A package that provides measures and methodologies for detecting outlying and influential studies in network meta-analysis.

• 1) Simply outlier and influential detection measures: Raw, Standardized, Studentized residuals; Mahalanobis distance and leverage.
• 2) Outlier and influential detection measures by considering a study deletion (Shift the mean): Raw, Standardized, Studentized deleted residuals; Cook distance; COVRATIO; weight “leave one out”; leverage “leave one out”; heterogeneity “leave one out”; R heterogeneity; R Qtotal; R Qheterogeneity; R Qinconsistency and DFBETAS.
• Plots for all the above outlier and influential detection measures (simple and deletion
  measures) and Q-Q plot for network meta-analysis.
• 3) Forward search algorithm in network meta-analysis (FS).
• Forward plots (fwdplot) for the monitoring measures in each step of forward search algorithm. Monitoring measures: P-scores; z-values for difference of direct and indirect evidence with back-calculation method; Standardized residuals; heterogeneity variance estimator; cook distance; ratio of variances; Q statistics.
• Forward plot for summary estimates and their confidence intervals for each treatment in each step of forward search algorithm.

You can install the NMAoutlier package from GitHub repository as follows:

Installation using R package devtools:

install.packages("devtools")
devtools::install_github("petropouloumaria/NMAoutlier")

Example of network meta-analysis comparing the relative effects of four smoking cessation counseling programs, no contact (A), self-help (B), individual counseling (C) and group counseling (D). The outcome is the number of individuals with successful smoking cessation at 6 to 12 months. The data are in contrast format with odds ratio (OR) and its standard error. Arm-level data can be found in Dias et al. (2013).

Reference:

Higgins D, Jackson JK, Barrett G, Lu G, Ades AE, and White IR. Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods 2012, 3(2): 98–110.

Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, and Ades AE. Evidence Synthesis for Decision Making 4: Inconsistency in networks of evidence based on randomized controlled trials. Medical Decision Making 2013, 33: 641–656.

You can load the NMAoutlier library

library(NMAoutlier)

Load the dataset smoking cessation from netmeta package.

data(smokingcessation, package = "netmeta")

Transform data from arm-based to contrast-based format using the function pairwise from netmeta package.

library(netmeta)
p1 <- pairwise(list(treat1, treat2, treat3),
               list(event1, event2, event3),
               list(n1, n2, n3),
               data = smokingcessation,
               sm = "OR")

Part 1: Simply outlier detection measures

You can calculate simply outlier and influential detection measures with NMAoutlier.measures function as follows:

measures <- NMAoutlier.measures(p1)

You can see the Mahalanobis distance for each study

measures$Mahalanobis.distance

You can plot the Mahalanobis distance for each study with measplot function as follows:

measplot(measures, "mah")

You can figure out the Q-Q plot for network meta-analysis with Qnetplot function as follows:

Qnetplot(measures)

Part 2: Outlier detection measures considered deletion (Shift the mean)

You can calculate outlier and influential detection measures considered study deletion with NMAoutlier,measures function as follows:

deletion <- NMAoutlier,measures(p1, measure = "deletion")

You can see the standardized deleted residuals for each study

deletion$estand.deleted

You can see the COVRATIO for each study

deletion$Covratio

You can plot the R statistic for Qinconsistency with function measplot as follows:

measplot(deletion, "rqinc", measure = "deletion")

Part 3: Forward Search Algorithm - (Outlier detection Methodology)

You can conduct the Forward Search algorithm with NMAoutlier function as follows:

FSresult <- NMAoutlier(p1, small.values = "bad")

You can see the forward plots with fwdplot function for Cook distance as follows:

fwdplot(FSresult,"cook")

Or you can plot the Ratio of variances as follows:

fwdplot(FSresult,"ratio")

You can plot the differences of direct and indirect estimates (z-values) as follows:

fwdplot(FSresult,"nsplit")

You can see the forward plots for summary relative treatment estimates of B, C and D versus the reference A with fwdplotest function as follows:

fwdplotest(FSresult)