# meta-transf: Auxiliary functions for (back) transformations In meta: General Package for Meta-Analysis

 meta-transf R Documentation

## Auxiliary functions for (back) transformations

### Description

Auxiliary functions to (back) transform effect estimates or confidence / prediction interval limit(s).

### Usage

transf(x, sm, func = NULL, args = NULL)

cor2z(x)

p2asin(x)

p2logit(x)

VE2logVR(x)

backtransf(x, sm, n, time, func = NULL, args = NULL)

asin2ir(x, time = NULL)

asin2p(x, n = NULL)

logit2p(x)

logVR2VE(x)

z2cor(x)

### Arguments

 x Numerical vector with effect estimates, lower or upper confidence / prediction interval limit(s). sm Summary measure. func User-specified function for (back) transformation. args Function arguments for user-specified function. n Sample size(s) to back transform Freeman-Tukey transformed proportions. time Time(s) to back transform Freeman-Tukey transformed incidence rates.

### Details

Often in a meta-analysis, effect estimates are transformed before calculating a weighted average. For example, the log odds ratio and its standard error is used instead of the odds ratio in R function metagen. To report the results of a meta-analysis, effect estimates are typically back transformed to the original scale. R package meta provides some auxiliary functions for (back) transformations.

#### Transformations

The following auxiliary functions are provided by R package meta to transform effect estimates or confidence / prediction interval limits.

 Function Transformation cor2z Correlations to Fisher's Z transformed correlations p2logit Proportions to logit transformed proportions p2asin Proportions to arcsine transformed proportions VE2logVR Vaccine efficacy / effectiveness to log vaccine ratio

Note, no function for the Freeman-Tukey arcsine transformation is provided as this transformation is based on the number of events and sample sizes instead of the effect estimates.

R function transf is a wrapper function for the above and additional transformations, e.g., the log transformation using log for odds or risk ratios. Argument sm is mandatory to specify the requested transformation. It is also possible to specify a different function with arguments func and args.

#### Back transformations

The following auxiliary functions are available to back transform effect estimates or confidence / prediction interval limits.

 Function Transformation asin2ir Freeman-Tukey arcsine transformed rates to rates asin2p (Freeman-Tukey) arcsine transformed proportions to proportions logit2p Logit transformed proportions to proportions logVR2VE Log vaccine ratio to vaccine efficacy / effectiveness z2cor Fisher's Z transformed correlations to correlations

Argument time is mandatory in R function asin2ir.

If argument n is provided in R function asin2p, Freeman-Tukey arcsine transformed proportions are back transformed. Otherwise, arcsine transformed proportions are back transformed.

R function backtransf is a wrapper function for the above and additional transformations, e.g., the exponential transformation using exp for log odds or log risk ratios. Argument sm is mandatory to specify the requested transformation. For the Freeman-Tukey transformations, argument n or time is mandatory.

It is also possible to specify a different function with arguments func and args.

### Author(s)

Guido Schwarzer guido.schwarzer@uniklinik-freiburg.de