Adjust a pooled effect for suppressed small studies

An asymmetric funnel suggests studies are missing from one side. Trim and fill strips the asymmetric tail, re-estimates the centre, then puts back mirror images so the funnel is symmetric. The filled studies are fabrications: this is a sensitivity analysis, and the quantity of interest is how far the pooled effect moves, not where it lands.

Usage

Matrim(yi, vi, side = "left", n_iter = 50)

Arguments

yi

Study effect sizes.

vi

Study sampling variances.

side

Side the missing studies are on, "left" or "right".

n_iter

Trim-and-refit rounds.

Value

List with theta_adj, estimate, k_filled, fill_yi, theta_raw, k.

Details

Determinism: fixed number of trim-refit rounds, ranks tied by position, no stopping rule.

Formula: L0 = (4 T_n - n(n+1))/(2n - 1) with T_n the rank sum on the suppressed-opposite side; filled values are 2 theta - y_i.

References

Duval, S. & Tweedie, R. (2000). Trim and fill. Biometrics 56:455-463, equation (2) and section 3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Matrim(V, V)
#> $theta_adj
#> [1] 1.92
#> 
#> $estimate
#> [1] 1.92
#> 
#> $k_filled
#> [1] 4
#> 
#> $fill_yi
#> [1] -1.16 -2.16 -3.16 -4.16
#> 
#> $theta_raw
#> [1] 2.943495
#> 
#> $k
#> [1] 8
#> 
#> $method
#> [1] "Duval-Tweedie trim and fill, L0 estimator"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"