Table 6 |
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Impact of Percentage Missing Under Conditions 1, 2, and 3. |
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a. Condition 1a |
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|
Scenario |
Variable* |
Method |
Mean β |
Mean SE |
Mean Bias |
MSE |
RelMSE |
Coverage |
|
|
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|
A1: 20% missing |
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|
|
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.002 |
0.211 |
0.002 |
0.044 |
0.543 |
95.0 (93.6,96.4) |
|
|
CC |
1.000 |
0.284 |
-0.000 |
0.081 |
1.000 |
95.8 (94.6,97.0) |
||
|
MI |
1.062 |
0.230 |
0.062 |
0.052 |
0.644 |
95.9 (94.7,97.1) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.549 |
0.378 |
0.049 |
0.166 |
0.068 |
95.4 (94.1,96.7) |
|
|
CC |
2.713 |
4.822 |
0.213 |
2.436 |
1.000 |
97.0 (95.9,98.1) |
||
|
MI |
2.543 |
0.426 |
0.043 |
0.178 |
0.072 |
96.8 (95.7,97.9) |
||
|
Interaction (True effect = 1.5) |
Full |
1.547 |
0.434 |
0.047 |
0.204 |
0.082 |
95.7 (94.4,97.0) |
|
|
CC |
1.713 |
4.894 |
0.213 |
2.503 |
1.000 |
96.7 (95.6,97.8) |
||
|
MI |
1.482 |
0.483 |
-0.018 |
0.205 |
0.082 |
96.1 (94.9,97.3) |
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|
A2: 30% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.003 |
0.211 |
0.003 |
0.044 |
0.358 |
94.6 (93.2,96.0) |
|
|
CC |
0.992 |
0.345 |
-0.008 |
0.122 |
1.000 |
95.0 (93.6,96.4) |
||
|
MI |
1.095 |
0.245 |
0.095 |
0.065 |
0.531 |
94.9 (93.5,96.3) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.558 |
0.379 |
0.058 |
0.146 |
0.014 |
97.2 (96.2,98.2) |
|
|
CC |
3.288 |
25.207 |
0.788 |
10.689 |
1.000 |
98.5 (97.7,99.3) |
||
|
MI |
2.557 |
0.462 |
0.057 |
0.178 |
0.017 |
98.3 (97.5,99.1) |
||
|
Interaction (True effect = 1.5) |
Full |
1.555 |
0.435 |
0.055 |
0.195 |
0.018 |
96.1 (94.9,97.3) |
|
|
CC |
2.295 |
25.290 |
0.795 |
10.904 |
0.018 |
96.1 (94.9,97.3) |
||
|
MI |
1.462 |
0.515 |
-0.038 |
0.219 |
0.020 |
97.8 (96.9,98.7) |
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|
A3: 40% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.020 |
0.211 |
0.020 |
0.045 |
0.258 |
95.6 (94.3,96.8) |
|
|
CC |
0.991 |
0.411 |
-0.009 |
0.175 |
1.000 |
95.5 (94.2,96.8) |
||
|
MI |
1.137 |
0.263 |
0.137 |
0.083 |
0.474 |
94.1 (92.6,95.6) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.540 |
0.377 |
0.040 |
0.140 |
0.006 |
96.6 (95.5,97.7) |
|
|
CC |
4.121 |
64.794 |
1.621 |
23.920 |
1.000 |
96.5 (95.4,97.6) |
||
|
MI |
2.536 |
0.489 |
0.036 |
0.177 |
0.007 |
97.5 (96.5,98.5) |
||
|
Interaction (True effect = 1.5) |
Full |
1.520 |
0.433 |
0.020 |
0.191 |
0.008 |
96.0 (94.8,97.2) |
|
|
CC |
3.131 |
64.890 |
1.631 |
24.283 |
1.000 |
97.0 (95.9,98.1) |
||
|
MI |
1.399 |
0.538 |
-0.101 |
0.220 |
0.009 |
97.2 (96.2,98.2) |
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|
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|
b. Condition 2b |
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|
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|
Scenario |
Variable |
Method |
Mean β |
Mean SE |
Mean Bias |
MSE |
RelMSE |
Coverage |
|
|
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|
A4: 20% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.007 |
0.108 |
0.007 |
0.012 |
0.590 |
95.5 (94.2,96.8) |
|
|
CC |
1.010 |
0.147 |
0.010 |
0.021 |
1.000 |
95.9 (94.7,97.1) |
||
|
MI |
1.059 |
0.115 |
0.059 |
0.017 |
0.820 |
92.5 (90.9,94.1) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.552 |
0.279 |
0.052 |
0.089 |
0.909 |
93.7 (92.2,95.2) |
|
|
CC |
2.548 |
0.298 |
0.048 |
0.098 |
1.000 |
93.4 (91.9,94.9) |
||
|
MI |
2.593 |
0.281 |
0.093 |
0.095 |
0.966 |
94.5 (93.1,95.9) |
||
|
Interaction (True effect = 1.5) |
Full |
1.544 |
0.300 |
0.044 |
0.102 |
0.872 |
93.6 (92.1,95.1) |
|
|
CC |
1.538 |
0.332 |
0.038 |
0.117 |
1.000 |
94.0 (92.5,95.5) |
||
|
MI |
1.534 |
0.304 |
0.034 |
0.101 |
0.863 |
94.0 (92.5,95.5) |
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|
A5: 30% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.003 |
0.108 |
0.003 |
0.012 |
0.437 |
94.5 (93.1,95.9) |
|
|
CC |
1.008 |
0.168 |
0.008 |
0.027 |
1.000 |
94.6 (93.2,96.0) |
||
|
MI |
1.079 |
0.118 |
0.079 |
0.020 |
0.741 |
92.4 (90.8,94.0) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.532 |
0.277 |
0.032 |
0.078 |
0.798 |
95.7 (94.4,97.0) |
|
|
CC |
2.529 |
0.317 |
0.029 |
0.098 |
1.000 |
96.2 (95.0,97.4) |
||
|
MI |
2.612 |
0.284 |
0.112 |
0.091 |
0.928 |
95.6 (94.3,96.9) |
||
|
Interaction (True effect = 1.5) |
Full |
1.529 |
0.297 |
0.029 |
0.091 |
0.731 |
95.4 (94.1,96.7) |
|
|
CC |
1.521 |
0.359 |
0.021 |
0.125 |
1.000 |
94.8 (93.4,96.2) |
||
|
MI |
1.533 |
0.308 |
0.033 |
0.093 |
0.743 |
95.4 (94.1,96.7) |
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|
A6: 40% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.005 |
0.108 |
0.005 |
0.011 |
0.330 |
95.8 (94.6,97.0) |
|
|
CC |
1.007 |
0.197 |
0.007 |
0.035 |
1.000 |
95.9 (94.7,97.1) |
||
|
MI |
1.109 |
0.123 |
0.109 |
0.026 |
0.749 |
87.5 (85.5,89.5) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.551 |
0.279 |
0.051 |
0.081 |
0.620 |
95.7 (94.4,97.0) |
|
|
CC |
2.563 |
0.355 |
0.063 |
0.131 |
1.000 |
96.2 (95.0,97.4) |
||
|
MI |
2.675 |
0.295 |
0.175 |
0.112 |
0.852 |
94.3 (92.9,95.7) |
||
|
Interaction (True effect = 1.5) |
Full |
1.547 |
0.300 |
0.047 |
0.094 |
0.563 |
95.1 (93.8,96.4) |
|
|
CC |
1.557 |
0.406 |
0.057 |
0.168 |
1.000 |
95.3 (94.0,96.6) |
||
|
MI |
1.565 |
0.319 |
0.065 |
0.098 |
0.588 |
96.9 (95.8,98.0) |
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|
|
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|
c. Condition 3c |
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|
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|
Scenario |
Variable |
Method |
Mean β |
Mean SE |
Mean Bias |
MSE |
RelMSE |
Coverage |
|
|
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|
A7: 20% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.012 |
0.108 |
0.012 |
0.012 |
0.076 |
94.7 (93.3,96.1) |
|
|
CC |
0.616 |
0.119 |
-0.384 |
0.162 |
1.000 |
11.9 (9.9,13.9) |
||
|
MI |
0.999 |
0.109 |
-0.001 |
0.012 |
0.077 |
94.3 (92.9,95.7) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.549 |
0.279 |
0.049 |
0.080 |
0.667 |
96.1 (94.9,97.3) |
|
|
CC |
2.320 |
0.289 |
-0.180 |
0.120 |
1.000 |
87.1 (85.0,89.2) |
||
|
MI |
2.551 |
0.280 |
0.051 |
0.080 |
0.666 |
96.2 (95.0,97.4) |
||
|
Interaction (True effect = 1.5) |
Full |
1.537 |
0.300 |
0.037 |
0.091 |
0.635 |
96.1 (94.9,97.3) |
|
|
CC |
1.704 |
0.313 |
0.204 |
0.143 |
1.000 |
92.6 (91.0,94.2) |
||
|
MI |
1.552 |
0.301 |
0.052 |
0.092 |
0.642 |
95.7 (94.4,97.0) |
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|
A8: 30% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.006 |
0.108 |
0.006 |
0.012 |
0.027 |
95.0 (93.6,96.4) |
|
|
CC |
0.331 |
0.127 |
-0.669 |
0.466 |
1.000 |
0.3 (0,0.6) |
||
|
MI |
0.983 |
0.110 |
-0.017 |
0.013 |
0.028 |
95.0 (93.6,96.4) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.528 |
0.277 |
0.028 |
0.075 |
0.179 |
95.8 (94.6,97.0) |
|
|
CC |
1.927 |
0.299 |
-0.573 |
0.419 |
1.000 |
48.6 (45.5,51.7) |
||
|
MI |
2.492 |
0.277 |
-0.008 |
0.072 |
0.171 |
95.6 (94.3,96.9) |
||
|
Interaction (True effect = 1.5) |
Full |
1.522 |
0.297 |
0.022 |
0.084 |
0.743 |
96.0 (94.8,97.2) |
|
|
CC |
1.596 |
0.325 |
0.096 |
0.113 |
1.000 |
95.7 (94.4,97.0) |
||
|
MI |
1.509 |
0.298 |
0.009 |
0.081 |
0.713 |
96.1 (94.9,97.3) |
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|
A9: 40% missing |
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|
X1 (X2 = 0) (True effect = 1.0) |
Full |
1.007 |
0.108 |
0.007 |
0.011 |
0.012 |
95.8 (94.6,97.0) |
|
|
CC |
0.027 |
0.139 |
-0.973 |
0.966 |
1.000 |
0.0 (0.0,0.0) |
||
|
MI |
0.968 |
0.110 |
-0.032 |
0.013 |
0.013 |
94.1 (92.6,95.6) |
||
|
X1 (X2 = 1) (True effect = 2.5) |
Full |
2.537 |
0.277 |
0.037 |
0.079 |
0.092 |
95.6 (94.3,96.9) |
|
|
CC |
1.627 |
0.312 |
-0.873 |
0.864 |
1.000 |
23.1 (20.5,25.7) |
||
|
MI |
2.461 |
0.276 |
-0.039 |
0.073 |
0.085 |
95.4 (94.1,96.7) |
||
|
Interaction (True effect = 1.5) |
Full |
1.531 |
0.298 |
0.031 |
0.089 |
0.683 |
96.1 (94.9,97.3) |
|
|
CC |
1.600 |
0.342 |
0.100 |
0.130 |
1.000 |
95.2 (93.9,96.5) |
||
|
MI |
1.493 |
0.297 |
-0.007 |
0.081 |
0.627 |
96.9 (95.8,98.0) |
||
|
|
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|
Results From Fitting Full, Complete-Case, and Multiple Imputation Models to 1000 Simulated Data Sets With a Sample Size of 1000 Where the Covariate of Interest and as a Result the Interaction Term Were Missing for Some Subjects and the Auxiliary Information Was Strong. aCondition 1: X1 is 7.4 times more likely to be missing if X1 = 1, where X1 is binary bCondition 2: Extreme values of X1 are more likely to be missing (probability of missing is a quadratic function of X1 or the log odds of missing X1 = γ 0+γ 1 X1 + γ 2 X12, where γ 1 = -1 and γ 2 = 2), where X1 is continuous cCondition 3: A 1-unit increase in X1 corresponds to a 7.4 times decrease in the probability of missing for controls, but a 7.4 times increase for cases, where X1 is continuous |
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|
Desai et al. Epidemiologic Perspectives & Innovations 2011 8:5 doi:10.1186/1742-5573-8-5 |
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