smoke::TRUE/FALSE hbp::1/0
sh_2x2 %>%
risk_diff()
# # A tibble: 1 x 6
#   measure         estimate ci_lower ci_upper exposure          outcome
#   <chr>              <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Difference     0.15   0.0368    0.263 smoke::TRUE/FALSE hbp::1/0

Alternatively, users can directly perform data analysis without first creating a twoxtwo object:

sh %>%
odds_ratio(., exposure = smoke, outcome = hbp, alpha = 0.05)
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Odds Ratio        2     1.20     3.34 smoke::TRUE/FALSE hbp::1/0
sh %>%
risk_ratio(., exposure = smoke, outcome = hbp, alpha = 0.05)
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Ratio      1.6     1.14     2.25 smoke::TRUE/FALSE hbp::1/0
sh %>%
risk_diff(., exposure = smoke, outcome = hbp, alpha = 0.05)
# # A tibble: 1 x 6
#   measure         estimate ci_lower ci_upper exposure          outcome
#   <chr>              <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Risk Difference     0.15   0.0368    0.263 smoke::TRUE/FALSE hbp::1/0

Hypothesis testing

As with measures of effect, hypothesis tests (Fisher’s exact test for count data and Pearson’s $$\chi^2$$ test) can be run on a twoxtwo:

sh_2x2 %>%
fisher()
# # A tibble: 1 x 9
#   test       estimate ci_lower ci_upper statistic df    pvalue exposure  outcome
#   <chr>         <dbl>    <dbl>    <dbl> <lgl>     <lgl>  <dbl> <chr>     <chr>
# 1 Fisher's …     2.00     1.16     3.44 NA        NA    0.0108 smoke::T… hbp::1…
sh_2x2 %>%
chisq()
# # A tibble: 1 x 9
#   test        estimate ci_lower ci_upper statistic    df pvalue exposure outcome
#   <chr>       <lgl>    <lgl>    <lgl>        <dbl> <int>  <dbl> <chr>    <chr>
# 1 Pearson's … NA       NA       NA            6.45     1 0.0111 smoke::… hbp::1…

Or without first creating a twoxtwo object:

sh %>%
fisher(., exposure = smoke, outcome = hbp)
# # A tibble: 1 x 9
#   test       estimate ci_lower ci_upper statistic df    pvalue exposure  outcome
#   <chr>         <dbl>    <dbl>    <dbl> <lgl>     <lgl>  <dbl> <chr>     <chr>
# 1 Fisher's …     2.00     1.16     3.44 NA        NA    0.0108 smoke::T… hbp::1…
sh %>%
chisq(., exposure = smoke, outcome = hbp)
# # A tibble: 1 x 9
#   test        estimate ci_lower ci_upper statistic    df pvalue exposure outcome
#   <chr>       <lgl>    <lgl>    <lgl>        <dbl> <int>  <dbl> <chr>    <chr>
# 1 Pearson's … NA       NA       NA            6.45     1 0.0111 smoke::… hbp::1…

Customizing orientation of twoxtwo

All processing of exposure and outcome requires that both variables must have only two levels. By default, variables are coerced to factors and reversed. The result is that, as in the example presented above, a value of TRUE or 1 will be oriented as exposure or outcome “+” and a corresponding value of FALSE or 0 will be oriented as exposure or outcome “-”.

The twoxtwo() constructor function is flexible enough to allow user-specified ordering via a named list passed to the “levels” argument:

sh %>%
twoxtwo(.,
exposure = smoke,
outcome = hbp,
levels = list(exposure = c(FALSE,TRUE), outcome = c(1,0)))
# |         |            |OUTCOME |OUTCOME |
# |:--------|:-----------|:-------|:-------|
# |         |            |hbp=1   |hbp=0   |
# |EXPOSURE |smoke=FALSE |50      |150     |
# |EXPOSURE |smoke=TRUE  |40      |60      |

As mentioned above, the twoxtwo() function is abstracted in other analysis functions. Each of these functions inherits all arguments that can be passed to twoxtwo, including the “levels” parameter:

sh %>%
odds_ratio(.,
exposure = smoke,
outcome = hbp,
levels = list(exposure = c(FALSE,TRUE), outcome = c(1,0)))
# # A tibble: 1 x 6
#   measure    estimate ci_lower ci_upper exposure          outcome
#   <chr>         <dbl>    <dbl>    <dbl> <chr>             <chr>
# 1 Odds Ratio      0.5    0.300    0.835 smoke::FALSE/TRUE hbp::1/0

1. Users can override this behavior with twoxtwo(..., retain = FALSE)↩︎