Density plots of local inconsistency results and Kullback-Leibler divergence (When dataset is created by the user)

When the user has extracted results obtained from a method of local inconsistency evaluation (e.g., loop-specific, back-calculation or node-splitting approaches) as reported in publication, this function provides the same output with the function kld_inconsistency. 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.

Usage

kld_inconsistency_user(
  dataset,
  threshold = 1e-05,
  level = 0.05,
  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

dataset: A data-frame of seven columns and as many rows as the split nodes. The first column contains the names of the split nodes, and the remaining columns have the point estimate and standard error of the direct, indirect and inconsistency parameter in that order.
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.
level: A number indicating the significance level. Suggested values are 0.05 and 0.10. The default value is 0.05.
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 (1 - level)% 'pseudo' confidence interval of the inconsistency parameter based on the corresponding normal z-scores, with a darker grey line referring to the point estimate. The names of the selected comparisons appear at the top of each plot. 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 Kullback-Leibler divergence value when approximating the direct with indirect estimate (blue bars), and the Kullback-Leibler divergence value when approximating the indirect with direct estimate (black bars). Values parentheses refer to the corresponding Kullback-Leibler divergence value. Bars are sorted in ascending order of the 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 are taken from Table II in Dias et al. (2010)
# Treatments compared
treat <-
c("SK", "t-PA", "Acc t-PA", "SK+t-PA", "r-PA", "TNK", "PTCA", "UK", "ASPAC")

# Baseline arm (from each selected comparison)
base <- rep(1:3, c(6, 3, 5))

# Non-baseline arm (from each selected comparison)
nonbase <- c(2, 3, 5, 7, 8, 9, 7, 8, 9, 4, 5, 7, 8, 9)

# Compared treatments with their names
treat_comp <-
mapply(function(x, y) paste(treat[x], "vs", treat[y]), base, nonbase)

# Direct results
direct_mean <- c(0.000, -0.158, -0.060, -0.666, -0.369, 0.009, -0.545,
                 -0.295, 0.006, 0.126, 0.019, -0.216, 0.143, 1.409)
direct_sd <- c(0.030, 0.048, 0.089, 0.185, 0.518, 0.037, 0.417, 0.347, 0.037,
               0.054, 0.066, 0.118, 0.356, 0.415)

# Indirect results
indirect_mean <- c(0.189, -0.247, -0.175, -0.393, -0.168, 0.424, -0.475,
                   -0.144, 0.471, 0.630, 0.135, -0.477, -0.136, 0.165)
indirect_sd <- c(0.235, 0.092, 0.081, 0.120, 0.244, 0.252, 0.108, 0.290,
                 0.241, 0.697, 0.101, 0.174, 0.288, 0.057)

# Inconsistency
incons_mean <- c(-0.190, 0.088, 0.115, -0.272, -0.207, -0.413, -0.073,
                 -0.155, -0.468, -0.506, -0.116, 0.260, 0.277, 1.239)
incons_sd <- c(0.236, 0.104, 0.121, 0.222, 0.575, 0.253, 0.432, 0.452, 0.241,
               0.696, 0.120, 0.211, 0.461, 0.420)

# Collect results in a data-frame (exactly as required from the function)
dias_results <- data.frame(treat_comp, direct_mean, direct_sd, indirect_mean,
                           indirect_sd, incons_mean, incons_sd)

# Apply the function
kld_inconsistency_user(dataset = dias_results,
                       threshold = 0.13,
                       outcome = "Odds ratio (logarithmic scale)")
} # }