Random-effects meta-analysis

Parametric, non-parametric, robust, and Bayesian random-effects meta-analysis.

Usage

meta_analysis(
  data,
  type = "parametric",
  random = "mixture",
  digits = 2L,
  conf.level = 0.95,
  ...
)

Arguments

data

A data frame. It must contain columns named estimate (effect sizes or outcomes) and std.error (corresponding standard errors). These two columns will be used:

as yi and sei arguments in metafor::rma() (for parametric test) or metaplus::metaplus() (for robust test)
as y and SE arguments in metaBMA::meta_random() (for Bayesian test).

type

A character specifying the type of statistical approach:

"parametric"
"nonparametric"
"robust"
"bayes"

You can specify just the initial letter.

random

The type of random effects distribution. One of "normal", "t-dist", "mixture", for standard normal, \(t\)-distribution or mixture of normals respectively.

digits

Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).

conf.level

Scalar between 0 and 1 (default: 95% confidence/credible intervals, 0.95). If NULL, no confidence intervals will be computed.

...

Additional arguments passed to the respective meta-analysis function.

Value

The returned tibble data frame can contain some or all of the following columns (the exact columns will depend on the statistical test):

statistic: the numeric value of a statistic
df: the numeric value of a parameter being modeled (often degrees of freedom for the test)
df.error and df: relevant only if the statistic in question has two degrees of freedom (e.g. anova)
p.value: the two-sided p-value associated with the observed statistic
method: the name of the inferential statistical test
estimate: estimated value of the effect size
conf.low: lower bound for the effect size estimate
conf.high: upper bound for the effect size estimate
conf.level: width of the confidence interval
conf.method: method used to compute confidence interval
conf.distribution: statistical distribution for the effect
effectsize: the name of the effect size
n.obs: number of observations
expression: pre-formatted expression containing statistical details

For examples, see data frame output vignette.

Note

Important: The function assumes that you have already downloaded the needed package ({metafor}, {metaplus}, or {metaBMA}) for meta-analysis. If they are not available, you will be asked to install them.

The table below provides summary about:

statistical test carried out for inferential statistics
type of effect size estimate and a measure of uncertainty for this estimate
functions used internally to compute these details

Hypothesis testing and Effect size estimation

Type	Test	CI available?	Function used
Parametric	Pearson's correlation coefficient	Yes	`correlation::correlation()`
Non-parametric	Spearman's rank correlation coefficient	Yes	`correlation::correlation()`
Robust	Winsorized Pearson's correlation coefficient	Yes	`correlation::correlation()`
Bayesian	Bayesian Pearson's correlation coefficient	Yes	`correlation::correlation()`

Examples

# setup
set.seed(123)
library(statsExpressions)

# let's use `mag` dataset from `{metaplus}`
data(mag, package = "metaplus")
dat <- dplyr::rename(mag, estimate = yi, std.error = sei)

# ----------------------- parametric -------------------------------------

meta_analysis(dat)
#> # A tibble: 1 × 14
#>   term    effectsize                     estimate std.error conf.level conf.low
#>   <chr>   <chr>                             <dbl>     <dbl>      <dbl>    <dbl>
#> 1 Overall meta-analytic summary estimate   -0.767     0.212       0.95    -1.18
#>   conf.high statistic  p.value weight method                        conf.method
#>       <dbl>     <dbl>    <dbl>  <dbl> <chr>                         <chr>      
#> 1    -0.351     -3.62 0.000295     NA Meta-analysis using 'metafor' Wald       
#>   n.obs expression
#>   <int> <list>    
#> 1    16 <language>

# ----------------------- robust ----------------------------------

meta_analysis(dat, type = "random", random = "normal")
#> # A tibble: 1 × 14
#>   term    effectsize                     estimate std.error conf.low conf.high
#>   <chr>   <chr>                             <dbl>     <dbl>    <dbl>     <dbl>
#> 1 Overall meta-analytic summary estimate   -0.746     0.234    -1.26    -0.343
#>   statistic  p.value weight conf.level method                               
#>       <dbl>    <dbl>  <dbl>      <dbl> <chr>                                
#> 1     -3.20 0.000501     NA       0.95 Robust meta-analysis using 'metaplus'
#>   conf.method n.obs expression
#>   <chr>       <int> <list>    
#> 1 Wald           16 <language>

# ----------------------- Bayesian ----------------------------------

meta_analysis(dat, type = "bayes")
#> # A tibble: 2 × 20
#>   term    effectsize                       estimate std.error conf.level
#>   <chr>   <chr>                               <dbl>     <dbl>      <dbl>
#> 1 Overall meta-analytic posterior estimate   -0.643     0.220       0.95
#> 2 tau     meta-analytic posterior estimate    0.484     0.182       0.95
#>   conf.low conf.high weight  bf10  rhat   ess component prior.distribution
#>      <dbl>     <dbl>  <dbl> <dbl> <dbl> <dbl> <chr>     <chr>             
#> 1   -1.11     -0.242     NA  53.0     1 3507  meta      Student's t       
#> 2    0.205     0.909     NA  53.0     1 3460. meta      Inverse gamma     
#>   prior.location prior.scale method                                 conf.method
#>            <dbl>       <dbl> <chr>                                  <chr>      
#> 1              0       0.707 Bayesian meta-analysis using 'metaBMA' ETI        
#> 2              1       0.15  Bayesian meta-analysis using 'metaBMA' ETI        
#>   log_e_bf10 n.obs expression
#>        <dbl> <int> <list>    
#> 1       3.97    16 <language>
#> 2       3.97    16 <language>