metafor (version 1.9-2)

fsn: Compute Fail-Safe N (File Drawer Analysis)

Description

Function to compute the fail-safe N.

Usage

fsn(yi, vi, sei, weights, data, type="Rosenthal", alpha=.05, target, subset, digits=4)

Arguments

yi

vector with the observed effect sizes or outcomes. See Details

vi

vector with the corresponding sampling variances. See Details

sei

vector with the corresponding standard errors. See Details

weights

vector of length $k$ with the corresponding inverse sampling variances. See Details.

data

optional data frame containing the variables given to the arguments above.

type

vector indicating the method to use for the calculation of the fail-safe N. Possible options are "Rosenthal", "Orwin", or "Rosenberg". See below for more details.

alpha

target alpha level to use for the Rosenthal and Rosenberg methods (.05 by default).

target

target average effect size to use for the Orwin method. If undefined, then the target average effect size will be equal to the observed average effect size divided by 2.

subset

optional vector indicating the subset of studies that should be used for the calculation. This can be a logical vector of length $k$ or a numeric vector indicating the indices of the observations to include.

digits

integer specifying the number of decimal places to which the printed results should be rounded (default is 4).

Value

• An object of class "fsn". The object is a list containing the following components:
• type
  the method used.
• fsnum
  the calculated fail-safe N.
• alpha
  the target alpha level.
• pval
  the p-value of the observed results. NA for the Orwin method.
• meanes
  the average effect size of the observed results. NA for the Rosenthal method.
• target
  the target effect size. NA for the Rosenthal and Rosenberg methods.
• The results are formated and printed with the print.fsn function.

Details

The function can be used in conjunction with any of the usual effect size or outcome measures used in meta-analyses (e.g., log odds ratios, log relative risks, risk differences, mean differences, standardized mean differences, raw correlation coefficients, correlation coefficients transformed with Fisher's r-to-z transformation, and so on). Simply specify the observed outcomes via the yi argument and the corresponding sampling variances via the vi argument (instead of specifying vi, one can specify the standard errors (the square root of the sampling variances) via the sei argument or the inverse of the sampling variances via the weights argument). The escalc function can be used to compute a wide variety of effect size and outcome measures (and the corresponding sampling variances) based on summary statistics. The Rosenthal method (sometimes called a file drawer analysis) calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce the combined significance level (p-value) to a target alpha level (e.g., .05). The calculation is based on Stouffer's method to combine p-values and is described in Rosenthal (1979). The Orwin method calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce the (unweighted) average effect size to a target (unweighted) average effect size. The method is described in Orwin (1983). The Rosenberg method calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce significance level (p-value) of the (weighted) average effect size (based on a fixed-effects model) to a target alpha level (e.g., .05). The method is described in Rosenberg (2005).

References

Rosenthal, R. (1979). The "file drawer problem" and tolerance for null results. Psychological Bulletin, 86, 638--641. Orwin, R. G. (1983). A fail-safe N for effect size in meta-analysis. Journal of Educational Statistics, 8, 157--159. Rosenberg, M. S. (2005). The file-drawer problem revisited: A general weighted method for calculating fail-safe numbers in meta-analysis. Evolution, 59, 464--468. 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/.

See Also

ranktest, regtest, trimfill

Examples

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

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

fsn(yi, vi, data=dat)
fsn(yi, vi, data=dat, type="Orwin")
fsn(yi, vi, data=dat, type="Rosenberg")