Hands-on Exercise 4.4 - Funnel Plots for Fair Comparisons

Author

Nguyen Nguyen Ha (Summer)

Published

May 6, 2025

Modified

May 6, 2025

1. Overview

A funnel plot is a specialized data visualization tool designed for making unbiased comparisons between outlets, stores, or business entities. This hands-on exercise provides practical experience in:

  • Creating funnel plots using the funnelPlotR package.

  • Generating static funnel plots with ggplot2.

  • Developing interactive funnel plots by combining plotly and ggplot2.

2. Installing and Launching R Packages

For this exercise, we will use four R packages as below:

  • readr for importing csv into R.

  • FunnelPlotR for creating funnel plot.

  • ggplot2 for creating funnel plot manually.

  • knitr for building static html table.

  • plotly for creating interactive funnel plot.

pacman::p_load(tidyverse, FunnelPlotR, plotly, knitr)

3. Importing Data

In this section, COVID-19_DKI_Jakarta will be used. The data was downloaded from Open Data Covid-19 Provinsi DKI Jakarta portal. We are going to compare the cumulative COVID-19 cases and death by sub-district (i.e. kelurahan) as of 31st July 2021, DKI Jakarta.

The code chunk below imports the data into R and save it into a tibble data frame called covid19.

covid19 <- read_csv("data/COVID-19_DKI_Jakarta.csv") %>%
  mutate_if(is.character, as.factor)

4. FunnelPlotR methods

The funnelPlotR package utilizes ggplot2 to generate funnel plots. It requires three key inputs:

  • Numerator: The number of events of interest.

  • Denominator: The total population being considered.

  • Group: The categorical grouping variable.

Key customization options include:

  • limit: Specifies plot limits (e.g., 95% or 99% confidence limits).

  • label_outliers: Determines whether outliers should be labeled (TRUE or FALSE).

  • Poisson_limits: Adds Poisson confidence limits to the plot.

  • OD_adjust: Applies overdispersion-adjusted limits.

  • xrange & yrange: Defines the display range for axes, acting as a zoom function.

  • Aesthetic components: Customizations such as graph title, axis labels, and other stylistic elements.

4.1. FunnelPlotR methods: The basic plot

The code chunk below plots a funnel plot.

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

A funnel plot object with 267 points of which 0 are outliers. 
Plot is adjusted for overdispersion.

Key Takeaways from the Code Chunk:

  • Group Definition: Unlike in a scatterplot, the group argument here determines the level at which data points are plotted (e.g., Sub-district, District, or City). If “City” is selected, only six data points will be displayed.

  • Data Type: The data_type argument defaults to "SR".

  • Plot Limits (limit): Defines confidence limits for the funnel plot. Acceptable values are 95 (95% confidence interval) or 99 (99.8% confidence interval).

4.2. FunnelPlotR methods: Makeover 1

The code chunk below plots a funnel plot.

funnel_plot(
  .data = covid19,
  numerator = Death,
  denominator = Positive,
  group = `Sub-district`,
  data_type = "PR",     #<<
  x_range = c(0, 6500),  #<<
  y_range = c(0, 0.05)   #<<
)

A funnel plot object with 267 points of which 7 are outliers. 
Plot is adjusted for overdispersion.

Key takeaways from the above code chunk:

  • 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

The code chunk below plots a funnel plot.

funnel_plot(
  .data = covid19,
  numerator = Death,
  denominator = Positive,
  group = `Sub-district`,
  data_type = "PR",   
  x_range = c(0, 6500),  
  y_range = c(0, 0.05),
  label = NA,
  title = "Cumulative COVID-19 Fatality Rate by Cumulative Total Number of COVID-19 Positive 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.

Key arguments from the above code chunk:

  • label = NA removes the default label outliers feature.

  • title adds plot title.

  • x_label and y_label add/edit x-axis and y-axis titles.

5. Funnel Plot for Fair Visual Comparison: ggplot2 methods

In this section, we explore how to build funnel plots step-by-step using ggplot2.

5.1. Computing the basic derived fields

First we derive cumulative death rate and standard error of cumulative death rate using below code chunk.

df <- covid19 %>%
  mutate(rate = Death / Positive) %>%
  mutate(rate.se = sqrt((rate*(1-rate)) / (Positive))) %>%
  filter(rate > 0)

Next, fit.mean is computed using the code chunk 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

The below code chunk below computes the lower and upper limits for 95% confidence interval.

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)

5.3. Plotting a static funnel plot

The code chunk below uses ggplot2 functions are used to plot a static funnel plot.

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 = "grey40", 
            linetype = "dashed") +
  geom_line(data = dfCI, 
            aes(x = number.seq, 
                y = number.ul95), 
            size = 0.4, 
            colour = "grey40", 
            linetype = "dashed") +
  geom_line(data = dfCI, 
            aes(x = number.seq, 
                y = number.ll999), 
            size = 0.4, 
            colour = "grey40") +
  geom_line(data = dfCI, 
            aes(x = number.seq, 
                y = number.ul999), 
            size = 0.4, 
            colour = "grey40") +
  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

The funnel plot created using ggplot2 functions can be made interactive with ggplotly() of plotly package.

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

6. References