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Table 6 Impact of Percentage Missing Under Conditions 1, 2, and 3.

From: The use of complete-case and multiple imputation-based analyses in molecular epidemiology studies that assess interaction effects

a. Condition 1a
Scenario Variable* Method Mean β Mean SE Mean Bias MSE RelMSE Coverage
A1: 20% missing         
  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)
A2: 30% missing         
  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)
A3: 40% missing         
  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)
b. Condition 2b
Scenario Variable Method Mean β Mean SE Mean Bias MSE RelMSE Coverage
A4: 20% missing         
  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)
A5: 30% missing         
  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)
A6: 40% missing         
  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)
c. Condition 3c
Scenario Variable Method Mean β Mean SE Mean Bias MSE RelMSE Coverage
A7: 20% missing         
  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)
A8: 30% missing         
  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)
A9: 40% missing         
  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)
  1. 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.
  2. aCondition 1: X1 is 7.4 times more likely to be missing if X1 = 1, where X1 is binary
  3. 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
  4. 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