Size of the DerSimonian-Laird truncation bias under homogeneity

Draws n_draws sets of site estimates from a common effect with the given variances (so the true \(\tau^2\) is zero) and reports the mean DerSimonian-Laird \(\hat\tau^2\), the share of draws in which it is positive, and the mean ratio of the random- to the fixed-effect variance. The mean is positive because \(E[\max(X,0)] = E[X] + E[\max(-X,0)]\) with \(E[X] = 0\) and \(P(X > 0) > 0\) (Research.P13.truncation_bias, pos_part_pos, dl_biased_under_homogeneity); the estimator cannot average to the truth it is estimating. Draws come from the Philox stream, so the R and Python arms report identical numbers for a seed.

Usage

morie_meta_dl_bias(variances, n_draws = 2000L, seed = 0)

Arguments

variances: Site sampling variances, positive; at least two.
n_draws: Number of simulated meta-analyses.
seed: Philox seed (non-negative).

Value

A list with k, mean_tau2, share_positive, mean_variance_ratio, mean_Q (close to \(k - 1\)), n_draws and theorems.

Examples

morie_meta_dl_bias(c(0.010, 0.020, 0.015, 0.030, 0.012), n_draws = 500, seed = 1)
#> $k
#> [1] 5
#> 
#> $mean_tau2
#> [1] 0.00368358
#> 
#> $share_positive
#> [1] 0.364
#> 
#> $mean_variance_ratio
#> [1] 1.261934
#> 
#> $mean_Q
#> [1] 3.787251
#> 
#> $n_draws
#> [1] 500
#> 
#> $theorems
#> [1] "Research.P13.truncation_bias"            
#> [2] "Research.P13.pos_part_pos"               
#> [3] "Research.P13.dl_biased_under_homogeneity"
#>