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Finding the Number of Studies Needed to Obtain a Certain Amount of Power

Source: R/min_studies_MADE.R
min_studies_MADE.Rd

Compute the minimum number of studies needed to obtain a specified power level in a meta-analysis of dependent effect size estimates, given an effect size of practical concern, estimation method, and further assumptions about the distribution of studies.

Usage

min_studies_MADE(
  mu,
  tau,
  omega,
  rho,
  alpha = 0.05,
  target_power = 0.8,
  d = 0,
  model = "CHE",
  var_df = "RVE",
  sigma2_dist = NULL,
  n_ES_dist = NULL,
  iterations = 100,
  seed = NULL,
  warning = TRUE,
  upper = 100,
  show_lower = FALSE
)

Arguments

mu

Effect size of practical concern. Can be one value or a vector of multiple values.

tau

Between-study SD. Can be one value or a vector of multiple values.

omega

Within-study SD. Can be one value or a vector of multiple values.

rho

Correlation coefficient between effect size estimates from the same study. Can be one value or a vector of multiple values.

alpha

Level of statistical significance. Can be one value or a vector of multiple values. Default is 0.05.

target_power

Numerical value specifying the target power level. Can be one value or a vector of multiple values.

d

Contrast value. Can be one value or a vector of multiple values. Default is 0.

model

Assumed working model for dependent effect sizes, either "CHE" for the correlated-and-hierarchical effects model, "CE" for the correlated effects model, or "MLMA" for the multi-level meta-analysis model. Default is "CHE". Can be one value or a vector of multiple values.

var_df

Indicates the technique used to obtain the sampling variance of the average effect size estimate and the degrees of freedom, either "Model" for model-based variance estimator with degrees of freedom of J - 1, "Satt" for model-based variance estimator with Satterthwaite degrees of freedom, or "RVE" for robust variance estimator with Satterthwaite degrees of freedom. Default is "RVE". Can be one value or a vector of multiple values.

sigma2_dist

Distribution of sampling variance estimates from each study. Can be either a single value, a vector of plausible values, or a function that generates random values.

n_ES_dist

Distribution of the number of effect sizes per study. Can be either a single value, a vector of plausible values, or a function that generates random values.

iterations

Number of iterations per condition (default is 100).

seed

Numerical value for a seed to ensure reproducibility of the iterated power approximations.

warning

Logical indicating whether to return a warning when either sigma2_dist or n_ES_dist is based on balanced assumptions.

upper

Numerical value containing the upper bound of the interval to be searched for the minimum number of studies.

show_lower

Logical value indicating whether to report lower bound of the interval searched for the minimum number of studies. Default is FALSE.

Value

Returns a tibble with information about the expectation of the effect size of practical concern, the between-study and within-study variance components, the sample correlation, the contrast effect, the level of statistical significance, the target power value(s), the number of studies needed, the number of iterations, the model to handle dependent effect sizes, and the methods used to obtain sampling variance estimates as well as the number effect sizes per study.

Examples


min_studies_MADE(
  mu = 0.3,
  tau = 0.05,
  omega = 0.01,
  rho = 0.2,
  target_power = .7,
  alpha = 0.05,
  model = "CE",
  var_df = "RVE",
  sigma2_dist = 4 / 200,
  n_ES_dist = 5.5,
  seed = 10052510
)
#> Warning: Notice: It is generally recommended not to draw on balanced assumptions regarding the study precision (sigma2js) or the number of effect sizes per study (kjs). See Figures 2A and 2B in Vembye, Pustejovsky, and Pigott (2022).
#> # A tibble: 1 × 12
#>      mu   tau omega   rho     d alpha target_power studies_needed iterations
#>   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>        <dbl>          <dbl>      <dbl>
#> 1   0.3  0.05  0.01   0.2     0  0.05          0.7              5        100
#> # ℹ 3 more variables: model <chr>, samp_method_sigma2 <chr>,
#> #   samp_method_kj <chr>