Robustness index when 'metafor' or 'netmeta' are used

Calculates the robustness index for a sensitivity analysis (Spineli et al., 2021) performed using the results of the analysis performed via the R-package netmeta or metafor. The user defines the input and the function returns the robustness index.

Usage

robustness_index_user(sens, pkg, attribute, threshold)

Arguments

sens: A list of R objects of class netmeta, netmetabin (see netmeta) or rma, rma.glmm, rma.mh, rma.mv, rma.peto, and rma.uni (see metafor). The number of elements equals the number of analyses using the same dataset and the same R-package. The first element should refer to the primary analysis. Hence, the list should include at least two elements (see 'Details').
pkg: Character string indicating the R-package with values "netmeta", or "metafor".
attribute: This is relevant only for netmeta. A vector of at least two characters with values "TE.common" or "TE.random". See 'Values' in netmeta or netmetabin.
threshold: A number indicating the threshold of robustness, that is, the minimally allowed deviation between the primary analysis (the first element in sens) and re-analysis results. See 'Details' below.

Value

robustness_index_user prints on the R console a message in red text on the threshold of robustness determined by the user. Then, the function returns the following list of elements:

robust_index: A numeric scalar or vector on the robustness index values. In the case of a pairwise meta-analysis, robust_index is scalar as only one summary effect size is obtained. In the case of network meta-analysis, robust_index is a vector with length equal to the number of possible pairwise comparisons; one robustness index per pairwise comparison.
robust: A character or character vector (of same length with robust_index) on whether the primary analysis results are robust or frail to the different re-analyses.
kld: A vector or matrix on the Kullback-Leibler divergence (KLD) measure in the summary effect size from a subsequent re-analysis to the primary analysis. In the case of a pairwise meta-analysis, kld is a vector with length equal to the number of total analyses (one KLD value is obtained per analysis). The number of total analyses equals the length of sens. In the case of network meta-analysis, robust_index is a matrix with number of rows equal to the number of total analyses and number of columns equal to the number of possible pairwise comparisons; one KLD value per analysis and possible comparison.
attribute: The attributes considered.
threshold: The threshold used to be inherited by the heatmap_robustness function. See 'Details'.

Details

Thresholds of robustness have been proposed only for the odds ratio and standardised mean difference (Spineli et al., 2021). The user may consider the values 0.28 and 0.17 in the argument threshold for the odds ratio and standardised mean difference effect measures (the default values), respectively, or consider other plausible values. When the argument threshold has not been defined, robustness_index considers the default values 0.28 and 0.17 as threshold for robustness for binary and continuous outcome, respectively, regardless of the effect measure (the default thresholds may not be proper choices for other effect measures; hence, use these threshold with great caution in this case). Spineli et al. (2021) offers a discussion on specifying the threshold of robustness.

When other effect measure is used (other than odds ratio or standardised mean difference) or the elements in sens refer to different effect measures, the execution of the function will be stopped and an error message will be printed in the R console.

In robust, the value "robust" appears when the calculated robust_index is less than threshold; otherwise, the value "frail" appears.

References

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

Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478

Author

Loukia M. Spineli

Examples


if (FALSE) { # \dontrun{
library(netmeta)

data(Baker2009)

# Transform from arm-based to contrast-based format
p1 <- pairwise(treatment, exac, total, studlab = paste(study, year),
data = Baker2009, sm = "OR")

# Conduct standard network meta-analysis
net1 <- netmeta(p1, ref = "Placebo")

# Calculate the robustness index (random-effects versus fixed-effect)
robustness_index_user(sens = list(net1, net1),
                      pkg = "netmeta",
                      attribute = c("TE.random", "TE.common"),
                      threshold = 0.28)
} # }