transf {metafor}R Documentation

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)
transf.dtou1(xi)
transf.dtou2(xi)
transf.dtou3(xi)
transf.dtorpb(xi, n1i, n2i)
transf.dtobesd(xi)
transf.dtomd(xi, targs)
transf.lnortord(xi, pc)
transf.lnortorr(xi, pc)
transf.lnortod.norm(xi)
transf.lnortod.logis(xi)
transf.dtolnor.norm(xi)
transf.dtolnor.logis(xi)
transf.lnortortet.pearson(xi)
transf.lnortortet.digby(xi)

Arguments

xi

vector of values to be transformed.

ni

vector of sample sizes.

n1i

vector of sample sizes for the first group.

n2i

vector of sample sizes for the second group.

ti

vector of person-times at risk.

pc

control group risk (either a single value or a vector).

targs

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

Details

The following transformation functions are currently implemented:

Value

A vector with the transformed values.

Note

The integral transformation method for a transformation function \(h(z)\) is given by \[\int_{\textrm{lower}}^{\textrm{upper}} h(z) f(z) dz\] 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.

Author(s)

Wolfgang Viechtbauer wvb@metafor-project.org https://www.metafor-project.org

References

Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics, 27(4), 335–340. https://doi.org/10.3102/10769986027004335

Chinn, S. (2000). A simple method for converting an odds ratio to effect size for use in meta-analysis. Statistics in Medicine, 19(22), 3127–3131. https://doi.org/10.1002/1097-0258(20001130)19:22<3127::aid-sim784>3.0.co;2-m

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Cox, D. R., & Snell, E. J. (1989). Analysis of binary data (2nd ed.). London: Chapman & Hall.

Digby, P. G. N. (1983). Approximating the tetrachoric correlation coefficient. Biometrics, 39(3), 753–757. https://doi.org/10.2307/2531104

Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron, 1, 1–32. http://hdl.handle.net/2440/15169

Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21(4), 607–611. https://doi.org/10.1214/aoms/1177729756

Hakstian, A. R., & Whalen, T. E. (1976). A k-sample significance test for independent alpha coefficients. Psychometrika, 41(2), 219–231. https://doi.org/10.1007/BF02291840

McGraw, K. O., & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111(2), 361–365. https://doi.org/10.1037/0033-2909.111.2.361

Miller, J. J. (1978). The inverse of the Freeman-Tukey double arcsine transformation. American Statistician, 32(4), 138. https://doi.org/10.1080/00031305.1978.10479283

Pearson, K. (1900). Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable. Philosophical Transactions of the Royal Society of London, Series A, 195, 1–47. https://doi.org/10.1098/rsta.1900.0022

Rosenthal, R., & Rubin, D. B. (1982). A simple, general purpose display of magnitude of experimental effect. Journal of Educational Psychology, 74(2), 166–169. https://doi.org/10.1037/0022-0663.74.2.166

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. https://doi.org/10.18637/jss.v036.i03

Examples

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### fit random-effects model
res <- rma(yi, vi, data=dat)

### average risk ratio with 95% CI (but technically, this provides an
### estimate of the median risk ratio, not the mean risk ratio!)
predict(res, transf=exp)

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

### this also works
predict(res, transf=transf.exp.int, targs=list(tau2=res$tau2))

### this as well
predict(res, transf=transf.exp.int, targs=res$tau2)

[Package metafor version 4.0-0 Index]