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. 2022 Apr 23;24(3):776–794. doi: 10.1093/biostatistics/kxac006

Table 1.

Comparing distributed Cox regression (Dist), pooled Cox regression (pooled), multivariate meta-analysis (MultiV) and univariate meta-analysis (UniV) with simulated data of sample sizes Inline graphic under unstratified and stratified models. Sizes for the data-contributing sites are approximately the same and provided in the table below. Covariates distributions for all the data-contributing sites are the same. True log HR value is Inline graphic. Number of replications Inline graphic 10 000

  Data generating model: unstratified     Data generating model: stratified
Method Unstratified Stratified Meta-analysis     Unstratified Stratified Meta-analysis
  Pooled Dist Pooled Dist MulV UniV     Pooled Dist Pooled Dist MulV UniV
  Inline graphic ; Inline graphic; Inline graphic     Inline graphic ; Inline graphic; Inline graphic
bias 0.0035 0.0146 0.0033 0.0145 0.0026 0.0047   bias Inline graphic 0.0316 Inline graphic 0.0168 0.0033 0.0143 0.0026 0.0046
cr 0.9542 0.9556 0.9523 0.9530 0.9525 0.9501   cr 0.9404 0.9711 0.9536 0.9519 0.9544 0.9518
mae 0.0785 0.0805 0.0796 0.0816 0.0794 0.0803   mae 0.0834 0.0818 0.0791 0.0811 0.0789 0.0799
cios 0.9500 0.9455 0.9470 0.9429 0.9470 0.9453   cios 0.9053 0.9141 0.9500 0.9462 0.9500 0.9483
sse 0.0985 0.0999 0.0999 0.1015 0.0997 0.1009   sse 0.0994 0.1011 0.0993 0.1008 0.0991 0.1004
ese 0.0992 0.1012 0.1005 0.1026 0.1004 0.1011   ese 0.0987 0.1031 0.1003 0.1023 0.1001 0.1009
rse 0.0984 0.1025           rse 0.0993 0.1161        
  Inline graphic ; Inline graphic; Inline graphic     Inline graphic ; Inline graphic; Inline graphic
bias 0.0011 0.0066 0.0011 0.0065 0.0008 0.0018   bias Inline graphic 0.0344 Inline graphic 0.0255 0.0009 0.0064 0.0006 0.0016
cr 0.9494 0.9498 0.9485 0.9505 0.9488 0.9483   cr 0.9189 0.9604 0.9469 0.9483 0.9470 0.9467
mae 0.0557 0.0565 0.0561 0.0568 0.0561 0.0565   mae 0.0628 0.0604 0.0562 0.0568 0.0562 0.0565
cios 0.9500 0.9480 0.9484 0.9466 0.9484 0.9475   cios 0.8898 0.9058 0.9500 0.9482 0.9500 0.9491
sse 0.0699 0.0704 0.0704 0.0708 0.0703 0.0708   sse 0.0707 0.0712 0.0704 0.0709 0.0703 0.0708
ese 0.0698 0.0704 0.0703 0.0709 0.0702 0.0705   ese 0.0695 0.0712 0.0701 0.0707 0.0701 0.0703
rse 0.0695 0.0708           rse 0.0701 0.0800        
  Inline graphic ; Inline graphic; Inline graphic     Inline graphic ; Inline graphic; Inline graphic
bias 0.0002 0.0020 0.0002 0.0020 0.0001 0.0005   bias Inline graphic 0.0353 Inline graphic 0.0304 0.0001 0.0019 0.0000 0.0004
cr 0.9542 0.9534 0.9532 0.9530 0.9532 0.9529   cr 0.8577 0.9224 0.9519 0.9511 0.9521 0.9529
mae 0.0320 0.0321 0.0320 0.0322 0.0320 0.0321   mae 0.0440 0.0413 0.0320 0.0321 0.0320 0.0321
cios 0.9500 0.9494 0.9494 0.9488 0.9494 0.9491   cios 0.8292 0.8629 0.9500 0.9494 0.9500 0.9497
sse 0.0400 0.0401 0.0401 0.0402 0.0400 0.0401   sse 0.0404 0.0406 0.0400 0.0401 0.0400 0.0401
ese 0.0401 0.0403 0.0403 0.0404 0.0402 0.0403   ese 0.0400 0.0404 0.0402 0.0403 0.0401 0.0402
rse 0.0401 0.0403           rse 0.0405 0.0455        

cr: coverage rate; mae: mean absolute error; cios: confidence interval overlap statistics; sse: sample standard error; ese: estimated standard error; rse: robust standard error estimate.