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. Author manuscript; available in PMC: 2018 Aug 30.
Published in final edited form as: Stat Med. 2017 Jun 5;36(19):3059–3074. doi: 10.1002/sim.7344

Table 2.

Comparison of mCCI and MCI for μ

n σ [c, d] μ
μ^
sd(μ^)
 mCC MCI
Ave(SE) CP AW Ave(SE) CP AW
30 0.06 [1, n] 0.1483 0.1481 0.0017 0.0041 1.000 0.0162 0.0017 0.920 0.0066
[n/4, 3n/4] 0.3000 0.2992 0.0030 0.0058 0.999 0.0226 0.0030 0.920 0.0118
[n/2, 3n/4] 0.4000 0.3963 0.0078 0.0107 0.966 0.0436 0.0075 0.911 0.0292
[5n/8, 7n/8 0.1000 0.1000 0.0042 0.0072 0.996 0.0281 0.0041 0.927 0.0162
0.1 [1, n] 0.1483 0.1479 0.0029 0.0069 1.000 0.0272 0.0028 0.924 0.0110
[n/4, 3n/4] 0.3000 0.2981 0.0047 0.0096 1.000 0.0376 0.0050 0.933 0.0198
[n/2, 3n/4] 0.4000 0.3923 0.0124 0.0177 0.962 0.0713 0.0125 0.911 0.0491
[5n/8, 7n/8 0.1000 0.1001 0.0069 0.0120 0.998 0.0471 0.0069 0.943 0.0271
0.6 [1, n] 0.1483 0.1441 0.0219 0.0535 1.000 0.2099 0.0171 0.873 0.0670
[n/4, 3n/4] 0.3000 0.2899 0.0273 0.0690 0.928 0.2712 0.0259 0.843 0.1017
[n/2, 3n/4] 0.4000 0.3565 0.0671 0.1235 0.787 0.4880 0.0546 0.748 0.2142
[5n/8, 7n/8 0.1000 0.1074 0.0632 0.1077 0.935 0.4224 0.0502 0.870 0.1966
1.2 [1, n] 0.1483 0.1406 0.0508 0.1207 0.999 0.4732 0.0356 0.840 0.1395
[n/4, 3n/4] 0.3000 0.2861 0.0536 0.1299 0.906 0.5116 0.0455 0.837 0.1783
[n/2, 3n/4] 0.4000 0.3415 0.1241 0.2116 0.619 0.8346 0.0872 0.633 0.3419
[5n/8, 7n/8 0.1000 0.1068 0.1296 0.1997 0.828 0.7862 0.1007 0.796 0.3949
n σ [c, d] μ
μ^
sd(μ^)
 mCC MCI
Ave(SE) CP AW Ave(SE) CP AW
50 0.06 [1, n] 0.1490 0.1490 0.0008 0.0019 1.000 0.0075 0.0008 0.939 0.0031
[n/4, 3n/4] 0.3000 0.2997 0.0015 0.0026 0.998 0.0103 0.0014 0.916 0.0055
[n/2, 3n/4] 0.4000 0.3983 0.0038 0.0049 0.967 0.0197 0.0035 0.917 0.0136
[5n/8, 7n/8 0.1000 0.1001 0.0020 0.0033 0.996 0.0131 0.0019 0.932 0.0075
0.1 [1, n] 0.1490 0.1490 0.0014 0.0032 1.000 0.0125 0.0013 0.940 0.0052
[n/4, 3n/4] 0.3000 0.2991 0.0023 0.0044 0.998 0.0171 0.0024 0.935 0.0092
[n/2, 3n/4] 0.4000 0.3962 0.0061 0.0082 0.963 0.0325 0.0059 0.909 0.0231
[5n/8, 7n/8 0.1000 0.1001 0.0033 0.0056 0.998 0.0218 0.0032 0.940 0.0125
0.6 [1, n] 0.1490 0.1484 0.0086 0.0209 1.000 0.0821 0.0080 0.925 0.0313
[n/4, 3n/4] 0.3000 0.2936 0.0125 0.0296 0.995 0.1160 0.0132 0.908 0.0518
[n/2, 3n/4] 0.4000 0.3738 0.0332 0.0538 0.908 0.2122 0.0314 0.827 0.1230
[5n/8, 7n/8 0.1000 0.1052 0.0253 0.0418 0.986 0.1637 0.0212 0.902 0.0830
1.2 [1, n] 0.1490 0.1463 0.0225 0.0589 1.000 0.2307 0.0168 0.893 0.0657
[n/4, 3n/4] 0.3000 0.2893 0.0266 0.0787 0.917 0.3090 0.0236 0.829 0.0927
[n/2, 3n/4] 0.4000 0.3546 0.0637 0.1452 0.776 0.5708 0.0494 0.725 0.1938
[5n/8, 7n/8 0.1000 0.1129 0.0640 0.1297 0.912 0.5086 0.0511 0.862 0.2002
n σ [c, d] μ
μ^
sd(μ^)
 mCC MCI
Ave(SE) CP AW Ave(SE) CP AW
100 0.06 [1, n] 0.1495 0.1495 0.0003 0.0007 1.000 0.0027 0.0003 0.953 0.0011
[n/4, 3n/4] 0.3000 0.2999 0.0004 0.0009 0.997 0.0037 0.0005 0.964 0.0021
[n/2, 3n/4] 0.4000 0.3995 0.0013 0.0018 0.983 0.0070 0.0012 0.946 0.0049
[5n/8, 7n/8 0.1000 0.1001 0.0007 0.0012 0.999 0.0048 0.0007 0.952 0.0027
0.1 [1, n] 0.1495 0.1495 0.0005 0.0011 1.000 0.0045 0.0005 0.944 0.0019
[n/4, 3n/4] 0.3000 0.2997 0.0008 0.0016 0.997 0.0061 0.0009 0.936 0.0034
[n/2, 3n/4] 0.4000 0.3987 0.0022 0.0029 0.968 0.0116 0.0021 0.915 0.0084
[5n/8, 7n/8 0.1000 0.1001 0.0012 0.0020 0.999 0.0079 0.0011 0.934 0.0045
0.6 [1, n] 0.1495 0.1495 0.0029 0.0068 1.000 0.0268 0.0029 0.945 0.0114
[n/4, 3n/4] 0.3000 0.2973 0.0042 0.0093 1.000 0.0365 0.0051 0.940 0.0199
[n/2, 3n/4] 0.4000 0.3900 0.0116 0.0172 0.955 0.0678 0.0129 0.909 0.0505
[5n/8, 7n/8 0.1000 0.1006 0.0072 0.0122 0.999 0.0479 0.0069 0.939 0.0271
1.2 [1, n] 0.1495 0.1492 0.0058 0.0138 1.000 0.0542 0.0058 0.946 0.0227
[n/4, 3n/4] 0.3000 0.2949 0.0083 0.0189 1.000 0.0741 0.0098 0.933 0.0383
[n/2, 3n/4] 0.4000 0.3802 0.0228 0.0343 0.920 0.1349 0.0240 0.861 0.0939
[5n/8, 7n/8 0.1000 0.1024 0.0160 0.0256 1.000 0.1004 0.0142 0.924 0.0556

• mCCI: modified conditional confidence interval; MCI: confidence interval based on Muggeo [4]

• sd(μ^): standard deviation of the simulated values of μ^

• AVE(SE): average of standard error estimates obtained by each method

• CP: coverage probability

• AW: average width of 95% confidence intervals