R: Network meta-analysis of binary outcome data

netmetabin {netmeta}

R Documentation

Network meta-analysis of binary outcome data

Description

Provides three models for the network meta-analysis of binary data (Mantel-Haenszel method, based on the non-central hypergeometric distribution, and the inverse variance method).

Usage

netmetabin(
  event1,
  n1,
  event2,
  n2,
  treat1,
  treat2,
  studlab,
  data = NULL,
  subset = NULL,
  sm,
  method = "MH",
  cc.pooled = FALSE,
  incr,
  allincr,
  addincr,
  allstudies,
  level = gs("level"),
  level.ma = gs("level.ma"),
  common = gs("common"),
  random = method == "Inverse" & (gs("random") | !is.null(tau.preset)),
  prediction = FALSE,
  level.predict = gs("level.predict"),
  reference.group = "",
  baseline.reference = TRUE,
  all.treatments = NULL,
  seq = NULL,
  tau.preset = NULL,
  tol.multiarm = 0.001,
  tol.multiarm.se = NULL,
  details.chkmultiarm = FALSE,
  details.chkdata = TRUE,
  sep.trts = ":",
  nchar.trts = 666,
  func.inverse = invmat,
  backtransf = gs("backtransf"),
  title = "",
  keepdata = gs("keepdata"),
  warn = TRUE,
  warn.deprecated = gs("warn.deprecated"),
  ...
)

Arguments

`event1`	Number of events (first treatment).
`n1`	Number of observations (first treatment).
`event2`	Number of events (second treatment).
`n2`	Number of observations (second treatment)
`treat1`	Label/Number for first treatment.
`treat2`	Label/Number for second treatment.
`studlab`	An optional - but important! - vector with study labels (see Details).
`data`	An optional data frame containing the study information.
`subset`	An optional vector specifying a subset of studies to be used.
`sm`	A character string indicating underlying summary measure, i.e., `"RD"`, `"RR"`, `"OR"`, `"ASD"`.
`method`	A character string indicating which method is to be used for pooling of studies. One of `"Inverse"`, `"MH"`, or `"NCH"`, can be abbreviated.
`cc.pooled`	A logical indicating whether `incr` should be used as a continuity correction, when calculating the network meta-analysis estimates.
`incr`	A numerical value which is added to each cell count, i.e., to the numbers of events and non-events, of all treatment arms in studies with zero events or non-events in any of the treatment arms ("continuity correction").
`allincr`	A logical indicating whether `incr` should be added to each cell count of all studies if a continuity correction was used for at least one study (only considered if `method = "Inverse"`). If FALSE (default), `incr` is used as continuity correction only for studies with zero events or zero non-events in any of the treatment arms.
`addincr`	A logical indicating whether `incr` should be added to each cell count of all studies, irrespective of zero cell counts (only considered if `method = "Inverse"`).
`allstudies`	A logical indicating whether studies with zero events or non-events in all treatment arms should be included in an inverse variance meta-analysis (applies only if `method = "Inverse"` and `sm` is equal to either `"RR"` or `"OR"`).
`level`	The level used to calculate confidence intervals for individual studies.
`level.ma`	The level used to calculate confidence intervals for network estimates.
`common`	A logical indicating whether a common effects network meta-analysis should be conducted.
`random`	A logical indicating whether a random effects network meta-analysis should be conducted.
`prediction`	A logical indicating whether a prediction interval should be printed (only considered if `method = "Inverse"`).
`level.predict`	The level used to calculate prediction interval for a new study (only considered if `method = "Inverse"`).
`reference.group`	Reference treatment.
`baseline.reference`	A logical indicating whether results should be expressed as comparisons of other treatments versus the reference treatment (default) or vice versa. This argument is only considered if `reference.group` has been specified.
`all.treatments`	A logical or `"NULL"`. If `TRUE`, matrices with all treatment effects, and confidence limits will be printed.
`seq`	A character or numerical vector specifying the sequence of treatments in printouts.
`tau.preset`	An optional value for manually setting the square-root of the between-study variance `\tau^2` (only considered if `method = "Inverse"`).
`tol.multiarm`	A numeric for the tolerance for consistency of treatment estimates in multi-arm studies which are consistent by design (only considered if `method = "Inverse"`).
`tol.multiarm.se`	A numeric for the tolerance for consistency of standard errors in multi-arm studies which are consistent by design (only considered if the argument is not `NULL` and `method = "Inverse"`).
`details.chkmultiarm`	A logical indicating whether treatment estimates and / or variances of multi-arm studies with inconsistent results or negative multi-arm variances should be printed (only considered if `method = "Inverse"`).
`details.chkdata`	A logical indicating whether number of events and participants of studies with inconsistent data should be printed.
`sep.trts`	A character used in comparison names as separator between treatment labels.
`nchar.trts`	A numeric defining the minimum number of characters used to create unique treatment names (see Details).
`func.inverse`	R function used to calculate the pseudoinverse of the Laplacian matrix L (see `netmeta`).
`backtransf`	A logical indicating whether results should be back transformed in printouts and forest plots. If `backtransf = TRUE`, results for `sm = "OR"` are presented as odds ratios rather than log odds ratios, for example.
`title`	Title of meta-analysis / systematic review.
`keepdata`	A logical indicating whether original data (set) should be kept in netmeta object.
`warn`	A logical indicating whether warnings should be printed (e.g., if studies are excluded from meta-analysis due to zero standard errors).
`warn.deprecated`	A logical indicating whether warnings should be printed if deprecated arguments are used.
`...`	Additional arguments (to catch deprecated arguments).

Details

This function implements three models for the network meta-analysis of binary data:

The Mantel-Haenszel network meta-analysis model, as described in Efthimiou et al. (2019) (method = "MH");
a network meta-analysis model using the non-central hypergeometric distribution with the Breslow approximation, as described in Stijnen et al. (2010) (method = "NCH");
the inverse variance method for network meta-analysis (method = "Inverse"), also provided by netmeta.

Comparisons belonging to multi-arm studies are identified by identical study labels (argument studlab). It is therefore important to use identical study labels for all comparisons belonging to the same multi-arm study.

Data entry for this function is in contrast-based format, that is, each line of the data corresponds to a single pairwise comparison between two treatments (arguments treat1, treat2, event1, n1, event2, and n2). If data are provided in arm-based format, that is, number of events and participants are given for each treatment arm separately, function pairwise can be used to transform the data to contrast-based format (see help page of function pairwise).

Note, all pairwise comparisons must be provided for a multi-arm study. Consider a multi-arm study of p treatments with known variances. For this study, the number of events and observations must be provided for each treatment, for each of p(p - 1) / 2 possible comparisons in separate lines in the data. For instance, a three-arm study contributes three pairwise comparisons, a four-arm study even six pairwise comparisons. Function pairwise automatically calculates all pairwise comparisons for multi-arm studies.

For method = "Inverse", both common and random effects models are calculated regardless of values choosen for arguments common and random. Accordingly, the network estimates for the random effects model can be extracted from component TE.random of an object of class "netmeta" even if argument random = FALSE. However, all functions in R package netmeta will adequately consider the values for common and random. E.g. function print.summary.netmeta will not print results for the random effects model if random = FALSE.

For the random-effects model, the direct treatment estimates are based on the common between-study variance \tau^2 from the network meta-analysis.

For method = "MH" and method = "NCH", only a common effects model is available.

By default, treatment names are not abbreviated in printouts. However, in order to get more concise printouts, argument nchar.trts can be used to define the minimum number of characters for abbreviated treatment names (see abbreviate, argument minlength). R function treats is utilised internally to create abbreviated treatment names.

Names of treatment comparisons are created by concatenating treatment labels of pairwise comparisons using sep.trts as separator (see paste). These comparison names are used in the covariance matrices Cov.common and Cov.random and in some R functions, e.g, decomp.design. By default, a colon is used as the separator. If any treatment label contains a colon the following characters are used as separator (in consecutive order): "-", "_", "/", "+", ".", "|", and "*". If all of these characters are used in treatment labels, a corresponding error message is printed asking the user to specify a different separator.

Value

An object of class netmetabin and netmeta with corresponding print, summary, forest, and netrank functions. The object is a list containing the following components:

`studlab`, `treat1`, `treat2`	As defined above.
`n1`, `n2`, `event1`, `event2`	As defined above.
`TE`	Estimate of treatment effect, i.e. difference between first and second treatment (e.g. log odds ratio).
`seTE`	Standard error of treatment estimate.
`k`	Total number of studies.
`m`	Total number of pairwise comparisons.
`n`	Total number of treatments.
`d`	Total number of designs (corresponding to the unique set of treatments compared within studies).
`trts`	Treatments included in network meta-analysis.
`k.trts`	Number of studies evaluating a treatment.
`n.trts`	Number of observations receiving a treatment.
`events.trts`	Number of events observed for a treatment.
`studies`	Study labels coerced into a factor with its levels sorted alphabetically.
`narms`	Number of arms for each study.
`designs`	Unique list of designs present in the network. A design corresponds to the set of treatments compared within a study.
`TE.common`, `seTE.common`	nxn matrix with estimated overall treatment effects and standard errors for common effects model.
`lower.common`, `upper.common`	nxn matrices with lower and upper confidence interval limits for common effects model.
`statistic.common`, `pval.common`	nxn matrices with z-value and p-value for test of overall treatment effect under common effects model.
`TE.random`, `seTE.random`	nxn matrix with estimated overall treatment effects and standard errors for random effects model (only available if `method = "Inverse"`).
`lower.random`, `upper.random`	nxn matrices with lower and upper confidence interval limits for random effects model (only available if `method = "Inverse"`).
`statistic.random`, `pval.random`	nxn matrices with z-value and p-value for test of overall treatment effect under random effects model (only available if `method = "Inverse"`).
`TE.direct.common`, `seTE.direct.common`	nxn matrix with estimated treatment effects and standard errors from direct evidence under common effects model.
`lower.direct.common`, `upper.direct.common`	nxn matrices with lower and upper confidence interval limits from direct evidence under common effects model.
`statistic.direct.common`, `pval.direct.common`	nxn matrices with z-value and p-value for test of overall treatment effect from direct evidence under common effects model.
`TE.direct.random`, `seTE.direct.random`	nxn matrix with estimated treatment effects and standard errors from direct evidence under random effects model (only available if `method = "Inverse"`).
`lower.direct.random`, `upper.direct.random`	nxn matrices with lower and upper confidence interval limits from direct evidence under random effects model (only available if `method = "Inverse"`).
`statistic.direct.random`, `pval.direct.random`	nxn matrices with z-value and p-value for test of overall treatment effect from direct evidence under random effects model (only available if `method = "Inverse"`).
`Q`	Overall heterogeneity / inconsistency statistic. (only available if `method = "Inverse"`)
`df.Q`	Degrees of freedom for test of heterogeneity / inconsistency.
`pval.Q`	P-value for test of heterogeneity / inconsistency.
`I2`, `lower.I2`, `upper.I2`	I-squared, lower and upper confidence limits (only available if `method = "Inverse"`).
`tau`	Square-root of between-study variance (only available if `method = "Inverse"`).
`Q.heterogeneity`	Overall heterogeneity statistic. (only available if `method = "Inverse"`)
`df.Q.heterogeneity`	Degrees of freedom for test of overall heterogeneity.
`pval.Q.heterogeneity`	P-value for test of overall heterogeneity.
`Q.inconsistency`	Overall inconsistency statistic.
`df.Q.inconsistency`	Degrees of freedom for test of overall inconsistency.
`pval.Q.inconsistency`	P-value for test of overall inconsistency.
`A.matrix`	Adjacency matrix (nxn).
`H.matrix`	Hat matrix (mxm)
`n.matrix`	nxn matrix with number of observations in direct comparisons.
`events.matrix`	nxn matrix with number of events in direct comparisons.
`sm`, `method`, `level`, `level.ma`	As defined above.
`incr`, `allincr`, `addincr`, `allstudies`, `cc.pooled`	As defined above.
`common`, `random`	As defined above.
`prediction`, `level.predict`	As defined above.
`reference.group`, `baseline.reference`, `all.treatments`	As defined above.
`seq`, `tau.preset`, `tol.multiarm`, `tol.multiarm.se`	As defined above.
`details.chkmultiarm`, `details.chkdata`	As defined above.
`sep.trts`, `nchar.trts`	As defined above.
`backtransf`, `title`, `warn`, `warn.deprecated`	As defined above.
`data`	Data set (in contrast-based format).
`data.design`	List with data in arm-based format (each list element corresponds to a single design).
`call`	Function call.
`version`	Version of R package netmeta used to create object.

Author(s)

Orestis Efthimiou oremiou@gmail.com, Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de

References

Efthimiou O, Rücker G, Schwarzer G, Higgins J, Egger M, Salanti G (2019): A Mantel-Haenszel model for network meta-analysis of rare events. Statistics in Medicine, 38, 2992–3012

Senn S, Gavini F, Magrez D, Scheen A (2013): Issues in performing a network meta-analysis. Statistical Methods in Medical Research, 22, 169–89

Stijnen T, Hamza TH, Ozdemir P (2010): Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046–67

Examples

data(Dong2013)

# Only consider first ten studies (to reduce runtime of example)
#
first10 <- subset(Dong2013, id <= 10)

# Transform data from long arm-based format to contrast-based
# format. Argument 'sm' has to be used for odds ratio as summary
# measure; by default the risk ratio is used in the metabin
# function called internally.
#
p1 <- pairwise(treatment, death, randomized, studlab = id,
  data = first10, sm = "OR")

# Conduct Mantel-Haenszel network meta-analysis (without continuity
# correction)
#
nb1 <- netmetabin(p1, ref = "plac")
nb1

# Obtain the league table
#
netleague(nb1)

## Not run: 
# Conduct Mantel-Haenszel network meta-analysis for the whole
# dataset
#
p2 <- pairwise(treatment, death, randomized, studlab = id,
  data = Dong2013, sm = "OR")
netmetabin(p2, ref = "plac")
  
# Conduct network meta-analysis using the non-central
# hypergeometric model (without continuity correction)
#
netmetabin(p2, ref = "plac", method = "NCH")

# Conduct Mantel-Haenszel network meta-analysis (with continuity
# correction of 0.5; include all studies)
#
netmetabin(p2, ref = "plac", cc.pooled = TRUE)

data(Gurusamy2011)

p3 <- pairwise(treatment, death, n, studlab = study,
  data = Gurusamy2011, sm = "OR")

# Conduct Mantel-Haenszel network meta-analysis (without continuity
# correction)
#
netmetabin(p3, ref = "cont")

## End(Not run)

[Package netmeta version 2.9-0 Index]