meta-sm | R Documentation |

Description of summary measures available in R package **meta**

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.

Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de

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`

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