Density plots of local inconsistency results and Kullback-Leibler divergence when 'rnmamod', 'netmeta' or 'gemtc' R packages are used

A panel of density plots on the direct and indirect estimates of the selected comparisons based on approach for local inconsistency evaluation, such as back-calculation and node-splitting approaches (Dias et al., 2010; van Valkenhoef et al., 2016) and loop-specific approach (Bucher et al., 1997) accompanied by the average Kullback-Leibler divergence. Additionally, stacked bar plots on the percentage contribution of either Kullback-Leibler divergence (from direct to indirect, and vice-versa) to the total information loss for each selected comparison are presented. The function handles results also from the R-packages gemtc and netmeta.

Usage

kld_inconsistency(
  node,
  threshold = 1e-05,
  drug_names = NULL,
  outcome = NULL,
  scales = "free",
  show_incons = TRUE,
  y_axis_name = TRUE,
  title_name = NULL,
  axis_title_size = 13,
  axis_text_size = 13,
  text_size = 3.5,
  strip_text_size = 13,
  legend_title_size = 13,
  legend_text_size = 13,
  str_wrap_width = 10
)

Arguments

node: An object of S3 class run_nodesplit or class mtc.nodesplit (see gemtc) or class netsplit (see netmeta).
threshold: A positive number indicating the threshold of not concerning inconsistency, that is, the minimally allowed deviation between the direct and indirect estimates for a split node that does raise concerns for material inconsistency. The argument is optional.
drug_names: A vector of labels with the name of the interventions in the order they appear in the argument data. It is not relevant for gemtc and netmeta.
outcome: Optional argument to describe the effect measure used (the x-axis of the plots).
scales: A character on whether both axes should be fixed ("fixed") or free ("free") or only one of them be free ("free_x" or "free_y"). scales determines the scales argument found in function (facet_wrap) in the R-package ggplot2. The default is ("free").
show_incons: Logical to indicate whether to present the point estimate and 95 (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.
text_size: A positive integer for the font size of labels. text_size determines the size argument found in the geom_text function in the R-package ggplot2. The default option is 3.5.
strip_text_size: A positive integer for the font size of facet labels. 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_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.
str_wrap_width: A positive integer for wrapping the axis labels in the percent stacked bar-plot. str_wrap_width determines the str_wrap function of the R-package stringr.

Value

The first plot is a panel of density plots for each split node sorted in ascending order of the Kullback-Leibler divergence value. Blue and black lines refer to the direct and indirect estimates, respectively. The grey segment refers to the 95% credible (confidence) interval of the inconsistency parameter, when run_nodesplit (netsplit) has been applied, with a darker grey line referring to the point estimate. When mtc.nodesplit has been employed, the 95% confidence interval has been approximated using the Bucher's approach based on the corresponding direct and indirect results. This was necessary because mtc.nodesplit (version 1.0-2) returns only the inconsistency p-values rather than the posterior results on the inconsistency parameters. The mean estimate on the scale of the selected effect measure appears at the top of each density curve.

The Kullback-Leibler divergence value appears at the top left of each plot in three colours: black, if no threshold has been defined (the default), green, if the Kullback-Leibler divergence is below the specified threshold (not concerning inconsistency) and red, if the Kullback-Leibler divergence is at least the specified threshold (substantial inconsistency).

The second plot is a percent stacked bar plot on the percentage contribution of approximating direct with indirect estimate (and vice-versa) to the total information loss for each target comparison. Total information loss is defined as the sum of the KLD value when approximating the direct with indirect estimate (blue bars), and the KLD when approximating the indirect with direct estimate (black bars). Values parentheses refer to the corresponding KLD value.

The function also returns the data-frame average_KLD that includes the split comparisons and the corresponding average Kullback-Leibler divergence value.

References

Bucher HC, Guyatt GH, Griffith LE, Walter SD. The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol 1997;50(6):683–91.

Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767

Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22(1):79–86. doi: 10.1214/aoms/1177729694

van Valkenhoef G, Dias S, Ades AE, Welton NJ. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods 2016;7(1):80–93. doi: 10.1002/jrsm.1167

Author

Loukia M. Spineli

Examples


if (FALSE) { # \dontrun{
data("nma.baker2009")

# Read results from 'run_nodesplit' (using the default arguments)
node <- readRDS(system.file('extdata/node_baker.rds', package = 'rnmamod'))

# The names of the interventions in the order they appear in the dataset
interv_names <- c("placebo", "budesonide", "budesonide plus formoterol",
                  "fluticasone", "fluticasone plus salmeterol",
                  "formoterol", "salmeterol", "tiotropium")

# Apply the function
kld_inconsistency(node = node,
                  threshold = 0.64,
                  drug_names = interv_names,
                  outcome = "Odds ratio (logarithmic scale)",
                  str_wrap_width = 15)
} # }