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

Author

Vanessa Heng

Published

January 28, 2024

Modified

March 1, 2024

1 Overview

This exercise aims to gain hands-on experience in plotting funnel plots which are specially designed data visualisations for conducting unbiased comparison between outlets, stores or business entities by

  • 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.

2 Getting Started

2.1 Installing and loading the packages

For this exercise, the following R packages will be used, they are:

  • tidyverse, a family of R packages for data science processes,

  • plotly for creating interactive plot

  • FunnelPlotR for creating funnel plot.

  • knitr for building static html table.

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

2.2 Data import

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 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.

covid19 <- read_csv("data/COVID-19_DKI_Jakarta.csv") %>%
  mutate_if(is.character, as.factor)
covid19 
# A tibble: 267 × 7
   `Sub-district ID` City       District `Sub-district` Positive Recovered Death
               <dbl> <fct>      <fct>    <fct>             <dbl>     <dbl> <dbl>
 1        3172051003 JAKARTA U… PADEMAN… ANCOL              1776      1691    26
 2        3173041007 JAKARTA B… TAMBORA  ANGKE              1783      1720    29
 3        3175041005 JAKARTA T… KRAMAT … BALE KAMBANG       2049      1964    31
 4        3175031003 JAKARTA T… JATINEG… BALI MESTER         827       797    13
 5        3175101006 JAKARTA T… CIPAYUNG BAMBU APUS         2866      2792    27
 6        3174031002 JAKARTA S… MAMPANG… BANGKA             1828      1757    26
 7        3175051002 JAKARTA T… PASAR R… BARU               2541      2433    37
 8        3175041004 JAKARTA T… KRAMAT … BATU AMPAR         3608      3445    68
 9        3171071002 JAKARTA P… TANAH A… BENDUNGAN HIL…     2012      1937    38
10        3175031002 JAKARTA T… JATINEG… BIDARA CINA        2900      2773    52
# ℹ 257 more rows

3 Fair Visual Comparisons

3.1 Fair Visual Comparisons using 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.

The following basic plot shows a funnel plot object with 267 points of which 0 are outliers. Plot is adjusted for over-dispersion.

Show the code 
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.
Note

  • 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” (indirectly standardised ratios). Other options: “PR” for proportions, or “RC” for ratios of counts.

  • limit: Plot limits, accepted values are: 95 or 99, corresponding to 95% or 99.8% quantiles of the distribution.

The following funnel plot object has 267 points of which 7 are outliers. Plot is adjusted for over-dispersion.

Show the code 
funnel_plot(
  numerator = covid19$Death,
  denominator = covid19$Positive,
  group = covid19$`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.
Note
  • data_type argument is used to change from default “SR” to “PR” (i.e. proportions).
  • x_range and y_range are used to set the range of x-axis and y-axis
Show the code 
funnel_plot(
    numerator = covid19$Death,
    denominator = covid19$Positive,
    group = covid19$`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 \nCumulative 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.
Note

  • 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.

3.2 Fair Visual Comparisons using ggplot2 methods

We can also build 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.

We need to create some statistics from the data first by deriving 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)
fit.mean <- weighted.mean(df$rate, 1/df$rate.se^2)

Compute the upper and lower 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)
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 = "darkblue") +
  geom_line(data = dfCI, 
            aes(x = number.seq, y = number.ul999), 
            size = 0.4, 
            colour = "darkblue") +
  geom_hline(data = dfCI, 
             aes(yintercept = fit.mean), 
             linewidth = 0.4, 
             colour = "darkred") +
  coord_cartesian(ylim=c(0,0.05)) +
  labs(title = "Cumulative Fatality Rate by Cumulative Number of COVID-19 Cases",
       x = "Cumulative Number of COVID-19 Cases", 
       y = "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")) +
  annotate("text", x = 100, y = 0.03, label = "95%", size = 3, colour = "red") + 
  annotate("text", x = 600, y = 0.035, label = "99%", size = 3, colour = "red")

p

Use ggplotly to make the chart interactive.

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