metafor (version 1.9-2)

transf: Transformation Functions

Description

A set of transformation functions useful for meta-analyses.

Usage

transf.rtoz(xi, ...)
transf.ztor(xi, ...)
transf.logit(xi, ...)
transf.ilogit(xi, ...)
transf.arcsin(xi, ...)
transf.iarcsin(xi, ...)
transf.pft(xi, ni, ...)
transf.ipft(xi, ni, ...)
transf.ipft.hm(xi, targs, ...)
transf.isqrt(xi, ...)
transf.irft(xi, ti, ...)
transf.iirft(xi, ti, ...)
transf.ahw(xi, ...)
transf.iahw(xi, ...)
transf.abt(xi, ...)
transf.iabt(xi, ...)
transf.ztor.int(xi, targs, ...)
transf.exp.int(xi, targs, ...)
transf.ilogit.int(xi, targs, ...)

Arguments

xi

vector of values to be transformed.

ni

vector of sample sizes.

ti

vector of person-times at risk.

targs

list with additional arguments for the transformation function. See Details.

...

other arguments.

Value

• A vector with the transformed values.

Details

The following transformation functions are currently implemented:

• transf.rtoz: Fisher's r-to-z transformation.
• transf.ztor: inverse of the Fisher's r-to-z transformation.
• transf.logit: logit (log odds) transformation.
• transf.ilogit: inverse of the logit transformation.
• transf.arcsin: arcsine transformation.
• transf.iarcsin: inverse of the arcsine transformation.
• transf.pft: Freeman-Tukey (double arcsine) transformation for proportions. See Freeman & Tukey (1950). Thexiargument is used to specify the proportions and theniargument the corresponding sample sizes.
• transf.ipft: inverse of the Freeman-Tukey (double arcsine) transformation for proportions. See Miller (1978).
• transf.ipft.hm: inverse of the Freeman-Tukey (double arcsine) transformation for proportions using the harmonic mean of the sample sizes for the back-transformation. See Miller (1978). The sample sizes are specified via thetargsargument (the list element should be calledni).
• transf.isqrt: inverse of the square-root transformation (i.e., function to square a number).
• transf.irft: Freeman-Tukey transformation for incidence rates. See Freeman & Tukey (1950). Thexiargument is used to specify the incidence rates and thetiargument the corresponding person-time at risk.
• transf.iirft: inverse of the Freeman-Tukey transformation for incidence rates.
• transf.ahw: Transformation of coefficient alpha as suggested by Hakstian & Whalen (1976).
• transf.iahw: Inverse of the transformation of coefficient alpha as suggested by Hakstian & Whalen (1976).
• transf.abt: Transformation of coefficient alpha as suggested by Bonett (2002).
• transf.iabt: Inverse of the transformation of coefficient alpha as suggested by Bonett (2002).
• transf.ztor.int: integral transformation method for the z-to-r transformation.
• transf.exp.int: integral transformation method for the exponential transformation.
• transf.ilogit.int: integral transformation method for the inverse of the logit transformation.

The integral transformation method for a transformation function $h(z)$ integrates $h(z) f(z)$ over $z$ using the limits targs$lower and targs$upper, where $f(z)$ is the density of a normal distribution with mean equal to xi and variance equal to targs$tau2. An example is provided below.

References

Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics, 27, 335--340. Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample. Metron, 1, 1--32. Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607--611. Hakstian, A. R., & Whalen, T. E. (1976). A k-sample significance test for independent alpha coefficients. Psychometrika, 41, 219--231. Miller, J. J. (1978). The inverse of the Freeman-Tukey double arcsine transformation. American Statistician, 32, 138. Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. http://www.jstatsoft.org/v36/i03/.

Examples

### load BCG vaccine data
data(dat.bcg)

### meta-analysis of the log relative risks using a random-effects model
res <- rma(ai=tpos, bi=tneg, ci=cpos, di=cneg,
           measure="RR", data=dat.bcg, method="REML")

### average relative risk with 95\% CI
predict(res, transf=exp)

### average relative risk with 95\% CI using the integral transformation
predict(res, transf=transf.exp.int, targs=list(tau2=res$tau2, lower=-4, upper=4))