NMAoutlier: Detecting Outliers in Network Meta-Analysis

Description

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's 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's 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.

Installation

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

Installation using R package remotes:

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

Usage

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).

References:

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's 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)