NMAoutlier: Forward Search algorithm in network meta-analysis

In NMAoutlier: Detecting Outliers in Network Meta-Analysis

Description

This function employs the Forward Search algorithm to detect outliers and influential studies fitted in network meta-analysis model from graph-theory. This is an outlying diagnostic tool to detect outliers and studies that are potential sources for heterogeneity and inconsistency in network meta-analysis.

Monitoring measures during the search are:

• outlier detection measures (standardized residuals, Cook's distance, ratio of variance);

• ranking measures (P-scores);

• heterogeneity and inconsistency measures (Q statistics for overall heterogeneity / inconsistency, inconsistency by design-by-treatment interaction model, z-values for comparison between direct and indirect evidence by back-calculation method).

A description of the outlier detection methodology can be found in Petropoulou et al. (2021).

Usage

NMAoutlier(
  TE,
  seTE,
  treat1,
  treat2,
  studlab,
  data = NULL,
  crit1 = "R",
  crit2 = "R",
  studies = NULL,
  P = 100,
  sm,
  Isub = NULL,
  reference = "",
  small.values = "good",
  n_cores = NULL,
  ...
)

Arguments

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 non-basic 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 studies) for the choice of the initial subset. Default value is 100.
sm	A character string indicating underlying summary measure, e.g., "RD", "RR", "OR", "ASD", "HR", "MD", "SMD", or "ROM".
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 p-scores 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 netmeta.

Details

FS algorithm for network meta-analysis 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 two-arm 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 multi-arm 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 outlying-free). 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 non-basic set.

The FS algorithm gradually adds studies from the non-basic to the basic subset based on how close the former studies are to the hypothesized model fit in the basic set. A study from non-basic set entered into the basic set if optimize the criterion (argument crit2). Criterion (crit2) for selecting the study from non-basic 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 non-basic 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 meta-analysis 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 multi-arm studies); Cook's statistic; Ratio of determinants of variance-covariance matrix

Ranking measures: P-scores 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 design-based decomposition of Cochran Q as provided by Krahn et al. (2013); Overall heterogeneity Q statistic (Q); Between-designs Q statistic (Q), based on a random effects model with square-root of between-study variance estimated embedded in a full design-by-treatment interaction model. Implementation with (decomp.design function) from R package netmeta; Z-values (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.

Value

An object of class NMAoutlier; a list containing the following components:

dat	Matrix containing the data "TE", "seTE", "studlab", "treat1", "treat2" as defined above.
length.initial	The number of studies that constitute the initial (outlying-clean) 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 basic-initial 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 (Q) for the basic set in each iteration of forward search algorithm.
Qhb	Overall heterogeneity Q statistic (Q) for the basic set in each iteration of forward search algorithm.
Qib	Overall inconsistency Q statistic (Q) from design-by-treatment interaction model for the basic set in each iteration of forward search algorithm.
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 (COVRATIOj) of variance-covariance matrix of treatment estimates at iteration j to that iteration at (j-1).
cook_d	Cook's statistic (Cj) at iteration j of forward search algorithm.
p.score	P-score for ranking each treatment for the basic set in each iteration of forward search algorithm.
dif	Z-values for comparison between direct and indirect evidence for each iteration of forward search algorithm. Based on back-calculation 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

Author(s)

Maria Petropoulou <[e-mail]>

References

Dias S, Welton NJ, Caldwell DM, Ades AE (2010): Checking consistency in mixed treatment comparison meta-analysis. Statistics in Medicine, 29, 932–44

König J, Krahn U, Binder H (2013): Visualizing the flow of evidence in network meta-analysis 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 meta-analyses. 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 meta-analysis. Statistics in Medicine

Rücker G (2012): Network meta-analysis, electrical networks and graph theory. Research Synthesis Methods, 3, 312–24

Rücker G, Schwarzer G (2015): Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Medical Research Methodology, 15, 58

Examples

## 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 arm-based to contrast-based 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)

NMAoutlier documentation built on Oct. 11, 2021, 5:23 p.m.