Imputation method for missing data pattern

10 % missing

20 % missing

30 % Missing

40 % missing


Mean cost (€)

Bias (%)

SSE

SEE

CP

Mean cost

Bias (%)

SSE

SEE

CP

Mean cost

Bias (%)

SSE

SEE

CP

Mean cost

Bias (%)

SSE

SEE

CP


Complete sample

2102

–

59

61

–

–

–

59

61

–

–

–

59

61

–

–

–

59

61

–

MCAR

Complete cases

2102

−0.7 (−0.03 %)

63

64

1.00

2121

18 (0.9 %)

68

69

1.00

2156

53 (3 %)

75

76

1.00

2181

79 (4 %)

87

87

0.99

MI MCMC

2150

48 (2 %)

68

58

1.00

2218

115 (5 %)

78

57

0.46

2300

198 (9 %)

93

57

0.03

2410

308 (15 %)

118

57

0.00

MAR

Complete cases

1871

−231 (−11 %)

56

57

0.00

1723

−379 (−18 %)

54

55

0.00

1624

−478 (−23 %)

59

59

0.00

1499

−603 (−29 %)

59

61

0.00

MI MCMC

2158

55 (3 %)

112

57

0.76

2039

−64 (−3 %)

83

48

0.65

2218

116 (5 %)

202

52

0.38

2683

581 (28 %)

417

69

0.09

MNAR

Complete cases

1544

−558 (−27 %)

27

28

0.00

1291

−812 (−39 %)

22

22

0.00

1096

−1007 (−48 %)

20

19

0.00

929

−1173 (−56 %)

17

16

0.00

MI MCMC

1602

−501 (−24 %)

28

26

0.00

1383

−720 (−34 %)

22

19

0.00

1212

−890 (−42 %)

20

15

0.00

1043

−1059 (−50 %)

19

11

0.00

 % bias was calculated as (estimated−actual)/actual cost × 100), where actual cost was the mean cost for the complete sample
 Abbreviations: CP coverage probability, MCMC Markov Chain Monte Carlo, MI multiple imputation, SEE standard error estimate, SSE sampling standard error
 ^{a}1000 simulations and sample size 1497 for different levels of missing data (10–40 %)