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Table 3 Performance of various methods for handling 50% missingness in BMI for age z-scores; true ORa = 1.1(log(OR) = 0.1)

From: A comparison of multiple imputation methods for handling missing values in longitudinal data in the presence of a time-varying covariate with a non-linear association with time: a simulation study

Performance Measure

Method

Complete Case Analysis

FCS

MVNI

two-fold FCS (width = 1)c

two-fold FCS (width = 2)d

MCAR

 Absolute Biasb

0.001

0.000

0.000

0.002

0.001

 Relative Bias (%)

0.65

0.28

0.34

1.63

0.77

 Empirical SE

0.017

0.017

0.017

0.018

0.017

 Model-based SE

0.018

0.017

0.017

0.017

0.017

 Coverage (%)

95.6

95.8

95.9

95.3

95.9

 RMSE

0.017

0.017

0.017

0.018

0.017

MAR (weak)

 Absolute Biasb

0.015

0.000

0.000

0.000

0.000

 Relative Bias (%)

15.03

0.16

0.22

0.03

0.28

 Empirical SE

0.018

0.017

0.017

0.017

0.017

 Model-based SE

0.018

0.017

0.017

0.017

0.017

 Coverage (%)

86.3

94.4

94.5

94.3

94.6

 RMSE

0.023

0.017

0.017

0.017

0.017

MAR (strong)

 Absolute Biasb

0.020

0.000

0.000

0.003

0.002

 Relative Bias (%)

20.36

0.23

0.21

3.19

2.16

 Empirical SE

0.018

0.017

0.017

0.018

0.017

 Model-based SE

0.017

0.017

0.017

0.017

0.017

 Coverage (%)

77.8

95.0

94.9

93.6

93.9

 RMSE

0.027

0.017

0.017

0.018

0.018

  1. Empirical SE empirical standard error, FCS fully conditional specification, MAR missing at random, MCAR missing completely at random, Model-based SE model based standard error, MVNI multivariate normal imputation, RMSE root mean square error, two-fold FCS two-fold fully conditional specification algorithm
  2. aTrue OR represents the true odds ratio between sleep problems and BMI for age z-scores
  3. bMonte Carlo standard error did not exceed 0.0006
  4. cResults for the two-fold FCS with a time window width of 1, that is, including immediately adjacent time points
  5. dResults for the two-fold FCS with a time window width of 2, that is, including two adjacent time points