Table 2.
Summary statistics of simulationsa with missing data patterns (MCAR, MAR, MNAR)
| 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
a1000 simulations and sample size 1497 for different levels of missing data (10–40 %)