meta (version 2.3-0)

metaprop: Meta-analysis of single proportions

Description

Calculation of an overall proportion from studies reporting a single proportion.

Usage

metaprop(event, n, studlab,
         data = NULL, subset = NULL,
         sm="PFT", freeman.tukey,
         incr=0.5, allincr=FALSE, addincr=FALSE,
         level = 0.95, level.comb = level,
         comb.fixed=TRUE, comb.random=TRUE,
         hakn=FALSE,
         method.tau="DL", tau.preset=NULL, TE.tau=NULL,
         method.bias="linreg",
         title="", complab="", outclab="",
         byvar, bylab, print.byvar=TRUE,
         warn=TRUE)

Arguments

event

Number of events.

n

Number of observations.

studlab

An optional vector with study labels.

data

An optional data frame containing the study information, i.e., event and n.

subset

An optional vector specifying a subset of studies to be used.

sm

A character string indicating which summary measure ("PFT", "PAS", "PRAW", "PLN", or "PLOGIT") is to be used for pooling of studies, see Details.

freeman.tukey

Use of this argument is deprecated, please instead use argument sm, see Details.

incr

A numeric which is added to each cell frequency for studies with a zero cell count.

allincr

A logical indicating if incr is added to each cell frequency of all studies if at least one study has a zero cell count. If FALSE (default), incr is added only to each cell frequency of studies with a zero cell count.

addincr

A logical indicating if incr is added to each cell frequency of all studies irrespective of zero cell counts.

level

The level used to calculate confidence intervals for individual studies.

level.comb

The level used to calculate confidence intervals for pooled estimates.

comb.fixed

A logical indicating whether a fixed effect meta-analysis should be conducted.

comb.random

A logical indicating whether a random effects meta-analysis should be conducted.

hakn

A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.

method.tau

A character string indicating which method is used to estimate the between-study variance tau-squared. Either "DL", "REML", "ML", "HS", "SJ", "HE", or "EB"

tau.preset

Prespecified value for between-study variance tau-squared.

TE.tau

Overall treatment effect used to estimate the between-study variance tau-squared.

method.bias

A character string indicating which test is to be used. Either "rank", "linreg", or "mm", can be abbreviated.

title

Title of meta-analysis / systematic review.

complab

Comparison label.

outclab

Outcome label.

byvar

An optional vector containing grouping information (must be of same length as event.e).

bylab

A character string with a label for the grouping variable.

print.byvar

A logical indicating whether the name of the grouping variable should be printed in front of the group labels.

warn

A logical indicating whether the addition of incr to studies with zero cell frequencies should result in a warning.

Value

• An object of class c("metaprop", "meta") with corresponding print, summary, plot function. The object is a list containing the following components:
• event, n, studlab,
• sm, incr, allincr, addincr,
• level, level.comb,
  As defined above.
• comb.fixed, comb.random,
• hakn, method.tau, tau.preset, TE.tau, method.bias,
• byvar, bylab, print.byvar, warn
• TE, seTE
  Estimated (un)transformed proportion and its standard error for individual studies.
• w.fixed, w.random
  Weight of individual studies (in fixed and random effects model).
• TE.fixed, seTE.fixed
  Estimated overall (un)transformed proportion and standard error (fixed effect model).
• lower.fixed, upper.fixed
  Lower and upper confidence interval limits (fixed effect model).
• zval.fixed, pval.fixed
  z-value and p-value for test of overall effect (fixed effect model).
• TE.random, seTE.random
  Estimated overall (un)transformed proportion and standard error (random effects model).
• lower.random, upper.random
  Lower and upper confidence interval limits (random effects model).
• zval.random, pval.random
  z-value or t-value and corresponding p-value for test of overall effect (random effects model).
• k
  Number of studies combined in meta-analysis.
• Q
  Heterogeneity statistic Q.
• tau
  Square-root of between-study variance.
• sm
  A character string: "proportion"
• method
  A character string indicating method used for pooling: "Inverse"
• df.hakn
  Degrees of freedom for test of treatment effect for Hartung-Knapp method (only if hakn=TRUE).
• call
  Function call.
• version
  Version of R package meta used to create object.

Details

Fixed effect and random effects meta-analysis of single proportions to calculate an overall proportion. The following transformations of proportions are implemented to calculate an overall proportion:

• sm="PFT": Freeman-Tukey Double arcsine transformation
• sm="PAS": Arcsine transformation
• sm="PRAW": Raw, i.e. untransformed, proportions
• sm="PLN": Log transformation
• sm="PLOGIT": Logit transformation

In older versions of the R package meta (< 1.5.0), only the Freeman-Tukey Double arcsine transformation and the arcsine transformation were implemented and an argument freeman.tukey could be used to distinguish between these two methods. The use of the argument freeman.tukey is deprecated and the argument will probably removed from the function metaprop in the future. At the moment, a correponding warning message is printed if the argument freeman.tukey is used. If the summary measure is equal to "PRAW", "PLN", or "PLOGIT", a continuity correction is applied if any studies has a zero cell count. By default, 0.5 is added to all cell frequencies of studies with a zero cell count (argument incr).

Note, exact binomial confidence intervals will be calculated for individual study results, e.g. in R function summary.meta. Internally, both fixed effect and random effects models are calculated regardless of values choosen for arguments comb.fixed and comb.random. Accordingly, the estimate for the random effects model can be extracted from component TE.random of an object of class "meta" even if comb.random=FALSE. However, all functions in R package meta will adequately consider the values for comb.fixed and comb.random. E.g. function print.meta will not print results for the random effects model if comb.random=FALSE.

If R package metafor (Viechtbauer 2010) is installed, the following statistical methods are also available.

For the random effects model (argument comb.random=TRUE), the method by Hartung and Knapp (Knapp, Hartung 2003) is used to adjust test statistics and confidence intervals if argument hakn=TRUE (internally R function rma.uni of R package metafor is called).

Several methods are available to estimate the between-study variance $\tau^2$ (argument method.tau):

• DerSimonian-Laird estimator (method.tau="DL") (default)
• Restricted maximum-likelihood estimator (method.tau="REML")
• Maximum-likelihood estimator (method.tau="ML")
• Hunter-Schmidt estimator (method.tau="HS")
• Sidik-Jonkman estimator (method.tau="SJ")
• Hedges estimator (method.tau="HE")
• Empirical Bayes estimator (method.tau="EB").

For all but the DerSimonian-Laird method the R function rma.uni of R package metafor is called internally. See help page of R function rma.uni for more details on the various methods to estimate between-study variance $\tau^2$.

References

Edward JM et al. (2006), Adherence to antiretroviral therapy in sub-saharan Africa and North America - a meta-analysis. Journal of the American Medical Association, 296, 679--690.

Freeman MF & Tukey JW (1950), Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607--611.

Knapp G & Hartung J (2003), Improved Tests for a Random Effects Meta-regression with a Single Covariate. Statistics in Medicine, 22, 2693-710, doi: 10.1002/sim.1482 .

Miller JJ (1978), The inverse of the Freeman-Tukey double arcsine transformation. The American Statistician, 32, 138.

Pettigrew HM, Gart JJ, Thomas DG (1986), The bias and higher cumulants of the logarithm of a binomial variate. Biometrika, 73, 425--435.

Viechtbauer W (2010), Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1--48.

See Also

metacont, metagen, print.meta

Examples

metaprop(4:1, c(10, 20, 30, 40))
metaprop(4:1, c(10, 20, 30, 40), sm="PAS")
metaprop(4:1, c(10, 20, 30, 40), sm="PRAW")
metaprop(4:1, c(10, 20, 30, 40), sm="PLN")
metaprop(4:1, c(10, 20, 30, 40), sm="PLOGIT")