Description Usage Arguments Details Value Author(s) References Examples
This function employs the Forward Search algorithm to detect outliers and influential studies fitted in network metaanalysis model from graphtheory. This is an outlying diagnostic tool to detect outliers and studies that are potential sources for heterogeneity and inconsistency in network metaanalysis.
Monitoring measures during the search are:
outlier detection measures (standardized residuals, Cook's distance, ratio of variance);
ranking measures (Pscores);
heterogeneity and inconsistency measures (Q statistics for overall heterogeneity / inconsistency, inconsistency by designbytreatment interaction model, zvalues for comparison between direct and indirect evidence by backcalculation method).
A description of the outlier detection methodology can be found in Petropoulou et al. (2021).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 
TE 
Estimate of treatment effect, i.e. difference between first and second treatment (e.g. log odds ratio, mean difference, or log hazard ratio). This can also be a pairwise object (i.e. the result of pairwise function of netmeta package). In this case, the pairwise object should include the following: TE, seTE, treat1, treat2, studlab 
seTE 
Standard error of treatment estimate. 
treat1 
Label/Number for first treatment. 
treat2 
Label/Number for second treatment. 
studlab 
Study labels (important when multi arm studies are included). 
data 
A data frame containing the study information. 
crit1 
A character string indicating the criterion to be used for selecting the initial subset, this criterion may be the minimum of median absolute residuals ("R") or the maximum of median absolute likelihood contributions ("L"). Default value is "R". 
crit2 
A character string indicating the criterion to be used for selecting the study entered from nonbasic set to basic set, this criterion may be the minimum of absolute residuals ("R") or the maximum of absolute likelihood contributions ("L"). Default value is "R". 
studies 
An optional vector specifying the number of the initial subset of studies. The default value is the maximum of the number of treatments and the 20 percent of the total number of studies. 
P 
An optional vector specifying the number of candidate
sample of studies (with length equal to 
sm 
A character string indicating underlying summary measure,
e.g., 
Isub 
A vector for the studies to be included in the initial subset (default: NULL, the initial subset not specified by the user). 
reference 
Reference treatment group. 
small.values 
A character string indicating if small values are considered beneficial (option:"good") or harmfull (option:"bad") on outcome. This is requirement for pscores computation. The default value is considered benefial outcome ("good"). 
n_cores 
The number of cores that the process is running using the parallel (default: NULL, the process is running using all the available cores) 
... 
Additional arguments passed on to

FS algorithm for network metaanalysis model from graph theory is described in Petropoulou et al. (2021).
Let n be the number of treatments and let m be the
number of pairwise treatment comparisons. If there are only
twoarm studies, m is equal to the number of studies. Let TE
and seTE be the vectors of observed effects and their standard
errors. Comparisons belonging to multiarm studies are identified
by identical study labels (argument studlab
).
The FS algorithm is an outlier diagnostic iterative procedure. FS algorithm apart from three steps. It starts with a subset of studies and it gradually adds studies until all studies entered. After the search, statistical measures are monitored for sharp changes.
In more detail, the FS algorithm starts with an initial subset of
the dataset with size l. Let (argument P
)
(eg. P = 100) a large number of candidate subset of studies
with size l. The candidate subset that optimize the
criterion (argument crit1
) is taken as the initial subset
(considered ideally to be outlyingfree). Criterion (crit1
)
to be used for selecting the initial subset, can be the minimum of
median absolute residuals "R"
or the maximum of median
absolute likelihood contributions "L"
. It is conventionally
refer this subset as basic set, whereas the remaining studies
constitute the nonbasic set.
The FS algorithm gradually adds studies from the nonbasic to the
basic subset based on how close the former studies are to the
hypothesized model fit in the basic set. A study from nonbasic
set entered into the basic set if optimize the criterion (argument
crit2
). Criterion (crit2
) for selecting the study
from nonbasic to basic set may be the minimum of median absolute
residuals "R"
or the maximum of median absolute likelihood
contributions "L"
. The algorithm order the studies
according to their closeness to the basic set by adding the study
that optimize the criterion from nonbasic set to basic set.
The process is repeated until all studies are entered into the
basic set. The number of iterations of algorithm index is
equal to the total number of studies minus the number of studies
entered into the initial subset. Through the FS procedure,
parameter estimates (summary estmates, heterogeneity estimator) and
other statistics of interest (outlying measures, heterogeneity and
inconsistency measures, ranking measures) are monitored. In each
iteration, network metaanalysis model from graph theory (Rücker,
2012) is fitted (netmeta
function) with R package
netmeta.
Monitoring statistical measures for each FS iteration can be:
Outlying detection measures: Standardized residuals (arithmetic mean in case of multiarm studies); Cook's statistic; Ratio of determinants of variancecovariance matrix
Ranking measures:
Pscores for ranking of treatments (Rücker G & Schwarzer G, 2015)
for each basic set with implementation of (netrank
function)
from R package netmeta.
Heterogeneity and inconsistency measures:
Overall heterogeneity / inconsistency Q statistic (Q
) This
is the designbased decomposition of Cochran Q as provided by Krahn
et al. (2013); Overall heterogeneity Q statistic (Q
);
Betweendesigns Q statistic (Q
), based on a random effects
model with squareroot of betweenstudy variance estimated embedded
in a full designbytreatment interaction model. Implementation
with (decomp.design
function) from R package netmeta;
Zvalues (Dias et al., 2010; König et al., 2013) for comparison
between direct and indirect evidence in
each iteration of forward search algorithm. By monitoring
difference of direct and indirect evidence, potential sources of
consistency can be detected with the implementation of
(netsplit
function) from R package netmeta for each
iteration of the search.
An object of class NMAoutlier
; a list containing the
following components:
dat 
Matrix containing the data 
length.initial 
The number of studies that constitute the initial (outlyingclean) subset of studies. 
index 
The number of iterations of forward search algorithm. 
basic 
Studies entered into the basic set in each iteration of the search. At the first iteration, basic set constitute the studies that are included in the basicinitial subset. The number of studies in the first iteration is equal to length.initial. 
taub 
Heterogeneity estimator variance for basic set in each iteration of forward search algorithm. 
Qb 
Overall heterogeneity  inconsistency Q statistic ( 
Qhb 
Overall heterogeneity Q statistic ( 
Qib 
Overall inconsistency Q statistic ( 
estb 
Summary estimates for each treatment for the basic set in each iteration of forward search algorithm. 
lb 
Lower 95% confidence interval of summary estimates for the basic set in each iteration of forward search algorithm. 
ub 
Upper 95% confidence interval of summary estimates for the basic set in each iteration of forward search algorithm. 
Ratio 
Ratio of determinants ( 
cook_d 
Cook's statistic ( 
p.score 
Pscore for ranking each treatment for the basic set in each iteration of forward search algorithm. 
dif 
Zvalues for comparison between direct and indirect evidence for each iteration of forward search algorithm. Based on backcalculation method to derive indirect estimates from direct pairwise comparisons and network estimates. 
estand 
Standardized residuals for each study for the basic set in each iteration of forward search algorithm. 
call 
Function call 
Maria Petropoulou <petropoulou@imbi.unifreiburg.de>
Dias S, Welton NJ, Caldwell DM, Ades AE (2010): Checking consistency in mixed treatment comparison metaanalysis. Statistics in Medicine, 29, 932–44
König J, Krahn U, Binder H (2013): Visualizing the flow of evidence in network metaanalysis and characterizing mixed treatment comparisons. Statistics in Medicine, 32, 5414–29
Krahn U, Binder H, König J (2013): A graphical tool for locating inconsistency in network metaanalyses. BMC Medical Research Methodology, 13, 35
Petropoulou M, Salanti G, Rücker G, Schwarzer G, Moustaki I, Mavridis D (2021): A forward search algorithm for detecting extreme study effects in network metaanalysis. Statistics in Medicine
Rücker G (2012): Network metaanalysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312–24
Rücker G, Schwarzer G (2015): Ranking treatments in frequentist network metaanalysis works without resampling methods. BMC Medical Research Methodology, 15, 58
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  ## Not run:
data(smokingcessation, package = "netmeta")
smokingcessation$id < 1:nrow(smokingcessation)
study912 < subset(smokingcessation, id %in% 9:12)
p1 < netmeta::pairwise(list(treat1, treat2, treat3),
list(event1, event2, event3),
list(n1, n2, n3),
data = study912,
sm = "OR")
# Forward search algorithm
#
FSresult < NMAoutlier(p1, P = 1, small.values = "bad", n_cores = 2)
FSresult
data(smokingcessation, package = "netmeta")
# Transform data from armbased to contrastbased format
# We use 'sm' argument for odds ratios.
# We use function pairwise from netmeta package
#
p1 < netmeta::pairwise(list(treat1, treat2, treat3),
list(event1, event2, event3),
list(n1, n2, n3),
data = smokingcessation,
sm = "OR")
# Forward search algorithm
#
FSresult1 < NMAoutlier(p1, small.values = "bad")
# Basic set for each iteration of forward search algorithm
#
FSresult1$basic
# Forward search algorithm using the criteria (crit1, crit2)
# with the maximum of absolute likelihood contributions ("L")
#
FSresult2 < NMAoutlier(p1, crit1 = "L", crit2 = "L",
small.values = "bad")
FSresult2
## End(Not run)

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