12 Funnel Plots for Fair Comparisons

Published

December 4, 2023

Modified

May 3, 2024

12.1 Overview

Funnel plot is a specially designed data visualisation for conducting unbiased comparison between outlets, stores or business entities. By the end of this hands-on exercise, you will gain hands-on experience on:

plotting funnel plots by using funnelPlotR package,
plotting static funnel plot by using ggplot2 package, and
plotting interactive funnel plot by using both plotly R and ggplot2 packages.

12.2 Installing and Launching R Packages

In this exercise, four R packages will be used. They are:

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)

12.3 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. For this hands-on exercise, we are going to compare the cumulative COVID-19 cases and death by sub-district (i.e. kelurahan) as at 31st July 2021, DKI Jakarta.

The code chunk below imports 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

12.4 FunnelPlotR methods

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

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.

12.4.1 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.

Things to learn from the code chunk above.

group in this function is different from the scatterplot. Here, it defines the level of the points to be plotted i.e. Sub-district, District or City. If Cityc is chosen, there are only six data points.
By default, data_typeargument is “SR”.
limit: Plot limits, accepted values are: 95 or 99, corresponding to 95% or 99.8% quantiles of the distribution.

12.4.2 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",     #<<
  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 chunk above. + 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

12.4.3 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",   
  xrange = c(0, 6500),  
  yrange = 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.

Things to learn from the code chunk above.

label = NA argument is to removed 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.

12.5 Funnel Plot for Fair Visual Comparison: ggplot2 methods

In this section, you will gain hands-on experience on building funnel plots step-by-step by using ggplot2. It aims to enhance you working experience of ggplot2 to customise speciallised data visualisation like funnel plot.

12.5.1 Computing the basic derived fields

To plot the funnel plot from scratch, we need to derive cumulative death rate and standard error of cumulative death rate.

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

Next, the fit.mean is computed by using the code chunk below.

fit.mean <- weighted.mean(df$rate, 1/df$rate.se^2)

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

The code chunk below is used to compute 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)

12.5.3 Plotting a static funnel plot

In the code chunk below, 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

12.5.4 Interactive Funnel Plot: plotly + ggplot2

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

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

12.6 References

funnelPlotR package.
Funnel Plots for Indirectly-standardised ratios.
Changing funnel plot options
ggplot2 package.