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Table 4 Conversion of DerSimonian-Laird results into Hartung-Knapp-Sidik-Jonkman results for a logarithm based outcome: hazard ratios

From: The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method

DerSimonian and Laird results

Calculations for Hartung-Knapp-Sidik Jonkman

Study

Study results HR yi

Weights wi

ln(y i )

(ln(y i  )–ln(y)) 2

w i ×(ln(y i  )–ln(y)) 2

Cornelissen 2009

0.81

5.0

−0.21

0.00

0.02

De Witte 1994

0.67

2.1

−0.40

0.06

0.13

Fielding 2009

0.80

11.5

−0.22

0.01

0.06

Goldstone 2008

0.91

46.7

−0.09

0.00

0.15

Hunault 2004

0.56

2.9

−0.58

0.18

0.53

Labar 2004

0.98

9.3

−0.02

0.02

0.16

Ribera 2005

1.24

3.9

0.22

0.13

0.52

Sebban 1994

0.75

12.7

−0.29

0.02

0.24

Takeuchi 2002

0.95

3.9

−0.05

0.01

0.04

Ueda 1998

0.66

2.0

−0.42

0.07

0.14

 

y = 0.86

Sum: 100.0

  

Sum: 1.99

10 studies, I2 = 0.0, τ2 = 0.0.

DL pooled result [95% CI]: HR = 0.86 [0.77, 0.97]; z = −2.48; P–value = 0.013.

HKSJ pooled result [95% CI]: HR = 0.86 [0.77, 0.96]; t = −3.19; P–value = 0.011 (df = 9).

  1. HR: Hazard Ratio for donor versus no-donor; ln: natural logarithm; DL: DerSimonian & Laird meta-analysis method. HKSJ: Hartung-Knapp-Sidik-Jonkman meta-analysis method. CI: Confidence Interval, df: degrees of freedom, ×: multiplication sign. The pooled effect y and the weights wi originate from the DL random-effects analysis on log scale.