statsExpressions: Tidy Dataframes and Expressions with Statistical Details

Indrajeet Patil

doi:10.21105/joss.03236

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)
as yi and sei arguments in 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 object is a tibble data frame with the additional class "statsExpressions". The exact set of columns depends on the test and, for functions that accept a type argument, on the chosen analysis (parametric, non-parametric, robust, or Bayesian). Any given call therefore returns some (not all) of the columns below.

Hypothesis testing

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

Effect size estimation

effectsize: the name of the effect size
estimate: estimated value of the effect size
conf.level: the coverage level of the confidence/credible interval (e.g. 0.95); the interval itself spans conf.low to conf.high
conf.low: lower bound for the effect size estimate
conf.high: upper bound for the effect size estimate
conf.method: method used to compute the confidence/credible interval
conf.distribution: statistical distribution for the effect

Bayesian analysis (only when type = "bayes")

bf10: Bayes factor for the alternative hypothesis relative to the null
log_e_bf10: natural logarithm of the Bayes factor (present for most, but not all, Bayesian analyses)
prior.distribution, prior.scale, prior.location: prior specification used to compute the Bayes factor and posterior estimates

Pairwise comparisons (for pairwise_comparisons() and pairwise_contingency_table())

group1, group2: the two levels being compared
p.adjust.method: the adjustment method used for multiple comparisons
p.value.adj: the adjusted p-value; returned by pairwise_contingency_table(). Note that pairwise_comparisons() instead folds the adjusted value into p.value (and does not return a separate p.value.adj column)

Common columns

n.obs: number of observations
expression: a list-column of pre-formatted plotmath expressions; each element is a language object (not a character string) containing the statistical details, ready to be used in {ggplot2} (e.g. in labs() or annotate())

For a per-function, column-by-column breakdown of the output (and an explanation of the internal add_expression_col() engine that builds the expression column), see the Return value schema article. For more examples, see the 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.

Random-effects meta-analysis

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()`

Citation

Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes and Expressions with Statistical Details. Journal of Open Source Software, 6(61), 3236, https://doi.org/10.21105/joss.03236

Examples

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>