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.
robustness_index_user(sens, pkg, attribute, threshold)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:
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.
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.
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.
The attributes considered.
The threshold used to be inherited by the
heatmap_robustness function. See 'Details'.
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').
Character string indicating the R-package with values
"netmeta", or "metafor".
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.
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.
Loukia M. Spineli
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.
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
rma,
rma.glmm,
rma.mh, rma.mv,
rma.peto,
rma.uni,
netmeta,
netmetabin,
heatmap_robustness
if (FALSE) {
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)
}
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