Table 2 Results of doubly robust estimation

IPTW-logistic

 Propensity score IPTW

Reference

1.430 (1.118–1.830)

0.004

1.020(0.813–1.278)

0.866

2.483(1.859–3.317)

< 0.001

 Doubly robust with unbalanced covariables^a

Reference

1.522(1.189–1.948)

< 0.001

1.069(0.849–1.347)

0.568

2.877(2.099–3.945)

< 0.001

 Doubly robust with all covariables^b

Reference

1.473(1.152–1.884)

0.002

1.019(0.817–1.270)

0.869

2.545(1.893–3.422)

< 0.001

IPTW-XGBoost

 Propensity score IPTW

Reference

1.532(1.200–1.956)

0.001

0.977(0.771–1.238)

0.676

2.988(2.144–4.165)

< 0.001

 Doubly robust with unbalanced covariables^a

Reference

1.097(1.027–1.172)

< 0.001

0.986(0.940–1.035)

0.849

1.422(1.246–1.623)

< 0.001

 Doubly robust with all covariables^b

Reference

1.500(1.178–1.911)

0.001

0.936(0.750–1.168)

0.556

2.776(1.988–3.875)

< 0.001