Table 1 : Bias and MSE for estimated Mean and Standard deviation for varying proportion of missingness and sample sizes.


      Single imputation
LOCF method
Multiple imputation
MCMC method
Multiple imputation
Regression method
Multiple imputation
propensity score method

Proportion
missingness
Sample
size
Estimate Bias
(90% CI)
  MSE
(90% CI)
Bias
(90% CI)
  MSE
(90% CI)
Bias
(90% CI)
  MSE
(90% CI)
Bias
(90% CI)
MSE
(90% CI)

20% 50 Mean 0.4130
(0.2321, 0.6101)
  0.1831
(0.0538, 0.3723)
0.2638
(0.0388, 0.5293)
  0.0924
(0.0015, 0.2802)
0.0815
(0.0054, 0.2108)
  0.0108
(0.0000, 0.0444)
0.1165
(0.0066, 0.2832)
0.0224
(0.0000, 0.0802)
    Std dev 0.0840
(0.0064, 0.2093)
  0.0112
(0.0000, 0.0438)
0.1009
(0.0071, 0.2650)
  0.0171
(0.0001, 0.0702)
0.0889
(0.0064, 0.2269)
  0.0129
(0.0000, 0.0515)
0.1966
(0.0255, 0.4174)
0.0532
(0.0006, 0.1742)
  75 Mean 0.4157
(0.2638, 0.5674)
  0.1809
(0.0696, 0.3220)
0.2641
(0.0532, 0.5101)
  0.0875
(0.0028, 0.2602)
0.0704
(0.0045, 0.1784)
  0.0081
(0.0000, 0.0318)
0.0948
(0.0064, 0.2442)
0.0148
(0.0000, 0.0596)
    Std dev 0.0696
(0.0063, 0.1745)
  0.0079
(0.0000, 0.0305)
0.0782
(0.0075, 0.2007)
  0.0098
(0.0001, 0.0403)
0.0794
(0.0058, 0.1961)
  0.0099
(0.0000, 0.0385)
0.1814
(0.0289, 0.3502)
0.0424
(0.0008, 0.1227)
  120 Mean 0.4148
(0.3027, 0.5386)
  0.1773
(0.0916, 0.2901)
0.2597
(0.0908, 0.4327)
  0.0785
(0.0083, 0.1872)
0.0553
(0.0047, 0.1361)
  0.0048
(0.0000, 0.0185)
0.0743
(0.0059, 0.1866)
0.0087
(0.0000, 0.0348)
    Std dev 0.0563
(0.0051, 0.1410)
  0.0050
(0.0000, 0.0199)
0.0647
(0.0060, 0.1683)
  0.0068
(0.0000, 0.0283)
0.0726
(0.0074, 0.1729)
  0.0079
(0.0001, 0.0299)
0.1665
(0.0401, 0.3157)
0.0347
(0.0016, 0.0997)

30% 50 Mean 0.5909
(0.3825, 0.7974)
  0.3652
(0.1463, 0.6358)
0.4231
(0.0960, 0.7751)
  0.2212
(0.0092, 0.6007)
0.1147
(0.0073, 0.2938)
  0.0223
(0.0001, 0.0863)
0.1685
(0.0106, 0.4328)
0.0475
(0.0001, 0.1873)
    Std dev 0.1003
(0.0052, 0.2605)
  0.0165
(0.0000, 0.0679)
0.1399
(0.0129, 0.3636)
  0.0316
(0.0002, 0.1322)
0.1259
(0.0096, 0.3258)
  0.0255
(0.0001, 0.1061)
0.2500
(0.0304, 0.5292)
0.0858
(0.0009, 0.2801)
  75 Mean 0.5804
(0.4141, 0.7599)
  0.3474
(0.1715, 0.5774)
0.4122
(0.1246, 0.7370)
  0.2026
(0.0155, 0.5432)
0.0955
(0.0073, 0.2368)
  0.0148
(0.0001, 0.0561)
0.1289
(0.0094, 0.3147)
0.0271
(0.0001, 0.0990)
    Std dev 0.0869
(0.0073, 0.2131)
  0.0118
(0.0001, 0.0454)
0.1163
(0.0090, 0.2933)
  0.0220
(0.0001, 0.0860)
0.1126
(0.0096, 0.2715)
  0.0195
(0.0001, 0.0737)
0.2328
(0.0357, 0.4633)
0.0719
(0.0013, 0.2147)
  120 Mean 0.5833
(0.4479, 0.7157)
  0.3472
(0.2006, 0.5123)
0.4095
(0.1790, 0.6448)
  0.1875
(0.0320, 0.4158)
0.0781
(0.0070, 0.1922)
  0.0095
(0.0000, 0.0370)
0.1030
(0.0100, 0.2589)
0.0164
(0.0001, 0.0670)
    Std dev 0.0733
(0.0073, 0.1769)
  0.0081
(0.0001, 0.0313)
0.0933
(0.0062, 0.2431)
  0.0139
(0.0000, 0.0591)
0.1050
(0.0118, 0.2312)
  0.0156
(0.0001, 0.0535)
0.2146
(0.0409, 0.4067)
0.0579
(0.0017, 0.1654)

50% 50 Mean 0.9058
(0.6816, 1.1471)
  0.8401
(0.4646, 1.3159)
0.8548
(0.2980, 1.4540)
  0.8518
(0.0888, 2.1141)
0.3001
(0.0208, 0.7564)
  0.4743
(0.0004, 0.5722)
0.2810
(0.0182, 0.6889)
0.1219
(0.0003, 0.4746)
    Std dev 0.1325
(0.0104, 0.3131)
  0.0268
(0.0001, 0.0980)
0.3120
(0.0239, 0.7339)
  0.1464
(0.0006, 0.5386)
0.2957
(0.0242, 0.6567)
  0.1631
(0.0002, 0.6491)
0.3333
(0.0338, 0.7580)
0.1606
(0.0011, 0.5745)
  75 Mean 0.9012
(0.7167, 1.0871)
  0.8256
(0.5136, 1.1817)
0.8610
(0.3887, 1.3452)
  0.8174
(0.1511, 1.8095)
0.2124
(0.0175, 0.5172)
  0.0726
(0.0003, 0.2675)
0.2628
(0.0217, 0.6422)
0.1112
(0.0005, 0.4124)
    Std dev 0.1189
(0.0125, 0.2682)
  0.0214
(0.0002, 0.0720)
0.2799
(0.0259, 0.6286)
  0.1164
(0.0007, 0.3952)
0.2248
(0.0188, 0.5445)
  0.0778
(0.0004, 0.2965)
0.3253
(0.0247, 0.7417)
0.1555
(0.0006, 0.5500)
  120 Mean 0.8956
(0.7565, 1.0362)
  0.8096
(0.5722, 1.0736)
0.8606
(0.5175, 1.2047)
  0.7856
(0.2679, 1.4514)
0.1649
(0.0168, 0.3882)
  0.0417
(0.0003, 0.1507)
0.2274
(0.0200, 0.5705)
0.0814
(0.0004, 0.3255)
    Std dev 0.1037
(0.0094, 0.2342)
  0.0157
(0.0001, 0.0548)
0.2413
(0.0266, 0.5457)
  0.0834
(0.0007, 0.2978)
0.1993
(0.0194, 0.4376)
  0.0568
(0.0004, 0.1915)
0.3060
(0.0304, 0.6508)
0.1298
(0.0009, 0.4235)

Mishra et al.Journal of Medical Statistics and Informatics  2014 2:9DOI : 10.7243/2053-7662-2-9