Description of summary measures available in R package meta
Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de
The following summary measures (argument sm) are recognized
in R package meta.
metabin)| Argument | Summary measure |
sm = "OR" | Odds ratio (Fleiss, 1993) |
sm = "RR" | Risk ratio (Fleiss, 1993) |
sm = "RD" | Risk difference (Fleiss, 1993) |
sm = "ASD" | Arcsine difference (Rücker et al., 2009) |
sm = "DOR" | Diagnostic odds ratio (Moses et al., 1993) |
sm = "VE" | Vaccine efficacy or vaccine effectiveness |
Note, mathematically, odds ratios and diagnostic odds ratios are
identical, however, the labels in printouts and figures
differ. Furthermore, log risk ratio (logRR) and log vaccine ratio
(logVR) are mathematical identical, however, back-transformed
results differ as vaccine efficacy or effectiveness is defined as
VE = 100 * (1 - RR).
A continuity correction is used for some summary measures in the
case of a zero cell count (see metabin).
List elements TE, TE.common, TE.random, etc.,
contain transformed values, e.g., log odds ratios, log risk ratios
or log vaccine ratios. In printouts and plots transformed values
are back transformed if argument backtransf = TRUE
(default), with exception of the arcsine difference where no
back-transformation exists. Auxiliary function
logVR2VE is used to back-transform log vaccine ratios
to vaccine efficacy or effectiveness while exp
is used to back-transform log odds or risk ratios.
metacont)| Argument | Summary measure |
sm = "MD" | Mean difference |
sm = "SMD" | Standardised mean difference |
sm = "ROM" | Ratio of means |
Three variants to calculate the standardised mean difference are
available (see metacont).
For the ratio of means, list elements TE, TE.common,
TE.random, etc., contain the log transformed ratio of
means. In printouts and plots these values are back transformed
using exp if argument backtransf = TRUE
(default).
metacor)| Argument | Summary measure |
sm = "ZCOR" | Fisher's z transformed correlation |
sm = "COR" | Untransformed correlations |
For Fisher's z transformed correlations, list elements TE,
TE.common, TE.random, etc., contain the transformed
correlations. In printouts and plots these values are back
transformed using auxiliary function z2cor if
argument backtransf = TRUE (default).
metainc)| Argument | Summary measure |
sm = "IRR" | Incidence rate ratio |
sm = "IRD" | Incidence rate difference |
sm = "IRSD" | Square root transformed incidence rate difference |
sm = "VE" | Vaccine efficacy or vaccine effectiveness |
Note, log incidence rate ratio (logIRR) and log vaccine ratio
(logVR) are mathematical identical, however, back-transformed
results differ as vaccine efficacy or effectiveness is defined as
VE = 100 * (1 - IRR).
List elements TE, TE.common, TE.random, etc.,
contain the transformed incidence rates. In printouts and plots
these values are back transformed if argument backtransf =
TRUE (default). For back-transformation, exp
is used for the incidence rate ratio, power of 2 is used for square
root transformed rates and logVR2VE is used for
vaccine efficacy / effectiveness.
metamean)| Argument | Summary measure |
sm = "MRAW" | Raw, i.e. untransformed, means |
sm = "MLN" | Log transformed means |
Calculations are conducted on the log scale if sm =
"MLN". Accordingly, list elements TE, TE.common, and
TE.random contain the logarithm of means. In printouts and
plots these values are back transformed using
exp if argument backtransf = TRUE.
metaprop)
The following transformations of proportions are implemented to calculate an overall proportion:
| Argument | Summary measure |
sm = "PLOGIT" | Logit transformation |
sm = "PAS" | Arcsine transformation |
sm = "PFT" | Freeman-Tukey Double arcsine transformation |
sm = "PLN" | Log transformation |
sm = "PRAW" | No transformation |
List elements TE, TE.common, TE.random, etc.,
contain the transformed proportions. In printouts and plots these
values are back transformed if argument backtransf = TRUE
(default). For back-transformation, logit2p is used
for logit transformed proportions, asin2p is used for
(Freeman-Tukey) arcsine transformed proportions and
exp is used for log transformed proportions.
metarate)
The following transformations of incidence rates are implemented to calculate an overall rate:
| Argument | Summary measure |
sm = "IRLN" | Log transformation |
sm = "IRS" | Square root transformation |
sm = "IRFT" | Freeman-Tukey Double arcsine transformation |
sm = "IR" | No transformation |
List elements TE, TE.common, TE.random, etc.,
contain the transformed incidence rates. In printouts and plots
these values are back transformed if argument backtransf =
TRUE (default). For back-transformation, exp
is used for log transformed rates, power of 2 is used for square
root transformed rates and asin2ir is used for
Freeman-Tukey arcsine transformed rates.
metagen)
The following summary measures are recognised in addition to the above mentioned summary measures:
| Argument | Summary measure |
sm = "HR" | Hazard ratio |
sm = "VE" | Vaccine efficacy or vaccine effectiveness |
List elements TE, TE.common, TE.random, etc.,
contain transformed values, i.e., log hazard ratios and log vaccine
ratios. In printouts and plots these values are back transformed if
argument backtransf = TRUE (default); see also
meta-transf.
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
Fleiss JL (1993): The statistical basis of meta-analysis. Statistical Methods in Medical Research, 2, 121--45
Moses LE, Shapiro D, Littenberg B (1993): Combining Independent Studies of a Diagnostic Test into a Summary Roc Curve: Data-Analytic Approaches and Some Additional Considerations. Statistics in Medicine, 12, 1293--1316
Rücker G, Schwarzer G, Carpenter J, Olkin I (2009): Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells. Statistics in Medicine, 28, 721--38
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
meta-package, meta-transf,
meta-object, print.meta,
summary.meta, forest.meta