Background
Multiple imputation
Rubin’s rules (RR)
Statistical hypothesis testing of a variable after MI
Univariate testing
Multivariate testing
Multiple parameter Wald test (CHI pooling)
The pooled sampling variance (VAR pooling) method
Meng and Rubin pooling (MR pooling)
The median P rule (MPR)
Simulation
Simulation design
Comparing methods
Description of results
Cor | Full data | RR | MR | CHI | VAR | MPRin
| MPRout
| |
---|---|---|---|---|---|---|---|---|
0.2 | Factor | 0.057 |
a
| 0.019 | 0.024 | 0.018 | 0.065 | 0.038 |
covar1 | 0.056 | 0.048 | 0.052 | 0.057 | 0.048 | 0.104 | 0.028 | |
covar2 | 0.056 | 0.056 | 0.057 | 0.057 | 0.056 | 0.061 | 0.059 | |
covar3 | 0.043 | 0.051 | 0.057 | 0.055 | 0.051 | 0.063 | 0.052 | |
covar4 | 0.070 | 0.058 | 0.061 | 0.063 | 0.058 | 0.070 | 0.052 | |
0.4 | Factor | 0.057 |
a
| 0.020 | 0.026 | 0.025 | 0.065 | 0.035 |
covar1 | 0.056 | 0.046 | 0.048 | 0.052 | 0.046 | 0.094 | 0.030 | |
covar2 | 0.056 | 0.051 | 0.054 | 0.054 | 0.051 | 0.060 | 0.056 | |
covar3 | 0.043 | 0.059 | 0.063 | 0.061 | 0.059 | 0.070 | 0.052 | |
covar4 | 0.070 | 0.056 | 0.057 | 0.056 | 0.056 | 0.057 | 0.055 | |
0.6 | Factor | 0.061 |
a
| 0.026 | 0.026 | 0.026 | 0.068 | 0.023 |
covar1 | 0.058 | 0.048 | 0.049 | 0.051 | 0.048 | 0.088 | 0.031 | |
covar2 | 0.065 | 0.055 | 0.057 | 0.060 | 0.055 | 0.066 | 0.056 | |
covar3 | 0.059 | 0.051 | 0.054 | 0.053 | 0.051 | 0.058 | 0.051 | |
covar4 | 0.063 | 0.063 | 0.066 | 0.066 | 0.063 | 0.075 | 0.064 | |
0.8 | Factor | 0.057 |
a
| 0.026 | 0.026 | 0.025 | 0.077 | 0.033 |
covar1 | 0.056 | 0.057 | 0.058 | 0.058 | 0.057 | 0.098 | 0.019 | |
covar2 | 0.056 | 0.058 | 0.060 | 0.061 | 0.058 | 0.063 | 0.055 | |
covar3 | 0.043 | 0.060 | 0.061 | 0.061 | 0.060 | 0.070 | 0.043 | |
covar4 | 0.070 | 0.053 | 0.052 | 0.054 | 0.053 | 0.062 | 0.059 |
Outcome-based imputation
Outcome excluded from imputation model
Summary: Outcome-based imputation except for MPR
Application
Estimate | SE | Z |
p-value | |
---|---|---|---|---|
Intercept | −8.0215 | 2.4064 | −3.3333 | 0.0008 |
Group | 0.0516 | |||
Group (1)a
| 0.7535 | 0.3287 | 2.2927 | 0.0219 |
Group (2)a
| 0.5986 | 0.3338 | 1.7936 | 0.0729 |
Age | −0.0007 | 0.0141 | −0.0498 | 0.9602 |
Gender | 0.4247 | 0.3525 | 1.2049 | 0.2282 |
BMI | 0.0619 | 0.0352 | 1.7587 | 0.0786 |
Education | 0.5108 | |||
Education (1)a
| −0.1501 | 0.4058 | −0.3699 | 0.7114 |
Education (2)a
| −0.3208 | 0.4397 | −0.7297 | 0.4656 |
Education (3)a
| −0.5997 | 0.6829 | −0.8782 | 0.3798 |
Education (4)a
| −1.2694 | 0.8117 | −1.5639 | 0.1179 |
Sitting | 0.0195 | |||
Sitting (1)a
| 0.6305 | 0.3295 | 1.9134 | 0.0557 |
Sitting (2)a
| −0.3515 | 0.4795 | −0.7329 | 0.4636 |
Sitting (3)a
| 1.0407 | 0.5286 | 1.9690 | 0.0489 |
Lifting | 0.9830 | |||
Lifting (1)a
| 0.1441 | 0.3692 | 0.3903 | 0.6963 |
Lifting (2)a
| 0.0574 | 0.4127 | 0.1389 | 0.8894 |
Lifting (3)a
| 0.0990 | 0.4424 | 0.2238 | 0.8229 |
Vibration tools | 0.0090 | |||
Vibration tools (1)a
| −0.5406 | 0.3717 | −1.4543 | 0.1459 |
Vibration tools (2)a
| 0.0554 | 0.4165 | 0.1329 | 0.8942 |
Vibration tools (3)a
| −1.6335 | 0.5573 | −2.9313 | 0.0034 |
Pain at baseline | 0.3232 | 0.0836 | 3.8656 | 0.0001 |
Physical functioning | 0.3220 | 0.1919 | 1.6778 | 0.0934 |
Disability | −0.9110 | 0.3283 | −2.7747 | 0.0055 |
Kinesiophobia | 0.0299 | 0.0222 | 1.3524 | 0.1762 |
Full data | RR | MR | CHI | VAR | MPRout
| Listwise | |
---|---|---|---|---|---|---|---|
Group | 0.0515 |
a
| 0.0498 | 0.0583 | 0.0643 | 0.0549 | 0.3234 |
Age | 0.9602 | 0.9245 | 0.9283 | 0.8780 | 0.9244 | 0.8898 | 0.8245 |
Gender | 0.2250 | 0.3040 | 0.2854 | 0.3017 | 0.3041 | 0.2862 | 0.8836 |
BMI | 0.0764 | 0.0172 | 0.0222 | 0.0137 | 0.0173 | 0.0049 | 0.0103 |
Education | 0.5108 |
a
| 0.7546 | 0.7235 | 0.7468 | 0.4579 | 0.6141 |
Sitting | 0.0195 |
a
| 0.0396 | 0.0355 | 0.0498 | 0.0306 | 0.1196 |
Lifting | 0.9830 |
a
| 0.9485 | 0.8755 | 0.9484 | 0.7605 | 0.9289 |
Vibration Tools | 0.0090 |
a
| 0.0115 | 0.0130 | 0.0236 | 0.0109 | 0.0833 |
Pain baseline | 0.0000 | 0.0001 | 0.0000 | 0.0000 | 0.0001 | 0.0000 | 0.0008 |
Physical Functioning | 0.0913 | 0.0970 | 0.1095 | 0.0943 | 0.0970 | 0.0532 | 0.0608 |
Disability | 0.0049 | 0.0032 | 0.0009 | 0.0027 | 0.0032 | 0.0022 | 0.0595 |
Kinesiophobia | 0.1730 | 0.2115 | 0.2312 | 0.2084 | 0.2115 | 0.2018 | 0.0438 |