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Table 3 Comparisons of proposed weight, global weight and local weight to estimate the overall hazard ratio in the simulations, with homogenous design and treatment assignment generated with \(X_{1}\)~\(X_{4}\)

From: Covariate balance-related propensity score weighting in estimating overall hazard ratio with distributed survival data

   

\(\boldsymbol K\boldsymbol=\mathbf{5}\)

  

\(\boldsymbol K\boldsymbol=\mathbf{10}\)

  

\(\boldsymbol K\boldsymbol=\mathbf{20}\)

 
  

Global weight

Local weight

Proposed weight

Global weight

Local weight

Proposed weight

Global weight

Local weight

Proposed weight

\({n}_{k}=500\)

Bias

-0.009

-0.011

-0.014

0.003

0.000

-0.001

0.003

0.000

0.002

 

RMSE

0.104

0.106

0.098

0.071

0.073

0.065

0.053

0.055

0.048

 

r-RMSE

1.063

1.084

1.000 (Ref)

1.087

1.118

1.000 (Ref)

1.106

1.148

1.000 (Ref)

\({n}_{k}=1000\)

Bias

0.003

0.002

0.000

0.003

0.002

0.002

0.002

0.000

0.000

 

RMSE

0.071

0.074

0.068

0.053

0.054

0.049

0.035

0.036

0.032

 

r-RMSE

1.046

1.091

1.000 (Ref)

1.083

1.104

1.000 (Ref)

1.078

1.109

 

\({n}_{k}=2000\)

Bias

0.003

0.002

0.002

0.002

0.001

0.001

-0.001

-0.001

-0.001

 

RMSE

0.053

0.052

0.050

0.035

0.035

0.032

0.026

0.026

0.024

 

r-RMSE

1.064

1.044

1.000 (Ref)

1.087

1.087

1.000 (Ref)

1.069

1.069

1.000 (Ref)

  1. Bias Absolute bias, RMSE Root mean squared error, r-RMSE Ratio of RMSE of global weight or local weight against proposed weight