NMAoutlier (version 0.2.0)

NMAoutlier.measures: Outlier and influential detection measures in network meta-analysis.

Description

This function calculates several (simple or/and deletion) measures for detection of outliers and influential studies in network meta-analysis.

Outlier and influential detection measures are:

• Simple outlier and influential measures for each study (Raw residuals, Standardized residuals, Studentized residuals, Mahalanobis distance, leverage).

• Outlier and influential deletion measures for each study (Shift the mean) (Raw deleted residuals, Standardized deleted residuals, Studentized deleted residuals, Cook distance between the treatment estimates for study j and treatment estimates when study j is removed; Ratio of determinants of variance-covariance matrix of treatment estimates for study j to treatment estimates when study j is removed; weight leave one out;leverage leave one out; heterogeneity estimator leave one out; R statistic for heterogeneity; R statistic for Q (Qtotal), R statistic for heterogeneity Q (Qhet), R statistic for Qinconsistency (Qinc), DFbetas.)

Usage

NMAoutlier.measures(
  TE,
  seTE,
  treat1,
  treat2,
  studlab,
  data = NULL,
  sm,
  reference = "",
  measure = "simple",
  ...
)

Value

An object of class NMAoutlier.measures; with a list containing the following components when choosing simple measures:

dat

Matrix containing the data "TE", "seTE", "studlab", "treat1", "treat2" as defined above.

eraw

Raw residual for each study included in the network.

estand

Standardized residual for each study included in the network.

estud

Studentized residual for each study included in the network.

Mah

Mahalanobis distance for each pairwise comparison.

Mah.distance

Mahalanobis distance for each study included in the network.

leverage

Leverage for each study included in the network.

measure

type of measure used.

call

Function call

a list containing the following components,when choosing deletion measures:

dat

Matrix containing the data "TE", "seTE", "studlab", "treat1", "treat2" as defined above.

eraw.deleted

Raw deleted residual for each study included in the network.

estand.deleted

Standardized deleted residual for each study included in the network.

estud.deleted

Studentized deleted residual for each study included in the network.

Cooks.distance

Cook distance between the treatment estimates for study j and treatment estimates when study j is removed

Covratio

Ratio of determinants of variance-covariance matrix of treatment estimates for study j to treatment estimates when study j is removed.

w.leaveoneout

Weight leave one out.

H.leaveoneout

Leverage leave one out.

heterog.leaveoneout

Heterogeneity estimator leave one out.

Rheterogeneity

R statistic for heterogeneity.

Restimates

R statistis for estimates.

RQtotal

R statistic for Q (Qtotal).

RQhet

R statistic for heterogeneity Q (Qhet).

RQinc

R statistic for Qinconsistency (Qinc).

DFbetas

DFbetas.

measure

type of measure used.

call

Function call

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).

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.

sm

A character string indicating underlying summary measure, e.g., "RD", "RR", "OR", "ASD", "HR", "MD", "SMD", or "ROM".

reference

Reference treatment group.

measure

Outlier and influential detection measures, simple measures (default: "simple") or outlier and influential detection measures considered study deletion (measure = "deletion").

...

Additional arguments passed on to netmeta.

Author

Maria Petropoulou <[e-mail]>

Details

Outlier and influential detection measures (simple or deletion) for network meta-analysis. Network meta-analysis from graph-theory [Rücker, 2012] is fitted with (netmeta function) of R package netmeta [Rücker et al., 2015].

A description of the outlier and influential detection measures in the context of network meta-analysis can be found in Petropoulou (2020).

Let n be the number of treatments in a network and let m be the number of pairwise treatment comparisons. If there are only two-arm studies, m is 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).

This function calculates outlier and influential detection measures for each study. Simple outlier and influential measures (measure = "simple") are: Raw residuals, Standardized residuals, Studentized residuals, Mahalanobis distance and leverage for each study. For deletion outlier and influential measures (measure = "deletion"): Standardized deleted residual; Studentized deleted residual; Cook distance between the treatment estimates for study j and treatment estimates when study j is removed; Ratio of determinants of variance-covariance matrix of treatment estimates for study j to treatment estimates when study j is removed; Weight leave one out;leverage leave one out; heterogeneity estimator leave one out; R statistic for heterogeneity; R statistis for estimates; R statistic for Q (Qtotal), R statistic for heterogeneity Q (Qhet), R statistic for Qinconsistency (Qinc), DFbetas.

References

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

Petropoulou M (2020): Exploring methodological challenges in network meta-analysis models and developing methodology for outlier detection. PhD dissertation

Examples

library("netmeta")
data(smokingcessation)
smokingcessation$id <- 1:nrow(smokingcessation)

study912 <- subset(smokingcessation, id %in% 9:12)
p1 <- pairwise(list(treat1, treat2, treat3),
  list(event1, event2, event3), list(n1, n2, n3),
  data = study912, sm = "OR")

# Outlier and influential detection measures for studies 9, 10, 11, 12
meas <- NMAoutlier.measures(p1)

# Standardized residual for each study included in the network
meas$estand

if (FALSE) {
# Outlier and influential deletion measures for studies 9, 10, 11, 12.
delete <- NMAoutlier.measures(p1, measure = "deletion")

# Standardized deleted residual for studies 9, 10, 11, 12.
delete$estand.deleted

data(smokingcessation)

# Transform data from arm-based to contrast-based format
# We use 'sm' argument for odds ratios.
# We use function pairwise from netmeta package
#
p1 <- pairwise(list(treat1, treat2, treat3),
  list(event1, event2, event3), list(n1, n2, n3),
  data = smokingcessation, sm = "OR")

# Outlier and influential detection measures for each study in the network
meas <- NMAoutlier.measures(p1, measure = "simple")

# Mahalanobis distance for each study included in the network
meas$Mah
}