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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.