metagen: Generic inverse variance meta-analysis

In meta: General Package for Meta-Analysis

Generic inverse variance meta-analysis

Description

Common effect and random effects meta-analysis based on estimates (e.g. log hazard ratios) and their standard errors. The inverse variance method is used for pooling.

Three-level random effects meta-analysis (Van den Noortgate et al., 2013) is available by internally calling rma.mv function from R package metafor (Viechtbauer, 2010).

Usage

metagen(
  TE,
  seTE,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  cluster = NULL,
  rho = 0,
  cycles = NULL,
  sm = "",
  method.ci = if (missing(df)) "z" else "t",
  level = gs("level"),
  common = gs("common"),
  random = gs("random") | !is.null(tau.preset),
  overall = common | random,
  overall.hetstat = if (is.null(gs("overall.hetstat"))) common | random else
    gs("overall.hetstat"),
  prediction = gs("prediction") | !missing(method.predict),
  method.tau = gs("method.tau"),
  method.tau.ci = gs("method.tau.ci"),
  level.hetstat = gs("level.hetstat"),
  tau.preset = NULL,
  TE.tau = NULL,
  tau.common = gs("tau.common"),
  detail.tau = "",
  method.I2 = gs("method.I2"),
  level.ma = gs("level.ma"),
  method.random.ci = gs("method.random.ci"),
  adhoc.hakn.ci = gs("adhoc.hakn.ci"),
  level.predict = gs("level.predict"),
  method.predict = gs("method.predict"),
  adhoc.hakn.pi = gs("adhoc.hakn.pi"),
  seed.predict = NULL,
  null.effect = 0,
  method.bias = gs("method.bias"),
  n.e = NULL,
  n.c = NULL,
  pval,
  df,
  lower,
  upper,
  level.ci = 0.95,
  median,
  q1,
  q3,
  min,
  max,
  method.mean = "Luo",
  method.sd = "Shi",
  approx.TE,
  approx.seTE,
  transf = gs("transf") & missing(func.transf),
  backtransf = gs("backtransf") | !missing(func.backtransf),
  func.transf,
  func.backtransf,
  args.transf,
  args.backtransf,
  pscale = 1,
  irscale = 1,
  irunit = "person-years",
  text.common = gs("text.common"),
  text.random = gs("text.random"),
  text.predict = gs("text.predict"),
  text.w.common = gs("text.w.common"),
  text.w.random = gs("text.w.random"),
  title = gs("title"),
  complab = gs("complab"),
  outclab = "",
  label.e = gs("label.e"),
  label.c = gs("label.c"),
  label.left = gs("label.left"),
  label.right = gs("label.right"),
  col.label.left = gs("col.label.left"),
  col.label.right = gs("col.label.right"),
  subgroup,
  subgroup.name = NULL,
  print.subgroup.name = gs("print.subgroup.name"),
  sep.subgroup = gs("sep.subgroup"),
  test.subgroup = gs("test.subgroup"),
  prediction.subgroup = gs("prediction.subgroup"),
  seed.predict.subgroup = NULL,
  byvar,
  id,
  adhoc.hakn,
  keepdata = gs("keepdata"),
  keeprma = gs("keeprma"),
  warn = gs("warn"),
  warn.deprecated = gs("warn.deprecated"),
  control = NULL,
  ...
)

Arguments

TE	Estimate of treatment effect, e.g., log hazard ratio or risk difference or an R object created with pairwise.
seTE	Standard error of treatment estimate or standard deviation of n-of-1 trials.
studlab	An optional vector with study labels.
data	An optional data frame containing the study information.
subset	An optional vector specifying a subset of studies to be used (see Details).
exclude	An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots (see Details).
cluster	An optional vector specifying which estimates come from the same cluster resulting in the use of a three-level meta-analysis model.
rho	Assumed correlation of estimates within a cluster.
cycles	A numeric vector with the number of cycles per patient / study in n-of-1 trials.
sm	A character string indicating underlying summary measure, e.g., "RD", "RR", "OR", "ASD", "HR", "MD", "SMD", or "ROM".
method.ci	A character string indicating which method is used to calculate confidence intervals for individual studies, see Details.
level	The level used to calculate confidence intervals for individual studies.
common	A logical indicating whether a common effect meta-analysis should be conducted.
random	A logical indicating whether a random effects meta-analysis should be conducted.
overall	A logical indicating whether overall summaries should be reported. This argument is useful in a meta-analysis with subgroups if overall results should not be reported.
overall.hetstat	A logical value indicating whether to print heterogeneity measures for overall treatment comparisons. This argument is useful in a meta-analysis with subgroups if heterogeneity statistics should only be printed on subgroup level.
prediction	A logical indicating whether a prediction interval should be printed.
method.tau	A character string indicating which method is used to estimate the between-study variance \tau^2 and its square root \tau (see meta-package).
method.tau.ci	A character string indicating which method is used to estimate the confidence interval of \tau^2 and \tau (see meta-package).
level.hetstat	The level used to calculate confidence intervals for heterogeneity statistics.
tau.preset	Prespecified value for the square root of the between-study variance \tau^2.
TE.tau	Overall treatment effect used to estimate the between-study variance tau-squared.
tau.common	A logical indicating whether tau-squared should be the same across subgroups.
detail.tau	Detail on between-study variance estimate.
method.I2	A character string indicating which method is used to estimate the heterogeneity statistic I^2. Either "Q" or "tau2", can be abbreviated (see meta-package).
level.ma	The level used to calculate confidence intervals for meta-analysis estimates.
method.random.ci	A character string indicating which method is used to calculate confidence interval and test statistic for random effects estimate (see meta-package).
adhoc.hakn.ci	A character string indicating whether an ad hoc variance correction should be applied in the case of an arbitrarily small Hartung-Knapp variance estimate (see meta-package).
level.predict	The level used to calculate prediction interval for a new study.
method.predict	A character string indicating which method is used to calculate a prediction interval (see meta-package).
adhoc.hakn.pi	A character string indicating whether an ad hoc variance correction should be applied for prediction interval (see meta-package).
seed.predict	A numeric value used as seed to calculate bootstrap prediction interval (see meta-package).
null.effect	A numeric value specifying the effect under the null hypothesis.
method.bias	A character string indicating which test is to be used. Either "Begg", "Egger", or "Thompson", can be abbreviated. See function metabias.
n.e	Number of observations in experimental group (or total sample size in study).
n.c	Number of observations in control group.
pval	P-value (used to estimate the standard error).
df	Degrees of freedom (used in test or to construct confidence intervals).
lower	Lower limit of confidence interval (used to estimate the standard error).
upper	Upper limit of confidence interval (used to estimate the standard error).
level.ci	Level of confidence interval.
median	Median (used to estimate the treatment effect and standard error).
q1	First quartile (used to estimate the treatment effect and standard error).
q3	Third quartile (used to estimate the treatment effect and standard error).
min	Minimum (used to estimate the treatment effect and standard error).
max	Maximum (used to estimate the treatment effect and standard error).
method.mean	A character string indicating which method to use to approximate the mean from the median and other statistics (see Details).
method.sd	A character string indicating which method to use to approximate the standard deviation from sample size, median, interquartile range and range (see Details).
approx.TE	Approximation method to estimate treatment estimate (see Details).
approx.seTE	Approximation method to estimate standard error (see Details).
transf	A logical indicating whether inputs for arguments TE, lower and upper are already appropriately transformed to conduct the meta-analysis or on the original scale. If transf = TRUE (default), inputs are expected to be log odds ratios instead of odds ratios for sm = "OR" and Fisher's z transformed correlations instead of correlations for sm = "ZCOR", for example.
backtransf	A logical indicating whether results should be back transformed in printouts and plots. If backtransf = TRUE (default), results for sm = "OR" are printed as odds ratios rather than log odds ratios and results for sm = "ZCOR" are printed as correlations rather than Fisher's z transformed correlations, for example.
func.transf	A function used to transform inputs for arguments TE, lower and upper.
func.backtransf	A function used to back-transform results.
args.transf	An optional list to provide additional arguments to func.transf.
args.backtransf	An optional list to provide additional arguments to func.backtransf.
pscale	A numeric giving scaling factor for printing of single event probabilities or risk differences, i.e. if argument sm is equal to "PLOGIT", "PLN", "PRAW", "PAS", "PFT", or "RD".
irscale	A numeric defining a scaling factor for printing of single incidence rates or incidence rate differences, i.e. if argument sm is equal to "IR", "IRLN", "IRS", "IRFT", or "IRD".
irunit	A character specifying the time unit used to calculate rates, e.g. person-years.
text.common	A character string used in printouts and forest plot to label the pooled common effect estimate.
text.random	A character string used in printouts and forest plot to label the pooled random effects estimate.
text.predict	A character string used in printouts and forest plot to label the prediction interval.
text.w.common	A character string used to label weights of common effect model.
text.w.random	A character string used to label weights of random effects model.
title	Title of meta-analysis / systematic review.
complab	Comparison label.
outclab	Outcome label.
label.e	Label for experimental group.
label.c	Label for control group.
label.left	Graph label on left side of null effect in forest plot.
label.right	Graph label on right side of null effect in forest plot.
col.label.left	The colour of the graph label on the left side of the null effect.
col.label.right	The colour of the graph label on the right side of the null effect.
subgroup	An optional vector to conduct a meta-analysis with subgroups.
subgroup.name	A character string with a name for the subgroup variable.
print.subgroup.name	A logical indicating whether the name of the subgroup variable should be printed in front of the group labels.
sep.subgroup	A character string defining the separator between name of subgroup variable and subgroup label.
test.subgroup	A logical value indicating whether to print results of test for subgroup differences.
prediction.subgroup	A logical indicating whether prediction intervals should be printed for subgroups.
seed.predict.subgroup	A numeric vector providing seeds to calculate bootstrap prediction intervals within subgroups. Must be of same length as the number of subgroups.
byvar	Deprecated argument (replaced by 'subgroup').
id	Deprecated argument (replaced by 'cluster').
adhoc.hakn	Deprecated argument (replaced by 'adhoc.hakn.ci').
keepdata	A logical indicating whether original data (set) should be kept in meta object.
keeprma	A logical indicating whether rma.mv object from three-level meta-analysis should be stored.
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.
control	An optional list to control the iterative process to estimate the between-study variance \tau^2. This argument is passed on to rma.uni or rma.mv.
...	Additional arguments (to catch deprecated arguments).

Details

This function provides the generic inverse variance method for meta-analysis which requires treatment estimates and their standard errors (Borenstein et al., 2010). The method is useful, e.g., for pooling of survival data (using log hazard ratio and standard errors as input). Arguments TE and seTE can be used to provide treatment estimates and standard errors directly. However, it is possible to derive these quantities from other information.

Argument cycles can be used to conduct a meta-analysis of n-of-1 trials according to Senn (2024). In this case, argument seTE does not contain the standard error but standard deviation for individual trials / patients. Trial-specific standard errors are calculated from an average standard deviation multiplied by the number of cycles minus 1, i.e., the degrees of freedom. Details of the meta-analysis method are provided in Senn (2024). Note, arguments used in the approximation of means or standard errors, like lower and upper, or df, are ignored for the meta-analysis of n-of-1 trials.

A three-level random effects meta-analysis model (Van den Noortgate et al., 2013) is utilised if argument cluster is used and at least one cluster provides more than one estimate. Internally, rma.mv is called to conduct the analysis and weights.rma.mv with argument type = "rowsum" is used to calculate random effects weights.

Default settings are utilised for several arguments (assignments using gs function). These defaults can be changed for the current R session using the settings.meta function.

Furthermore, R function update.meta can be used to rerun a meta-analysis with different settings.

Approximate treatment estimates

Missing treatment estimates can be derived from

1. confidence limits provided by arguments lower and upper;

2. median, interquartile range and range (arguments median, q1, q3, min, and max);

3. median and interquartile range (arguments median, q1 and q3);

4. median and range (arguments median, min and max).

For confidence limits, the treatment estimate is defined as the center of the confidence interval (on the log scale for relative effect measures like the odds ratio or hazard ratio).

If the treatment effect is a mean it can be approximated from sample size, median, interquartile range and range.

By default, methods described in Luo et al. (2018) are utilised (argument method.mean = "Luo"):

• equation (7) if sample size, median and range are available,

• equation (11) if sample size, median and interquartile range are available,

• equation (15) if sample size, median, range and interquartile range are available.

Instead the methods described in Wan et al. (2014) are used if argument method.mean = "Wan":

• equation (2) if sample size, median and range are available,

• equation (14) if sample size, median and interquartile range are available,

• equation (10) if sample size, median, range and interquartile range are available.

The following methods are also available to estimate means from quantiles or ranges if R package estmeansd is installed:

• Method for Unknown Non-Normal Distributions (MLN) approach (Cai et al. (2021), argument method.mean = "Cai"),

• Quantile Estimation (QE) method (McGrath et al. (2020), argument method.mean = "QE-McGrath")),

• Box-Cox (BC) method (McGrath et al. (2020), argument method.mean = "BC-McGrath")).

By default, missing treatment estimates are replaced successively using these method, i.e., confidence limits are utilised before interquartile ranges. Argument approx.TE can be used to overwrite this default for each individual study:

• Use treatment estimate directly (entry "" in argument approx.TE);

• confidence limits ("ci" in argument approx.TE);

• median, interquartile range and range ("iqr.range");

• median and interquartile range ("iqr");

• median and range ("range").

Approximate standard errors

Missing standard errors can be derived from

1. p-value provided by arguments pval and (optional) df;

2. confidence limits (arguments lower, upper, and (optional) df);

3. sample size, median, interquartile range and range (arguments n.e and / or n.c, median, q1, q3, min, and max);

4. sample size, median and interquartile range (arguments n.e and / or n.c, median, q1 and q3);

5. sample size, median and range (arguments n.e and / or n.c, median, min and max).

For p-values and confidence limits, calculations are either based on the standard normal or t-distribution if argument df is provided. Furthermore, argument level.ci can be used to provide the level of the confidence interval.

Wan et al. (2014) describe methods to estimate the standard deviation (and thus the standard error by deviding the standard deviation with the square root of the sample size) from the sample size, median and additional statistics. Shi et al. (2020) provide an improved estimate of the standard deviation if the interquartile range and range are available in addition to the sample size and median. Accordingly, equation (11) in Shi et al. (2020) is the default (argument method.sd = "Shi"), if the median, interquartile range and range are provided (arguments median, q1, q3, min and max). The method by Wan et al. (2014) is used if argument method.sd = "Wan" and, depending on the sample size, either equation (12) or (13) is used. If only the interquartile range or range is available, equations (15) / (16) and (7) / (9) in Wan et al. (2014) are used, respectively. The sample size of individual studies must be provided with arguments n.e and / or n.c. The total sample size is calculated as n.e + n.c if both arguments are provided.

The following methods are also available to estimate standard deviations from quantiles or ranges if R package estmeansd is installed:

• Method for Unknown Non-Normal Distributions (MLN) approach (Cai et al. (2021), argument method.mean = "Cai"),

• Quantile Estimation (QE) method (McGrath et al. (2020), argument method.mean = "QE-McGrath")),

• Box-Cox (BC) method (McGrath et al. (2020), argument method.mean = "BC-McGrath")).

By default, missing standard errors are replaced successively using these method, e.g., p-value before confidence limits before interquartile range and range. Argument approx.seTE can be used to overwrite this default for each individual study:

• Use standard error directly (entry "" in argument approx.seTE);

• p-value ("pval" in argument approx.seTE);

• confidence limits ("ci");

• median, interquartile range and range ("iqr.range");

• median and interquartile range ("iqr");

• median and range ("range").

Confidence intervals for individual studies

For the mean difference (argument sm = "MD"), the confidence interval for individual studies can be based on the

• standard normal distribution (method.ci = "z"), or

• t-distribution (method.ci = "t").

By default, the first method is used if argument df is missing and the second method otherwise.

Note, this choice does not affect the results of the common effect and random effects meta-analysis.

Subgroup analysis

Argument subgroup can be used to conduct subgroup analysis for a categorical covariate. The metareg function can be used instead for more than one categorical covariate or continuous covariates.

Specify the null hypothesis of test for an overall effect

Argument null.effect can be used to specify the (treatment) effect under the null hypothesis in a test for an overall effect.

By default (null.effect = 0), the null hypothesis corresponds to "no difference" (which is obvious for absolute effect measures like the mean difference (sm = "MD") or standardised mean difference (sm = "SMD")). For relative effect measures, e.g., risk ratio (sm = "RR") or odds ratio (sm = "OR"), the null effect is defined on the log scale, i.e., log(RR) = 0 or log(OR) = 0 which is equivalent to testing RR = 1 or OR = 1.

Use of argument null.effect is especially useful for summary measures without a "natural" null effect, i.e., in situations without a second (treatment) group. For example, an overall proportion of 50% could be tested in the meta-analysis of single proportions with argument null.effect = 0.5.

Note, all tests for an overall effect are two-sided with the alternative hypothesis that the effect is unequal to null.effect.

Exclusion of studies from meta-analysis

Arguments subset and exclude can be used to exclude studies from the meta-analysis. Studies are removed completely from the meta-analysis using argument subset, while excluded studies are shown in printouts and forest plots using argument exclude (see Examples). Meta-analysis results are the same for both arguments.

Presentation of meta-analysis results

Internally, both common effect and random effects models are calculated regardless of values choosen for arguments common and random. Accordingly, the estimate for the random effects model can be extracted from component TE.random of an object of class "meta" even if argument random = FALSE. However, all functions in R package meta will adequately consider the values for common and random. For example, functions print.meta and forest.meta will not show results for the random effects model if random = FALSE.

A prediction interval will only be shown if prediction = TRUE.

Argument pscale can be used to rescale single proportions or risk differences, e.g. pscale = 1000 means that proportions are expressed as events per 1000 observations. This is useful in situations with (very) low event probabilities.

Argument irscale can be used to rescale single rates or rate differences, e.g. irscale = 1000 means that rates are expressed as events per 1000 time units, e.g. person-years. This is useful in situations with (very) low rates. Argument irunit can be used to specify the time unit used in individual studies (default: "person-years"). This information is printed in summaries and forest plots if argument irscale is not equal to 1.

Default settings for common, random, pscale, irscale, irunit and several other arguments can be set for the whole R session using settings.meta.

Value

An object of class c("metagen", "meta") with corresponding generic functions (see meta-object).

Note

R function rma.uni from R package metafor (Viechtbauer 2010) is called internally to estimate the between-study variance \tau^2.

Author(s)

Guido Schwarzer [e-mail]

References

Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010): A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods, 1, 97–111

Cai S, Zhou J, Pan J (2021): Estimating the sample mean and standard deviation from order statistics and sample size in meta-analysis. Statistical Methods in Medical Research, 30, 2701–2719

Luo D, Wan X, Liu J, Tong T (2018): Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range. Statistical Methods in Medical Research, 27, 1785–805

McGrath S, Zhao X, Steele R, et al. and the DEPRESsion Screening Data (DEPRESSD) Collaboration (2020): Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis. Statistical Methods in Medical Research, 29, 2520–2537

Senn S (2024): The analysis of continuous data from n-of-1 trials using paired cycles: a simple tutorial. Trials, 25.

Shi J, Luo D, Weng H, Zeng X-T, Lin L, Chu H, et al. (2020): Optimally estimating the sample standard deviation from the five-number summary. Research Synthesis Methods.

Viechtbauer W (2010): Conducting Meta-Analyses in R with the metafor Package. Journal of Statistical Software, 36, 1–48

Van den Noortgate W, López-López JA, Marín-Martínez F, Sánchez-Meca J (2013): Three-level meta-analysis of dependent effect sizes. Behavior Research Methods, 45, 576–94

Wan X, Wang W, Liu J, Tong T (2014): Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Medical Research Methodology, 14, 135

See Also

meta-package, update.meta, metabin, metacont, pairwise, print.meta, settings.meta

Examples

data(Fleiss1993bin)
m1 <- metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I")
m1

# Identical results using the generic inverse variance method with
# log risk ratio and its standard error:
# Note, argument 'n.e' in metagen() is used to provide the total
# sample size which is calculated from the group sample sizes n.e
# and n.c in meta-analysis m1.
m1.gen <- metagen(TE, seTE, studlab, n.e = n.e + n.c, data = m1, sm = "RR")
m1.gen
forest(m1.gen, leftcols = c("studlab", "n.e", "TE", "seTE"))

# Meta-analysis with prespecified between-study variance
#
metagen(m1$TE, m1$seTE, sm = "RR", tau.preset = sqrt(0.1))

# Meta-analysis of survival data:
#
logHR <- log(c(0.95, 1.5))
selogHR <- c(0.25, 0.35)
metagen(logHR, selogHR, sm = "HR")

# Paule-Mandel method to estimate between-study variance for data
# from Paule & Mandel (1982)
#
average <- c(27.044, 26.022, 26.340, 26.787, 26.796)
variance <- c(0.003, 0.076, 0.464, 0.003, 0.014)
#
metagen(average, sqrt(variance), sm = "MD", method.tau = "PM")

# Conduct meta-analysis using hazard ratios and 95% confidence intervals
#
# Data from Steurer et al. (2006), Analysis 1.1 Overall survival
# https://doi.org/10.1002/14651858.CD004270.pub2
#
study <- c("FCG on CLL 1996", "Leporrier 2001", "Rai 2000", "Robak 2000")
HR <- c(0.55, 0.92, 0.79, 1.18)
lower.HR <- c(0.28, 0.79, 0.59, 0.64)
upper.HR <- c(1.09, 1.08, 1.05, 2.17)
#
# Hazard ratios and confidence intervals as input
#
summary(metagen(HR, lower = lower.HR, upper = upper.HR,
  studlab = study, sm = "HR", transf = FALSE))
#
# Same result with log hazard ratios as input
#
summary(metagen(log(HR), lower = log(lower.HR), upper = log(upper.HR),
  studlab = study, sm = "HR"))
#
# Again, same result using an unknown summary measure and
# arguments 'func.transf' and 'func.backtransf'
#
summary(metagen(HR, lower = lower.HR, upper = upper.HR,
  studlab = study, sm = "Hazard ratio",
  func.transf = log, func.backtransf = exp))
#
# Finally, same result only providing argument 'func.transf' as the
# back-transformation for the logarithm is known
#
summary(metagen(HR, lower = lower.HR, upper = upper.HR,
  studlab = study, sm = "Hazard ratio",
  func.transf = log))

# Exclude MRC-1 and MRC-2 studies from meta-analysis, however,
# show them in printouts and forest plots
#
metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I",
  exclude = study %in% c("MRC-1", "MRC-2"))
#
# Exclude MRC-1 and MRC-2 studies completely from meta-analysis
#
metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I",
  subset = !(study %in% c("MRC-1", "MRC-2")))

# Exclude studies with total sample size above 1500
#
metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I",
  exclude = (n.asp + n.plac) > 1500)

# Exclude studies containing "MRC" in study name
#
metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I",
  exclude = grep("MRC", study))

# Use both arguments 'subset' and 'exclude'
#
metabin(d.asp, n.asp, d.plac, n.plac, study,
  data = Fleiss1993bin, sm = "RR", method = "I",
  subset = (n.asp + n.plac) > 1500,
  exclude = grep("MRC", study))

## Not run: 
# Three-level model: effects of modified school calendars on
# student achievement
data(dat.konstantopoulos2011, package = "metadat")
metagen(yi, sqrt(vi), studlab = study, data = dat.konstantopoulos2011,
  sm = "SMD",
  cluster = district, detail.tau = c("district", "district/school"))

## End(Not run)

meta documentation built on Oct. 31, 2024, 5:07 p.m.