meta_plot {puniform}

Meta-plot

Description

Function to create meta-plots for two-independent means, raw correlations, and odds ratios. See van Assen et al. (2023) for more information.

Usage

meta_plot(
  m1i,
  m2i,
  sd1i,
  sd2i,
  n1i,
  n2i,
  gi,
  vgi,
  ri,
  ni,
  ai,
  bi,
  ci,
  di,
  alpha = 0.05,
  method_tau2 = "PM",
  nr_lines = "all",
  pub_bias = TRUE,
  main = "",
  cex.pch = 1
)

Arguments

m1i

A vector of means in group 1 for two-independent means

m2i

A vector of means in group 2 for two-independent means

sd1i

A vector of standard deviations in group 1 for two-independent means

sd2i

A vector of standard deviations in group 2 for two-independent means

n1i

A vector of sample sizes in group 1 for two-independent means

n2i

A vector of sample sizes in group 2 for two-independent means

gi

A vector of Hedges' g values for two-independent means if group means and standard deviations are not available

vgi

A vector of Hedges' g sampling variances for two-independent means if group means and standard deviations are not available

ri

A vector of raw correlations

ni

A vector of sample sizes if raw correlations are the effect size measure

ai

A vector of frequencies in upper left cell of 2x2 frequency table (see Details)

bi

A vector of frequencies in upper right cell of 2x2 frequency table (see Details)

ci

A vector of frequencies in lower left cell of 2x2 frequency table (see Details)

di

A vector of frequencies in lower right cell of 2x2 frequency table (see Details)

alpha

A numerical value specifying the alpha level as used in primary studies (default is 0.05 but see Details)

method_tau2

A character indicating the estimation method for the between-study variance in true effect size in the meta-analysis (default is "PM", but see Details)

nr_lines

A character indicating whether all primary study's effect sizes ("all", default) or a selection of primary study's effect sizes ("summary") are plotted (see Details)

pub_bias

A logical indicating whether the expected results of the cumulative meta-analysis based on a zero true effect in combination with extreme publication bias should be plotted. The default value is NA implying that these results are only included if at least 80% of the primary studies is statistically significant. These results are always included if this argument is set to TRUE and never included if this argument is set to FALSE

main

A character indicating the title of the plot (default is no title)

cex.pch

A numerical value to control the size of the points in the plot

Details

The meta_plot function assumes that two-tailed hypothesis tests were conducted in the primary studies. In case one-tailed hypothesis tests were conducted in the primary studies, the submitted alpha argument to the meta_plot function has to be multiplied by two. For example, if one-tailed hypothesis tests were conducted with an alpha level of .05, an alpha of 0.1 has to be submitted to the meta_plot function.

Different estimators can be used for estimating the between-study variance in true effect size. The default estimator is the Paule-Mandel estimator (Paule & Mandel, 1982), because this estimator was recommended in Veroniki et al. (2016) and Langan, Higgins, and Simmonds (2016). However, all estimators that are included in the rma.uni function of the metafor package can be used, because this function is called in the meta_plot function.

When nr_lines = "summary" is specified, the estimates of meta-analyses based on primary studies with sufficient statistical power are displayed. Next to the estimate and 95% confidence interval of the meta-analysis including all studies (leftmost), it shows these results for studies with sufficient statistical power (80%) to detect a large true effect size (left vertical line), medium true effect size (middle), and small true effect size (right). Note that the summary meta-plot is just the meta-plot with many meta-analyses and confidence intervals left out, and keeping the leftmost meta-analysis and those just immediately to the right of the vertical lines.

The meta-plot can be created for standardized mean differences by providing the function with the sample means (m1i and m21), the sample sizes (n1i and n2i), and the standard deviations (sd1i and sd2i) or by specifying the standardized mean differences (i.e., Hedges' g; gi) together with the corresponding sampling variances (vgi) and the sample sizes (n1i and n2i). Hedges' g standardized mean differences and corresponding sampling variances are computed in the function if the sample means, sample sizes, and standard deviations are provided.

For creating a meta-plot based on odds ratios as effect size measure, the 2x2 frequency table should follow a specific format. The reason for this is that the probability for the outcome of interest in the control conditions has to be estimated. Hence, the 2x2 frequency table should look like this:

	Outcome 1	Outcome 2
Group 1	ai	bi
Group 2	ci	di

Value

An invisibly returned data frame consisting of the submitted data and

yi

Standardized effect sizes used in the analyses

vi

Sampling variances of the standardized effect sizes used in the analyses

est_cum

Estimates of the cumulative meta-analyses

lb_cum

Lower bounds of the 95% confidence intervals of the cumulative meta-analyses

ub_cum

Upper bounds of the 95% confidence intervals of the cumulative meta-analyses

pub_est

Estimates of cumulative meta-analyses based on Mill's ratios

info

Information of a primary study (only for two-independent means)

stand_info

Standardized information of a primary study (only for two-independent means)

preci

Precision of a primary study (only for odds ratios)

Author(s)

Robbie C.M. van Aert [e-mail]

References

Langan, D., Higgins, J. P. T., & Simmonds, M. (2016). Comparative performance of heterogeneity variance estimators in meta-analysis: A review of simulation studies. Research Synthesis Methods, 8(2), 181-198. doi:10.1002/jrsm.1198

Paule, R. C., & Mandel, J. (1982). Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87(5), 377-385.

van Assen, ..., & van Aert (2023). The meta-plot: A graphical tool for interpreting the results of a meta-analysis. Zeitschrift fur Psychologie, 231(1), 65-78. doi:10.1027/2151-2604/a000513

Veroniki, A. A., Jackson, D., Viechtbauer, W., Bender, R., Bowden, J., Knapp, G., . . . Salanti, G. (2016). Methods to estimate the between-study variance and its uncertainty in meta-analysis. Research Synthesis Methods, 7(1), 55-79. doi:10.1002/jrsm.1164

Examples

### Load data from meta-analysis by McCall and Carriger (1993)
data(data.mccall93)

### Create meta-plot
meta_plot(ri = data.mccall93$ri, ni = data.mccall93$ni)

### Create summary meta-plot
meta_plot(ri = data.mccall93$ri, ni = data.mccall93$ni, nr_lines = "summary")