Hands-on Exercise 4d - Funnel Plots for Fair Comparisons

Published

January 29, 2024

Modified

February 24, 2024

4.1 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, we 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.

4.2 Installing and Launching R packages

In this exercise, four R packages will be used:

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)

4.3 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)

head(covid19)

# A tibble: 6 × 7
  `Sub-district ID` City        District `Sub-district` Positive Recovered Death
              <dbl> <fct>       <fct>    <fct>             <dbl>     <dbl> <dbl>
1        3172051003 JAKARTA UT… PADEMAN… ANCOL              1776      1691    26
2        3173041007 JAKARTA BA… TAMBORA  ANGKE              1783      1720    29
3        3175041005 JAKARTA TI… KRAMAT … BALE KAMBANG       2049      1964    31
4        3175031003 JAKARTA TI… JATINEG… BALI MESTER         827       797    13
5        3175101006 JAKARTA TI… CIPAYUNG BAMBU APUS         2866      2792    27
6        3174031002 JAKARTA SE… MAMPANG… BANGKA             1828      1757    26

4.4 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.

4.4.1 FunnelPlotR methods: The basic plot

The code below plots a funnel plot.

funnel_plot(
  numerator = covid19$Positive,
  denominator = covid19$Death,
  group = covid19$`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 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.

4.4.2 FunnelPlotR methods: Makeover 1

funnel_plot(
  numerator = covid19$Death,
  denominator = covid19$Positive,
  group = covid19$`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.

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.

4.4.3 FunnelPlotR methods: Makeover 2

funnel_plot(
  numerator = covid19$Death,
  denominator = covid19$Positive,
  group = covid19$`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 \nCOVID-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.

label = NA argument is removes 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.

4.5 Funnel Plot for Fair Visual comparison: ggplot2 methods

In this section, we will gain hands-on experience on building funnel plots step-by-step by using ggplot2.

4.5.1 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 below.

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

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

The code 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)

4.5.3 Plotting a static funnel plot

In the code below, ggplot2 functions are used to plot a static funnel plot.

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 = "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

4.5.4 Interactive Funnel Plot: plotly + ggplot2

We will make the previous plot interactive, using ggplotly() of plotly package.

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

4.6 References

Main reference: Kam, T.S. (2024). Funnel Plots for Fair Comparisons.