Table 3 Mediation analysis considering age (< 50 and ≥ 50 years), gender (female, male), and body mass index (BMI < 25 and BMI ≥ 25). For each mediator is reported the network meta-analysis (NMA) and the network meta-regression (NMR) with the 95% credible intervals (CrI)

Intraoperative RBC

ECMOd

2.08

(1.83, 2.34)*

2.34

(1.93, 2.75)*

1.96

(1.3, 2.62)*

2.05

(1.8, 2.3)*

2.12

(1.82, 2.43)*

2.04

(1.45, 2.63)*

2.03

(1.79, 2.28)*

1.82

(1.53, 2.12)*

2.26

(1.71, 2.81)*

ECMOr

2.35

(1.73, 2.96)*

2.32

(1.7, 2.93)*

0.08

(− 4.28, 4.43)

2.35

(1.73, 2.97)*

2.36

(1.74, 2.97)*

2.59

(− 0.39, 5.57)

2.38

(1.76, 3.01)*

1.95

(− 0.96, 4.87)

2.36

(− 1.72, 6.44)

CPB

1.37

(0.86, 1.89)*

4.74

(3.5, 5.98)*

0.62

(− 1.22, 2.45)

1.40

(0.89, 1.91)*

1.07

(0.53, 1.61)*

4.25

(2.54, 5.95)*

1.29

(0.73, 1.84)*

1.01

(− 1.85, 3.88)

1.43

(− 2.6, 5.45)

Intraoperative FFP

ECMOd

2.15

(1.67, 2.6)*

2.70

(2.05, 3.35)*

2.13

(1.08, 3.17)*

2.33

(1.93, 2.77)*

2.17

(1.56, 2.78)*

2.45

(1.51, 3.38)*

2.09

(1.59, 2.56)*

1.14

(0.18, 2.1)*

2.69

(1.35, 4.04)*

ECMOr

2.01

(1.21, 2.82)*

2.04

(1.25, 2.83)*

 − 0.21

(− 4.41, 3.99)

2.02

(1.23, 2.82)*

2.01

(1.21, 2.8)*

2.16

(− 0.07, 4.39)

2.01

(1.2, 2.81)*

0.45

(− 2.55, 3.45)

2.02

(− 2.15, 6.18)

CPB

3.38

(2.56, 4.21)*

5.74

(4.64, 6.83)*

1.88

(0.12, 3.63)*

3.43 (2.63, 4.2)*

3.38

(2.45, 4.31)*

3.45

(1.95, 4.95)*

3.80

(2.92, 4.72)*

2.45

(− 0.66, 5.56)

4.02

(− 0.27, 8.3)

Postoperative IMV

ECMOd

2.13

(1.82, 2.45)*

1.68

(1.31, 2.05)*

2.98

(2.21, 3.75)*

2.28

(1.95, 2.65)*

2.23

(1.83, 2.63)*

2.42

(1.63, 3.2)*

2.55

(2.16, 3.05)*

2.19

(1.69, 2.69)*

2.99

(2.1, 3.88)*

CPB

7.43

(6.59, 8.28)*

7.17

(5.67, 8.67)*

7.64

(5.4, 9.88)*

7.02

(6.31, 7.75)*

7.12

(6.27, 7.97)*

6.96

(5.5, 8.43)*

8.79

(7.42, 10.15)*

8.08

(4.94, 11.23)*

8.91

(4.66, 13.15)*

ICU LOS

ECMOd

2.21

(1.63, 2.8)*

 − 0.44

(− 1.14, 0.25)

5.68

(4.34, 7.02)*

2.47

(1.83, 3.14)*

2.36

(1.49, 3.23)*

2.64

(1.09, 4.18)*

3.61

(2.73, 4.48)*

2.30

(0.75, 3.85)*

4.12

(1.72, 6.52)*

ECMOr

2.27

(1.02, 3.53)*

2.10

(0.85, 3.36)*

7.97

(4.98, 10.96)*

2.27

(1.02, 3.53)*

2.27

(1.03, 3.52)*

2.84

(− 0.13, 5.82)

2.34

(1.09, 3.6)*

0.56

(− 2.89, 4.02)

2.35

(− 2.37, 7.07)

CPB

8.09

(6.75, 9.44)*

4.29

(2.23, 6.35)*

9.89

(6.91, 12.86)*

8.57

(7.27, 9.88)*

8.38

(6.97, 9.79)*

9.15

(6.53, 11.76)*

10.98

(9.5, 12.46)*

9.35

(5.87, 12.84)*

11.16

(6.39, 15.93)*

Surgical duration

ECMOd

0.52

(0.34, 0.72)*

1.18

(0.65, 1.71)*

 − 0.95

(− 1.78, − 0.13)*

0.53

(0.34, 0.72)*

0.37

(0.12, 0.61)*

3.59

(2.64, 4.53)*

0.34

(0, 0.56)*

0.75

(0.51, 0.99)*

 − 0.98

(− 1.45, − 0.5)*

CPB

0.68

(0.02, 1.18)*

1.96

(− 0.94, 4.86)

 − 0.15

(− 4.24, 3.95)

0.56

(− 0.04, 1.15)

0.39

(− 0.21, 1)

3.88

(2.45, 5.3)*

0.49

(− 0.05, 1.03)

1.61

(− 1.24, 4.46)

 − 0.13

(− 4.16, 3.91)

Postoperative ECMO

ECMOd

12.27

(8.95, 17.04)*

3.70

(0.29, 46.61)

12.46

(0.35, 447.07)

12.21

(8.92, 16.98)*

7.51

(4.72, 11.94)*

17.96

(8.09, 39.9)*

11.93

(8.71, 16.59)*

1.40

(0.65, 3.01)

20.73

(6.55, 65.66)*

ECMOr

4.89

(1.06, 22.61)*

3.95

(0.78, 19.99)

19.07

(0.41, 896.43)

4.93

(1.06, 23.16)*

4.16

(0.91, 18.94)

9.85

(0.97, 100)

4.90 (1.07, 22.82)*

0.41

(0.02, 7.05)

6.20

(0.14, 269.13)

CPB

10.94

(7.35, 16.43)*

1.79

(0.11, 29.99)

11.42

(0.21, 613.7)

11.56

(7.82, 17.23)*

7.74

(4.82, 12.44)*

17.00

(6.06, 47.66)*

11.60

(7.76, 17.44)*

1.29

(0.12, 14.17)

18.87

(0.63, 566.85)

Mortality

ECMOd

2.61

(1.83, 3.74)*

2.02

(1.19, 3.4)*

3.04

(1.25, 7.39)*

2.44

(1.7, 3.52)*

2.53 (1.58, 4.04)*

2.27

(1, 5.17)*

2.45

(1.52, 4.03)*

1.27

(0.48, 3.37)

3.02

(0.69, 13.31)

ECMOr

1.81

(0.67, 4.65)

1.70

(0.65, 4.44)

3.13

(0.32, 31)

1.82

(0.68, 4.69)

1.98

(0.68, 5.83)

1.60

(0.35, 7.32)

2.08

(0.51, 7.88)

0.88

(0.03, 25.79)

2.16

(0.02, 208.82)

CPB

2.13

(1.43, 3.17)*

1.21

(0.59, 2.49)

2.72

(0.89, 8.29)

2.28

(1.54, 3.38)*

2.43

(1.56, 3.8)*

1.94

(0.8, 4.68)

1.70

(0.91, 3.2)

0.79

(0.04, 15.64)

2.01

(0.03, 138.93)