funnel_plot: Funnel plots for comparing institutional performance

Description Usage Arguments Details Value References Examples

View source: R/funnel_plot.R

Description

An implementation of funnel plots for indirectly standardised ratios, as described by Spiegelhalter (2005) <https://doi.org/10.1002/sim.1970>. There are several parameters for the input, with the assumption that you will want smooth, overdispersed, funnel control limits. Limits may be inflated for overdispersion based on the methods of DerSimonian & Laird (1986), buy calculating a between unit standard deviation (τ) and constructing an additive random effects models, originally used for meta-analyses of clinical trials data.

Usage

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funnel_plot(
  numerator,
  denominator,
  group,
  data_type = "SR",
  limit = 99,
  label = "outlier",
  highlight = NA,
  draw_unadjusted = FALSE,
  draw_adjusted = TRUE,
  sr_method = "SHMI",
  trim_by = 0.1,
  title = "Untitled Funnel Plot",
  multiplier = 1,
  x_label = "Expected",
  y_label,
  x_range = "auto",
  y_range = "auto",
  plot_cols = c("#FF7F0EFF", "#FF7F0EFF", "#1F77B4FF", "#1F77B4FF", "#9467BDFF",
    "#9467BDFF", "#2CA02CFF", "#2CA02CFF"),
  theme = funnel_clean(),
  label_outliers,
  Poisson_limits,
  OD_adjust,
  xrange,
  yrange
)

Arguments

numerator

A vector of the numerator (observed events/counts) values. Used as numerator of the Y-axis

denominator

A vector of denominator (predicted/population etc.) Used as denominator of the Y-axis and the scale of the x-axis

group

A vector of group names as character or factor. Used to aggregate and group points on plots

data_type

A string identifying the type of data used for in the plot, the adjustment used and the reference point. One of: "SR" for indirectly standardised ratios, such SHMI, "PR" for proportions, or "RC" for ratios of counts. Default is "SR".

limit

Plot limits, accepted values are: 95 or 99, corresponding to 95% or 99.8% quantiles of the distribution. Default=99,and applies to OD limits if both OD and Poisson are used.

label

Whether to label outliers, highlighted groups, both or none. Default is "outlier", by accepted values are:

  • "outlier" - Labels upper and lower outliers, determined in relation to the 'limit' argument.

  • "outlier_lower" - Labels just and lower outliers, determined in relation to the 'limit' argument.

  • "outlier_upper" - Labels just upper, determined in relation to the 'limit' argument.

  • "highlight" - Labels the value(s) given in the 'highlight'argument.

  • "both" - Labels both the highlighted values(s), upper and lower outliers, determined in relation to the 'limit' argument.

  • "both_lower" - Labels both the highlighted values(s) and lower outliers, determined in relation to the 'limit' argument.

  • "both_upper" - Labels both the highlighted values(s) and upper outliers, determined in relation to the 'limit' argument.

  • NA - No labels applied

highlight

Single or vector of points to highlight, with a different colour and point style. Should correspond to values specified to 'group'. Default is NA, for no highlighting.

draw_unadjusted

Draw control limits without overdispersion adjustment. (default=FALSE)

draw_adjusted

Draw overdispersed limits using hierarchical model, assuming at group level, as described in Spiegelhalter (2012). It calculates a second variance component ' for the 'between' standard deviation (τ), that is added to the 'within' standard deviation (sigma) (default=TRUE)

sr_method

Method for adjustment when using indirectly standardised ratios (type="SR") Either "CQC" or "SHMI" (default). There are a few methods for standardisation. "CQC"/Spiegelhalter uses a square-root transformation and Winsorises (rescales the outer most values to a particular percentile). SHMI, instead, uses log-transformation and doesn't Winsorise, but truncates the distribution before assessing overdisperison . Both methods then calculate a dispersion ratio (φ) on this altered dataset. This ratio is then used to scale the full dataset, and the plot is drawn for the full dataset.

trim_by

Proportion of the distribution for winsorisation/truncation. Default is 10 % (0.1). Note, this is applied in a two-sided fashion, e.g. 10% refers to 10% at each end of the distribution (20% winsorised/truncated)

title

Plot title

multiplier

Scale relative risk and funnel by this factor. Default to 1, but 100 sometime used, e.g. in some hospital mortality ratios.

x_label

Title for the funnel plot x-axis. Usually expected deaths, readmissions, incidents etc.

y_label

Title for the funnel plot y-axis. Usually a standardised ratio.

x_range

Manually specify the y-axis min and max, in form c(min, max), e.g. c(0, 200). Default, "auto", allows function to estimate range.

y_range

Manually specify the y-axis min and max, in form c(min, max), e.g. c(0.7, 1.3). Default, "auto", allows function to estimate range.

plot_cols

A vector of 8 colours for funnel limits, in order: 95% Poisson (lower/upper), 99.8% Poisson (lower/upper), 95% OD-adjusted (lower/upper), 99.8% OD-adjusted (lower/upper). Default has been chosen to avoid red and green which can lead to subconscious value judgements of good or bad. Default is hex colours: c("#FF7F0EFF", "#FF7F0EFF", "#1F77B4FF","#1F77B4FF", "#9467BDFF", "#9467BDFF", "#2CA02CFF", "#2CA02CFF")

theme

a ggplot theme function. This can be a canned theme such as theme_bw(), a theme() with arguments, or your own custom theme function. Default is new funnel_clean(), but funnel_classic() is original format.

label_outliers

Deprecated. Please use the 'label' argument instead.

Poisson_limits

Deprecated. Please use the 'draw_unadjusted' argument instead.

OD_adjust

Deprecated. Please use the 'draw_adjusted' argument instead.

xrange

Deprecated. Please use the 'x_range' argument instead.

yrange

Deprecated. Please use the 'y_range' argument instead.

Details

Outliers are marked based on the grouping, and the limits chosen, corresponding to either 95% or 99.8% quantiles of the normal distribution.
Labels can attached using the 'label' argument.
Overdispersion can be factored in based on the methods in Spiegelhalter et al. (2012), set 'draw_adjusted' to FALSE to suppress this.
To use Poisson limits set 'draw_unadjusted=TRUE'.
The plot colours deliberately avoid red-amber-green colouring, but you could extract this from the ggplot object and change manually if you like. Future versions of 'funnelplotr' may allow users to change this.

Value

A fitted 'funnelplot' object. A 'funnelplot' object is a list containing the following components:

print

Prints the number of points, outliers and whether the plot has been adjusted, and prints the plot

plot

A ggplot object with the funnel plot and the appropriate limits

limits_lookup

A lookup table with selected limits for drawing a plot in software that requires limits.

aggregated_data

A data.frame of the the aggregated dataset used for the plot.

outlier

A data frame of outliers from the data.

tau2

The between-groups standard deviation, τ^2.

phi

The dispersion ratio, φ.

draw_adjusted

Whether overdispersion-adjusted limits were used.

draw_unadjusted

Whether unadjusted Poisson limits were used.

References

DerSimonian & Laird (1986) <doi:10.1016/0197-2456(86)90046-2> Meta-analysis in clinical trials.

Spiegelhalter (2005) <doi:10.1002/sim.1970> Funnel plots for comparing institutional performance

Spiegelhalter et al. (2012) <doi:10.1111/j.1467-985X.2011.01010.x> Statistical methods for healthcare regulation: rating, screening and surveillance: <doi:10.1111/j.1467-985X.2011.01010.x>

NHS Digital (2020) SHMI Methodology v .134https://digital.nhs.uk/data-and-information/publications/clinical-indicators/shmi/current

Examples

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# We will use the 'medpar' dataset from the 'COUNT' package.
# Little reformatting needed

library(COUNT)
data(medpar)
medpar$provnum<-factor(medpar$provnum)
medpar$los<-as.numeric(medpar$los)

mod<- glm(los ~ hmo + died + age80 + factor(type)
      , family="poisson", data=medpar)

# Get predicted values for building ratio
medpar$prds<- predict(mod, type="response")

# Draw plot, returning just the plot object
fp<-funnel_plot(denominator=medpar$prds, numerator=medpar$los,
group = medpar$provnum, limit=95, title="An example funnel plot")

# Methods for viewing/extracting
print(fp)
plot(fp)
summary(fp)
limits(fp)
outliers(fp)
source_data(fp)
phi(fp)
tau2(fp)

FunnelPlotR documentation built on Sept. 30, 2021, 5:07 p.m.