metacont: Meta-analysis of continuous outcome data

In meta: General Package for Meta-Analysis

Meta-analysis of continuous outcome data

Description

Calculation of common and random effects estimates for meta-analyses with continuous outcome data; inverse variance weighting is used for pooling.

Usage

metacont(
  n.e,
  mean.e,
  sd.e,
  n.c,
  mean.c,
  sd.c,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  cluster = NULL,
  rho = 0,
  median.e,
  q1.e,
  q3.e,
  min.e,
  max.e,
  median.c,
  q1.c,
  q3.c,
  min.c,
  max.c,
  method.mean = "Luo",
  method.sd = "Shi",
  approx.mean.e,
  approx.mean.c = approx.mean.e,
  approx.sd.e,
  approx.sd.c = approx.sd.e,
  sm = gs("smcont"),
  method.ci = gs("method.ci.cont"),
  level = gs("level"),
  pooledvar = gs("pooledvar"),
  method.smd = gs("method.smd"),
  sd.glass = gs("sd.glass"),
  exact.smd = gs("exact.smd"),
  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"),
  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,
  method.bias = gs("method.bias"),
  backtransf = gs("backtransf"),
  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"),
  warn = gs("warn"),
  warn.deprecated = gs("warn.deprecated"),
  control = NULL,
  ...
)

Arguments

n.e	Number of observations in experimental group or an R object created with pairwise.
mean.e	Estimated mean in experimental group.
sd.e	Standard deviation in experimental group.
n.c	Number of observations in control group.
mean.c	Estimated mean in control group.
sd.c	Standard deviation in control group.
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.
exclude	An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
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.
median.e	Median in experimental group (used to estimate the mean and standard deviation).
q1.e	First quartile in experimental group (used to estimate the mean and standard deviation).
q3.e	Third quartile in experimental group (used to estimate the mean and standard deviation).
min.e	Minimum in experimental group (used to estimate the mean and standard deviation).
max.e	Maximum in experimental group (used to estimate the mean and standard deviation).
median.c	Median in control group (used to estimate the mean and standard deviation).
q1.c	First quartile in control group (used to estimate the mean and standard deviation).
q3.c	Third quartile in control group (used to estimate the mean and standard deviation).
min.c	Minimum in control group (used to estimate the mean and standard deviation).
max.c	Maximum in control group (used to estimate the mean and standard deviation).
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.mean.e	Approximation method to estimate means in experimental group (see Details).
approx.mean.c	Approximation method to estimate means in control group (see Details).
approx.sd.e	Approximation method to estimate standard deviations in experimental group (see Details).
approx.sd.c	Approximation method to estimate standard deviations in control group (see Details).
sm	A character string indicating which summary measure ("MD", "SMD", or "ROM") is to be used for pooling of studies.
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.
pooledvar	A logical indicating if a pooled variance should be used for the mean difference (sm="MD") or ratio of means (sm="ROM").
method.smd	A character string indicating which method is used to estimate the standardised mean difference (sm="SMD"). Either "Hedges" for Hedges' g (default), "Cohen" for Cohen's d, or "Glass" for Glass' delta, can be abbreviated.
sd.glass	A character string indicating which standard deviation is used in the denominator for Glass' method to estimate the standardised mean difference. Either "control" using the standard deviation in the control group (sd.c) or "experimental" using the standard deviation in the experimental group (sd.e), can be abbreviated.
exact.smd	A logical indicating whether exact formulae should be used in estimation of the standardised mean difference and its standard error (see Details).
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.
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).
method.bias	A character string indicating which test is to be used. Either "Begg", "Egger", "Thompson", or "Pustejovsky" (see metabias), can be abbreviated.
backtransf	A logical indicating whether results for ratio of means (sm="ROM") should be back transformed in printouts and plots. If TRUE (default), results will be presented as ratio of means; otherwise log ratio of means will be shown.
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.
warn	A logical indicating whether warnings should be printed (e.g., if studies are excluded from meta-analysis due to zero standard deviations).
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.
...	Additional arguments (to catch deprecated arguments).

Details

Calculation of common and random effects estimates for meta-analyses with continuous outcome data; inverse variance weighting is used for pooling.

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.

Three different types of summary measures are available for continuous outcomes:

• mean difference (argument sm = "MD")

• standardised mean difference (sm = "SMD")

• ratio of means (sm = "ROM")

Standardised mean difference

For the standardised mean difference three methods are implemented:

• Hedges' g (default, method.smd = "Hedges") - see Hedges (1981)

• Cohen's d (method.smd = "Cohen") - see Cohen (1988)

• Glass' delta (method.smd = "Glass") - see Glass (1976)

Hedges (1981) calculated the exact bias in Cohen's d which is a ratio of gamma distributions with the degrees of freedom, i.e. total sample size minus two, as argument. By default (argument exact.smd = FALSE), an accurate approximation of this bias provided in Hedges (1981) is utilised for Hedges' g as well as its standard error; these approximations are also used in RevMan 5. Following Borenstein et al. (2009) these approximations are not used in the estimation of Cohen's d. White and Thomas (2005) argued that approximations are unnecessary with modern software and accordingly promote to use the exact formulae; this is possible using argument exact.smd = TRUE. For Hedges' g the exact formulae are used to calculate the standardised mean difference as well as the standard error; for Cohen's d the exact formula is only used to calculate the standard error. In typical applications (with sample sizes above 10), the differences between using the exact formulae and the approximation will be minimal.

For Glass' delta, by default (argument sd.glass = "control"), the standard deviation in the control group (sd.c) is used in the denominator of the standard mean difference. The standard deviation in the experimental group (sd.e) can be used by specifying sd.glass = "experimental".

Ratio of means

Meta-analysis of ratio of means – also called response ratios – is described in Hedges et al. (1999) and Friedrich et al. (2008). Calculations are conducted on the log scale and list elements TE, TE.common, and TE.random contain the logarithm of the ratio of means. In printouts and plots these values are back transformed if argument backtransf = TRUE.

Approximate means from sample sizes, medians and other statistics

Missing means in the experimental group (analogously for the control group) can be derived from

1. sample size, median, interquartile range and range (arguments n.e, median.e, q1.e, q3.e, min.e, and max.e),

2. sample size, median and interquartile range (arguments n.e, median.e, q1.e, and q3.e), or

3. sample size, median and range (arguments n.e, median.e, min.e, and max.e).

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

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

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

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

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

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

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

• equation (2) if sample size, median and 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 means are replaced successively using interquartile ranges and ranges (if available), interquartile ranges (if available) and finally ranges. Arguments approx.mean.e and approx.mean.c can be used to overwrite this behaviour for each individual study and treatment arm:

• use means directly (entry "" in argument approx.mean.e or approx.mean.c);

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

• median and interquartile range ("iqr");

• median and range ("range").

Approximate standard deviations from sample sizes, medians and other statistics

Missing standard deviations in the experimental group (analogously for the control group) can be derived from

1. sample size, median, interquartile range and range (arguments n.e, median.e, q1.e, q3.e, min.e, and max.e),

2. sample size, median and interquartile range (arguments n.e, median.e, q1.e and q3.e), or

3. sample size, median and range (arguments n.e, median.e, min.e and max.e).

Wan et al. (2014) describe methods to estimate the standard deviation 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. 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 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 deviations are replaced successively using these method, i.e., interquartile ranges and ranges are used before interquartile ranges before ranges. Arguments approx.sd.e and approx.sd.c can be used to overwrite this default for each individual study and treatment arms:

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

• sample size, median and interquartile range ("iqr");

• sample size, 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", default), or

• t-distribution (method.ci = "t").

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.

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 in metagen). 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. E.g. function print.meta will not print results for the random effects model if random = FALSE.

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

Value

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

Note

The function metagen is called internally to calculate individual and overall treatment estimates and standard errors.

Author(s)

Guido Schwarzer [e-mail]

References

Borenstein M, Hedges LV, Higgins JPT, Rothstein HR (2009): Introduction to Meta-Analysis. Chichester: Wiley

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

Cohen J (1988): Statistical Power Analysis for the Behavioral Sciences (second ed.). Lawrence Erlbaum Associates

Friedrich JO, Adhikari NK, Beyene J (2008): The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: A simulation study. BMC Medical Research Methodology, 8, 32

Glass G (1976): Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3–8

Hedges LV (1981): Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28

Hedges LV, Gurevitch J, Curtis PS (1999): The meta-analysis of response ratios in experimental ecology. Ecology, 80, 1150–6

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

Review Manager (RevMan) [Computer program]. Version 5.4. The Cochrane Collaboration, 2020

Shi J, Luo D, Weng H, Zeng XT, Lin L, Chu H, Tong T (2020): Optimally estimating the sample standard deviation from the five-number summary. Research Synthesis Methods, 11, 641–54

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

White IR, Thomas J (2005): Standardized mean differences in individually-randomized and cluster-randomized trials, with applications to meta-analysis. Clinical Trials, 2, 141–51

See Also

meta-package, update.meta, metabin, metagen, pairwise

Examples

data(Fleiss1993cont)

# Meta-analysis with Hedges' g as effect measure
#
m1 <- metacont(n.psyc, mean.psyc, sd.psyc, n.cont, mean.cont, sd.cont,
  data = Fleiss1993cont, sm = "SMD")
m1
forest(m1)

# Use Cohen's d instead of Hedges' g as effect measure
#
update(m1, method.smd = "Cohen")

# Use Glass' delta instead of Hedges' g as effect measure
#
update(m1, method.smd = "Glass")

# Use Glass' delta based on the standard deviation in the experimental group
#
update(m1, method.smd = "Glass", sd.glass = "experimental")

# Calculate Hedges' g based on exact formulae
#
update(m1, exact.smd = TRUE)

data(amlodipine)
m2 <- metacont(n.amlo, mean.amlo, sqrt(var.amlo),
  n.plac, mean.plac, sqrt(var.plac),
  data = amlodipine, studlab = study)
m2

# Use pooled variance
#
update(m2, pooledvar = TRUE)

# Meta-analysis of response ratios (Hedges et al., 1999)
#
data(woodyplants)
m3 <- metacont(n.elev, mean.elev, sd.elev, n.amb, mean.amb, sd.amb,
  data = woodyplants, sm = "ROM")
m3
print(m3, backtransf = FALSE)

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