Mismatch between table output numbers and Venn diagram numbers

Question

I have the following R code, borrowed here, that generates a reproducible tibble table:

# Install/load packages only if needed
# ************************************
if (!require("pacman")) install.packages("pacman")
pacman::p_load(dplyr, expss, ggplot2, grid, purrr, rlang, tibble)

# Data Generation
# ***************

# Set the seed for reproducibility
set.seed(123)

# Generate random data
n <- 490
PTSD <- sample(c(1, 2, NA), n, replace = TRUE) #class(PTSD) = "numeric"
ANX <- sample(c(1, 2, NA), n, replace = TRUE) #class(ANX) = "numeric"
DEP <- sample(c(1, 2, NA), n, replace = TRUE) #class(DEP) = "numeric"

# Create the data frame
df <- data.frame(PTSD, ANX, DEP) #class(df) = "data.frame"

# Label the values: 1 = Low, 2 = High
expss::val_lab(df$PTSD) = expss::num_lab("1 Low\n2 High")
expss::val_lab(df$ANX) = expss::num_lab("1 Low\n2 High")
expss::val_lab(df$DEP) = expss::num_lab("1 Low\n2 High")

# Create a list of tables for each variable to count 1s, 2s, and NAs
count_results <- list(
  PTSD = table(df$PTSD, useNA = "ifany"),
  ANX = table(df$ANX, useNA = "ifany"),
  DEP = table(df$DEP, useNA = "ifany")
)

# Frequency count and data summary
# ********************************

# Combine the count tables into a single table
count_table <- do.call(rbind, count_results)

# Initialize empty vectors to store results
variable_names <- character()
sample_sizes <- numeric()

# Loop through the test results and extract relevant information
for (variable_name in names(count_results)) {
  sample_sizes <- c(sample_sizes, sum(count_results[[variable_name]]))
  variable_names <- c(variable_names, variable_name)
}

# Create summary data frame
summary_df <- data.frame(
  Variable = variable_names,
  N = sample_sizes
)

# Combine the count table and chi-squared summary table by columns
final_result <- cbind(count_table, summary_df)

# Remove Variable column in the middle of the table
final_result <- subset(final_result, select = -c(Variable))

# Combination of CMDs (CMD ≥ 1)
# *****************************

cmd <- c("PTSD","ANX","DEP")

combs <- map(seq_along(cmd),\(n)combn(cmd,n,simplify = FALSE)) |> purrr::flatten()

filts <- rlang::parse_exprs(map_chr(combs,\(x)paste0(x ,'== 2',collapse=' & ')))
filtsnames <- rlang::parse_exprs(map_chr(combs,\(x)paste0(x ,collapse=' + ')))
names(filts) <- filtsnames

output <- purrr::map_int(filts,\(x){
  df %>%
    mutate(id = row_number())%>%
    filter(!!(x))%>%
    summarise(
      n = n())
} |> pull(n)
)

tibble::enframe(output)

The output of the tibble table is supposed to show how many out of N = 490 have the following common mental disorders (CMDs), that is PTSD only, ANX only, DEP only, both PTSD and ANX, both PTSD and DEP, both ANX and DEP, and all 3 CMDs:

# A tibble: 7 × 2
  name             value
  <chr>            <int>
1 PTSD               167
2 ANX                156
3 DEP                156
4 PTSD + ANX          56
5 PTSD + DEP          52
6 ANX + DEP           51
7 PTSD + ANX + DEP    23

I wanted to visualise the table graphically so I thought about generating a Venn diagram. What I expected to see in the diagram is the following.

Expectation list:

• Intersection of all 3 = 23
• Intersection of ANX and DEP = 51
• Intersection of PTSD and DEP = 52
• Intersection of PTSD and ANX = 56
• DEP only = 156
• ANX only = 156
• PTSD only = 167

However, whilst none of the codes (examples below) generated any technical errors (i.e., R code errors) none of the packages I tried (VennDiagram and ggVennDiagram) showed the expected results (see Expectation list).

Here below are the 4 codes used to generate 4 different Venn diagrams, none of which gave the results outlined in Expectation list:

Using package VennDiagram Version 1

pacman::p_load(VennDiagram)

# Move to new plotting page
grid::grid.newpage()

# Calculate percentages
total_samples <- nrow(df)
percentages <- output / total_samples * 100

venn.plot <- VennDiagram::draw.triple.venn(
  area1 = output["PTSD"],
  area2 = output["ANX"],
  area3 = output["DEP"],
  n12 = output["PTSD + ANX"],
  n23 = output["ANX + DEP"],
  n13 = output["PTSD + DEP"],
  n123 = output["PTSD + ANX + DEP"],
  category = c("PTSD", "ANX", "DEP"),
  fill = c("red", "green", "blue"),
  lty = "blank",
  cex = rep(1.5,7),
  cat.cex = rep(1.5,3),
  cat.pos = c(-20,-40,-60),
  cat.dist = c(0.05,0.05,0.05),
  ind = TRUE,
  euler.d =TRUE,
)

grid.draw(venn.plot)

Using package VennDiagram 2

pacman::p_load(VennDiagram)

# Move to new plotting page
grid::grid.newpage()

# Use pre-calculated values from 'output'
VennDiagram::draw.triple.venn(
  area1 = output["PTSD"],
  area2 = output["ANX"],
  area3 = output["DEP"],
  n12 = output["PTSD + ANX"] + output["PTSD + ANX + DEP"], # Adjust for overlaps
  n23 = output["ANX + DEP"] + output["PTSD + ANX + DEP"], # Adjust for overlaps
  n13 = output["PTSD + DEP"] + output["PTSD + ANX + DEP"], # Adjust for overlaps
  n123 = output["PTSD + ANX + DEP"],
  category = c("PTSD", "ANX", "DEP"),
  col = "Red", fill = c("Green", "Yellow", "Blue"),
  cex = 1.5, cat.cex = 1.5, cat.pos = c(-20, 20, 180)
)

Using package VennDiagram 3

pacman::p_load(VennDiagram)

# Calculate exclusive counts for Venn diagram
ptsd_only <- output["PTSD"] - output["PTSD + ANX"] - output["PTSD + DEP"] + output["PTSD + ANX + DEP"]
anx_only <- output["ANX"] - output["PTSD + ANX"] - output["ANX + DEP"] + output["PTSD + ANX + DEP"]
dep_only <- output["DEP"] - output["PTSD + DEP"] - output["ANX + DEP"] + output["PTSD + ANX + DEP"]

ptsd_anx <- output["PTSD + ANX"] - output["PTSD + ANX + DEP"]
ptsd_dep <- output["PTSD + DEP"] - output["PTSD + ANX + DEP"]
anx_dep <- output["ANX + DEP"] - output["PTSD + ANX + DEP"]

ptsd_anx_dep <- output["PTSD + ANX + DEP"]

# Move to new plotting page
grid::grid.newpage()

# Create Venn diagram with 3 sets using adjusted values
VennDiagram::draw.triple.venn(
  area1 = ptsd_only,
  area2 = anx_only,
  area3 = dep_only,
  n12 = ptsd_anx,
  n23 = anx_dep,
  n13 = ptsd_dep,
  n123 = ptsd_anx_dep,
  category = c("PTSD", "ANX", "DEP"),
  col = "Red", fill = c("Green", "Yellow", "Blue"),
  cex = 1.5, cat.cex = 1.5, cat.pos = c(-20, 20, 180)
)

Using package ggVennDiagram

pacman::p_load(ggVennDiagram)

# Prepare data for Venn diagram
venn_data <- list(
  PTSD = which(df$PTSD == 2),
  ANX = which(df$ANX == 2),
  DEP = which(df$DEP == 2)
)

# Create Venn diagram with ggVennDiagram
ggVennDiagram(venn_data) +
  ggplot2::scale_fill_gradient(low = "white", high = "darkgrey") +
  theme_void()

---

My question: Short of drawing by hand the diagram, is there a way to generate a Venn diagram with R that reflects the same results as those found in the tibble table (see figure below)?

Conditions: The code that generates the tibble table (tibble::enframe(output)) should remain the same. The Venn diagram should reflect the results of the tibble table.

Caveat: Perhaps I am missing the point about Venn diagram and what they represent...

Answer 1

For the draw.triple.venn function, you need to add the individual totals to get the correct sizes of the sets. Try the following:

venn.plot <- VennDiagram::draw.triple.venn(
  area1 = output["PTSD"]+output["PTSD + ANX"]+output["PTSD + DEP"]+output["PTSD + ANX + DEP"],
  area2 = output["ANX"]+output["PTSD + ANX"]+output["ANX + DEP"]+output["PTSD + ANX + DEP"],
  area3 = output["DEP"]+output["ANX + DEP"]+output["PTSD + DEP"]+output["PTSD + ANX + DEP"],
  n12 = output["PTSD + ANX"]+output["PTSD + ANX + DEP"],
  n23 = output["ANX + DEP"]+output["PTSD + ANX + DEP"],
  n13 = output["PTSD + DEP"]+output["PTSD + ANX + DEP"],
  n123 = output["PTSD + ANX + DEP"],
  category = c("PTSD", "ANX", "DEP"),
  fill = c("red", "green", "blue"),
  lty = "blank",
  #cex = rep(1.5,7),
  cat.cex = rep(1.5,3),
  #cat.pos = c(-20,-40,-60),
  #cat.dist = c(0.05,0.05,0.05),
  ind = TRUE,
  euler.d =TRUE
)

---

---

If you want to start with the raw data, then you can skip the calculations.

# Create a list for each column, and determine `which` rows have values>=1. 
df.lst <- lapply(as.list(df), \(x) which(x>=1))

venn.diagram(df.lst, filename = 'Venn_3set_simple.tiff')

---

This differs from the expected, probably due to the way you calculated the totals and intersections.

Answer 2

Here is a straightforward way to draw a Venn diagram representing when these disorders are High.

library(dplyr)
library(ggplot2)
library(ComplexUpset)

set.seed(123)

# Generate random data
n <- 490
PTSD <- sample(c(1, 2, NA), n, replace = TRUE) #class(PTSD) = "numeric"
ANX <- sample(c(1, 2, NA), n, replace = TRUE) #class(ANX) = "numeric"
DEP <- sample(c(1, 2, NA), n, replace = TRUE) #class(DEP) = "numeric"

# Create the data frame

disorders <- c('PTSD', 'ANX', 'DEP')
df <- data.frame(PTSD, ANX, DEP)

# Create boolean indicators where "High" == TRUE
df[disorders] = df[disorders] == 2

# Either drop rows with NA
# df = na.omit(df)

# or impute missing values
df[is.na(df)] <- FALSE

glimpse(df)
#> Rows: 490
#> Columns: 3
#> $ PTSD <lgl> FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, FALSE, FALSE,…
#> $ ANX  <lgl> TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALS…
#> $ DEP  <lgl> FALSE, TRUE, FALSE, FALSE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE,…

ggplot() +
  theme_void() +
  coord_fixed() +
  geom_venn_circle(df, sets = disorders, size = 1) +
  geom_venn_label_set(df, sets = disorders, aes(label = region), outwards_adjust = 2) +
  geom_venn_label_region(df, sets = disorders, aes(label = size))

The intersection sizes here don't match your list of expectations because you misdefine them

Intersection of all 3 = 23 

Correct

Intersection of ANX and DEP = 51
Intersection of PTSD and DEP = 52
Intersection of PTSD and ANX = 56

Only if you include those 23 where all disorders are high

DEP only = 156
ANX only = 156
PTSD only = 167

None of these match the number of rows where only that disorder is high. Compare the results in the Venn diagrams with a table of counts.

df |>
  count(PTSD, ANX, DEP)
#>    PTSD   ANX   DEP   n
#> 1 FALSE FALSE FALSE 147
#> 2 FALSE FALSE  TRUE  76
#> 3 FALSE  TRUE FALSE  72
#> 4 FALSE  TRUE  TRUE  28
#> 5  TRUE FALSE FALSE  82
#> 6  TRUE FALSE  TRUE  29
#> 7  TRUE  TRUE FALSE  33
#> 8  TRUE  TRUE  TRUE  23