Hands-on_Ex04(4) - Funnel Plots for Fair Comparisons

Author

Hoa Nguyen Phuong

Modified

June 20, 2025

1 Overview

Funnel plot is a specially designed data visualisation for unbiased comparison between outlets, stores or business entities. We will learn the following in this chapter:

  • Plot funnel plots using funnelPlotR package
  • Plot static funnel plot with ggplot2 package
  • plot interactive funnel plot by using both plotly R and ggplot2 packages

2 Install and Launch R Packages

Four R packages will be used in this exercise:

  1. readr: import csv to R
  2. FunnerPlotR: create funnel plot
  3. ggplot2: create funner plot manually
  4. knitr: build static html table
  5. plotly: create interactive funner plot
pacman::p_load(tidyverse, FunnelPlotR, plotly, knitr)

3 Import Data

We use a new set of data for this exercise - COVID-19_DKI_Jakarta as of 31st July 2021 from Open Data Covid-19 Provinsi DKI Jakarta portal. In this exercise, we will compare the cumulative COVID-19 cases and death by sub-district (i.e. kelurahan).

First, we import the data into R and save it into a tibble data frame object called covid19.

covid19 <- read_csv("data/COVID-19_DKI_Jakarta.csv") %>%
  mutate_if(is.character, as.factor)
Sub-district ID City District Sub-district Positive Recovered Death
3172051003 JAKARTA UTARA PADEMANGAN ANCOL 1776 1691 26
3173041007 JAKARTA BARAT TAMBORA ANGKE 1783 1720 29
3175041005 JAKARTA TIMUR KRAMAT JATI BALE KAMBANG 2049 1964 31
3175031003 JAKARTA TIMUR JATINEGARA BALI MESTER 827 797 13
3175101006 JAKARTA TIMUR CIPAYUNG BAMBU APUS 2866 2792 27
3174031002 JAKARTA SELATAN MAMPANG PRAPATAN BANGKA 1828 1757 26

4 FunnelPlotR Methods

FunnelPlotR package uses ggplot to generate funner plots. It requires numerator (events of interest), denominator (population considered) and group. The key arguments selected for customisation are:

FunnelPlotR Installation

install.packages("FunnelPlotR")
  • limit: plot limits (95 or 99)
  • label_outliers: to label outliers (true or false)
  • Poisson_limits: to add Poisson limits to the plot
  • OD_adjust: to add overdispersed limits to the plot
  • xrange and yrange: to specify the range to display for axes, acts like a zoom function
  • Other aesthetic components, such as graph title, axis labels etc.

4.1 FunnelPlotR methods: Basic plot

The code below plots a funnel plot.

funnel_plot(
  .data = covid19,
  numerator = Death,
  denominator = Positive,
  group = `Sub-district`
)

A funnel plot object with 267 points of which 1 are outliers. 
Plot is adjusted for overdispersion.
Things to learn
  • group in this function is different from the scatterplot. Here is defines the level of the points to be plotted, ie., Sub-district, District or City. If City is chosen, there are only six data points.
  • By default, data_type argument is “SR”.
  • limit: Plot limits, accepted values are 95 or 99, corresponding to 95% or 99.8% quantiles of the distribution.

4.2 FunnelPlotR methods: Makeover 1

Adjust code to make over the previous plot.

Show the code 
funnel_plot(
  .data = covid19,
  numerator = Death,
  denominator = Positive,
  group = `Sub-district`,
  data_type = "PR",
  xrange = c(0, 6500),
  yrange = c(0, 0.05)
)

A funnel plot object with 267 points of which 7 are outliers. 
Plot is adjusted for overdispersion.
Things to learn from the code
  • +data_type argument is used to change from default “SR” to “PR” (i.e., proportions).
  • +xrange and yrange are used to set the range of x-axis and y-axis.

4.3 FunnelPlotR methods: Makeover 2

Makeover 2 is to add titles for x axis and y axis.

Show the code 
funnel_plot(
  .data = covid19,
  numerator = Death,
  denominator = Positive,
  group = `Sub-district`,
  data_type = "PR",
  xrange = c(0, 6500),
  yrange = c(0, 0.05),
  label = NA,
  title = "Cumulative COVID-19 Fatality Rate by \nCumulative Total Number of Postive Cases",
  x_label = "Cumulative COVID-19 Positive Cases",
  y_label = "Cumulative Fatality Rate",
  
)

A funnel plot object with 267 points of which 7 are outliers. 
Plot is adjusted for overdispersion.
Things to learn from code
  • label = NA argument is to remove the default label outliers feature.
  • title argument is used to add plot title.
  • x_label and y_label arguments are used to add/edit x-axis and y-axis titles.

5 Funnel Plot for Fair Visual Comparison: ggplot2 methods

In this exercise, we will build funnel plots step-by-step with ggplot2. This will enhance the skills using ggplot2 to customise specialised data visualisation like Funnel Plot.

5.1 Computing the basic derived fields

To plot the funnel plot from scratch:

  1. drive cumulative death rate
  2. standard error of cumulative death rate
df <- covid19 %>%
  mutate(rate = Death/Positive) %>%
  mutate(rate.se = sqrt((rate*(1-rate)) / (Positive))) %>%
  filter(rate > 0)
  1. fit.mean is computed by using the code below:
fit.mean <- weighted.mean(df$rate, 1/df$rate.se^2)

5.2 Calculate lower and upper limits for 95% and 99.9% CI

Next, we will compute the lower and upper limits for 95% Confidence Interval.

Show the code 
number.seq <- seq(1, max(df$Positive), 1)
number.ll95 <- fit.mean - 1.96 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ul95 <- fit.mean + 1.96 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ll999 <- fit.mean - 3.29 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
number.ul999 <- fit.mean + 3.29 * sqrt((fit.mean*(1-fit.mean)) / (number.seq))
dfCI <- data.frame(number.ll95, number.ul95, 
                   number.ll999, number.ul999,
                   number.seq, fit.mean)
Note

95% of the data falls within 1.96 standard deviations of the mean.

99.9% of the data falls within 3.29 standard deviations of the mean.

5.3 Plot a static funnel plot

Use the following code to plot a static funnel plot with ggplot2.

Show the code 
p <- ggplot(df, aes(x = Positive, y = rate)) +
  geom_point(aes(label = `Sub-district`),
             alpha = 0.4) +
  geom_line(data = dfCI,
            aes(x = number.seq,
                y = number.ll95),
            size = 0.4,
            colour = "skyblue",
            linetype = "dashed") +
  geom_line(data = dfCI,
            aes(x = number.seq,
                y = number.ul95),
            size = 0.4,
            colour = "skyblue",
            linetype = "dashed") +
  geom_line(data = dfCI,
            aes(x = number.seq,
                y = number.ll999),
            size = 0.4,
            colour = "skyblue") +
  geom_line(data = dfCI,
            aes(x = number.seq,
                y = number.ul999),
            size = 0.4,
            colour = 'skyblue') +
  geom_hline(data = dfCI,
             aes(yintercept = fit.mean),
             size = 0.4,
             colour = "grey40") +
  coord_cartesian(ylim=c(0, 0.05)) +
  annotate("text", x = 1, y = -0.13, label = "95%", size = 3, colour = "grey40") +
  annotate("text", x = 4.5, y = -0.18, label = "99%", size = 3, colour = "grey40") +
  ggtitle("Cumulative Fatality Rate by Cumulative Number of COVID-19 Cases") +
  xlab("Cumulative Number of COVID-19 Cases") +
  ylab("Cumulative Fatality Rate") +
  theme_light() +
  theme(plot.title = element_text(size = 12),
        legend.position = c(0.91, 0.85),
        legend.title = element_text(size = 7),
        legend.text = element_text(size = 7),
        legend.background = element_rect(colour = "grey60", linetype = "dotted"),
        legend.key.height = unit(0.3, "cm"))
p

5.4 Interactive funnel plot: plotly + ggplot2

to make the funnel plot interactive, we can use ggplot2 together with ggplotly() from plotly R package.

Show the code 
fp_ggplotly <- ggplotly(p,
                        tooltip = c("label",
                                    "x",
                                    "y"))
fp_ggplotly

6 References