Visualising the density of two prior distributions for the heterogeneity parameter

Creating the density plot of two prior distributions for the between-study variance (log-normal and location-scale t distributions) or between-study standard deviation (half-normal distribution).

Usage

heter_density_plot(
  distr,
  heter_prior1,
  heter_prior2,
  heter1 = "tau",
  heter2 = "tau",
  caption = FALSE,
  x_axis_name = TRUE,
  y_axis_name = TRUE,
  title_name = NULL,
  axis_title_size = 13,
  axis_text_size = 13,
  legend_title_size = 13,
  legend_text_size = 13
)

Arguments

distr: Character string indicating the prior distribution. Set distr equal to one of the following: "lognormal", "logt", or "halfnormal", which refers to a log-normal, location-scale, or half-normal distribution, respectively.
heter_prior1: A numeric vector with two values for the first prior distribution: 1) the mean value and 2) the standard deviation. When distr = "halfnormal", the first value should zero and the second a non-negative value referring to the scale parameter of the distribution.
heter_prior2: A numeric vector with two values for the second prior distribution: 1) the mean value and 2) the standard deviation. When distr = "halfnormal", the first value should zero and the second a non-negative value referring to the scale parameter of the distribution.
heter1: Character string indicating the heterogeneity parameter for heter_prior1. Set heter1 equal to one of the following: "tau", or "tau_omega", which refers to a between-study heterogeneity or between-design heterogeneity (inconsistency), respectively. This argument is relevant only when distr = "lognormal" or distr = "logt". The default is "tau".
heter2: Character string indicating the heterogeneity parameter for heter_prior2. Set heter2 equal to one of the following: "tau", or "tau_omega", which refers to a between-study heterogeneity or between-design heterogeneity (inconsistency), respectively. This argument is relevant only when distr = "lognormal" or distr = "logt". The default is "tau".
caption: Logical to indicate whether to report a caption at the bottom right of the plot. It is relevant only when distr = "lognormal" and distr = "logt". The default is FALSE (do not report).
x_axis_name: Logical to indicate whether to present the title of x-axis ('Between-study standard deviation'). The default is TRUE (report).
y_axis_name: Logical to indicate whether to present the title of y-axis ('Density'). The default is TRUE (report).
title_name: Text for the title of the plot. title_name determines the labs argument of the R-package ggplot2.
axis_title_size: A positive integer for the font size of axis title. axis_title_size determines the axis.title argument found in the theme's properties in the R-package ggplot2. The default option is 13.
axis_text_size: A positive integer for the font size of axis text. axis_text_size determines the axis.text argument found in the theme's properties in the R-package ggplot2. The default option is 13.
legend_title_size: A positive integer for the font size of legend title. legend_text_size determines the legend.text argument found in the theme's properties in the R-package ggplot2. The default option is 13.
legend_text_size: A positive integer for the font size of legend text. legend_text_size determines the legend.text argument found in the theme's properties in the R-package ggplot2. The default option is 13.

Value

A plot with the density of two selected prior distributions for the heterogeneity parameter. Two different colours are used to discern the distributions. A legend is also created with the name and hyper-parameters of the selected prior distributions. The filled area under each curved indicates the values up to the median of the corresponding distribution. The x-axis present the 0.1

heter_density_plot also returns a table with the percentiles of each distribution.

Details

Use this function to inspect the shape of the distribution and the range of between-study variance or standard deviation values before you define the argument heter_prior in run_model) to run random-effects network meta-analysis.

Turner et al. (2012), Turner et al. (2015), and Rhodes et al. (2016) provide predictive prior distributions for the between-study variance for a binary outcome, measured in the log-odds ratio scale, and a continuous outcome, measured in the standardised mean difference scale, respectively.

References

Rhodes KM, Turner RM, Higgins JP. Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data. J Clin Epidemiol 2015;68(1):52–60. doi: 10.1016/j.jclinepi.2014.08.012

Turner RM, Jackson D, Wei Y, Thompson SG, Higgins JP. Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis. Stat Med 2015;34(6):984–98. doi: 10.1002/sim.6381

Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JP. Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews. Int J Epidemiol 2012;41(3):818–27. doi: 10.1093/ije/dys041

Author

Loukia M. Spineli

Examples


if (FALSE) { # \dontrun{
## Two empirical priors for between-study variance of log odds ratio.
heter_density_plot(distr = "lognormal",
                   heter_prior1 = c(-2.56, 1.74),  # General healthcare setting
                   heter_prior2 = c(-1.83, 1.52))  # Pain and pharma vs. placebo/ctrl

## Two empirical priors for between-study variance of standardised mean
## difference.
heter_density_plot(distr = "logt",
                   heter_prior1 = c(-3.44, 2.59),  # General healthcare setting
                   heter_prior2 = c(-0.60, 2.61))  # Pain and pharma vs. placebo/ctrl for cancer

## Two half-normal prior distributions for between-study standard deviation
heter_density_plot(distr = "halfnormal",
                   heter_prior1 = c(0, 1),
                   heter_prior2 = c(0, 0.5))
} # }