Random-Effects Meta Mean

Problem

Return the DerSimonian-Laird random-effects pooled mean using weights 1/(se_i^2 + tau2), where tau2 = max(0, (Q - (k-1)) / (sum(w) - sum(w^2)/sum(w))) and Q is the fixed-effect Cochran statistic. Return 0.0 when fewer than two studies are given, any se <= 0, or the heterogeneity denominator is not positive.

Hint

Adding tau-squared to each variance downweights small, noisy studies.

Test cases

case 1

in: [[1,1.2],[0.1,0.1]]

expected: 1.0999999999999999

case 2

in: [[0.5,0.3,0.7],[0.1,0.2,0.15]]

expected: 0.5220856225860849

case 3

in: [[0.5,0.6],[0.05,0.5]]

expected: 0.500990099009901

case 4

in: [[1],[0.1]]

expected: 0

case 5

in: [[0.1,0.2],[0,0.1]]

expected: 0

Starter codePython

def random_effects_meta(yi, sei):
    # Your code here
    pass

5 test cases · run your code against them in the editor