Outcome-sensitive multiple imputation: a simulation study

Kontopantelis, Evangelos; White, Ian R.; Sperrin, Matthew; Buchan, Iain

doi:10.1186/s12874-016-0281-5

BMC Medical Research Methodology

Table 3 Performance results for exposure E, datasets of 10,000 observations^a

From: Outcome-sensitive multiple imputation: a simulation study

		% miss	A	B	C^b	D^b	E^b	F^b	G^b	H
MCAR	Mean bias^c	20	0.001	−0.089	−0.003	−0.008	−0.006	−0.003	−0.006	−0.413
		40	−0.005	−0.181	−0.016	−0.024	−0.009	−0.016	−0.021	−0.419
		60	−0.017	−0.268	−0.027	−0.035	−0.017	−0.028	−0.032	−0.421
		80	−0.021	−0.343	−0.023	−0.036	−0.033	−0.027	−0.032	−0.418
	Mean error^c	20	0.064	0.094	0.059	0.059	0.060	0.059	0.059	0.413
		40	0.088	0.182	0.071	0.072	0.071	0.070	0.071	0.419
		60	0.135	0.268	0.094	0.094	0.088	0.094	0.095	0.421
		80	0.270	0.343	0.150	0.144	0.148	0.148	0.143	0.418
	Coverage	20	0.962	0.792	0.959	0.965	0.948	0.959	0.959	0.000
		40	0.946	0.439	0.954	0.946	0.958	0.954	0.952	0.000
		60	0.943	0.291	0.956	0.931	0.965	0.958	0.939	0.007
		80	0.952	0.394	0.952	0.929	0.950	0.949	0.929	0.137
	Power	20	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.983
		40	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.935
		60	0.974	0.982	1.000	1.000	1.000	1.000	1.000	0.772
		80	0.518	0.635	0.949	0.943	0.956	0.946	0.944	0.547
MAR	Mean bias^c	20	0.005	−0.101	−0.005	−0.012	−0.009	−0.005	−0.013	−0.412
		40	0.001	−0.204	−0.031	−0.043	−0.032	−0.031	−0.042	−0.419
		60	−0.015	−0.275	−0.038	−0.046	−0.028	−0.037	−0.046	−0.423
		80	0.014	−0.349	−0.058	−0.068	−0.058	−0.058	−0.072	−0.415
	Mean error^c	20	0.064	0.104	0.059	0.058	0.060	0.058	0.058	0.412
		40	0.087	0.204	0.072	0.075	0.074	0.072	0.075	0.419
		60	0.135	0.275	0.096	0.098	0.092	0.095	0.097	0.423
		80	0.304	0.349	0.160	0.159	0.153	0.158	0.161	0.415
	Coverage	20	0.965	0.727	0.963	0.967	0.962	0.965	0.964	0.000
		40	0.952	0.334	0.958	0.940	0.947	0.951	0.935	0.000
		60	0.948	0.237	0.950	0.924	0.953	0.950	0.918	0.004
		80	0.944	0.356	0.935	0.918	0.943	0.941	0.926	0.161
	Power	20	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.987
		40	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.944
		60	0.977	0.982	0.999	1.000	1.000	1.000	1.000	0.792
		80	0.486	0.613	0.905	0.897	0.920	0.912	0.902	0.537
MNAR	Mean bias^c	20	0.003	−0.125	−0.023	−0.021	−0.024	−0.023	−0.024	−0.411
		40	−0.006	−0.250	−0.091	−0.072	−0.080	−0.091	−0.081	−0.417
		60	−0.003	−0.288	−0.016	0.010	0.005	−0.017	0.003	−0.420
		80	−0.026	−0.358	−0.186	−0.161	−0.186	−0.182	−0.176	−0.427
	Mean error^c	20	0.067	0.128	0.063	0.063	0.066	0.063	0.063	0.411
		40	0.112	0.250	0.113	0.102	0.107	0.113	0.107	0.417
		60	0.150	0.288	0.103	0.105	0.106	0.104	0.103	0.420
		80	0.456	0.367	0.253	0.237	0.258	0.252	0.241	0.428
	Coverage	20	0.952	0.643	0.948	0.947	0.935	0.949	0.947	0.000
		40	0.960	0.349	0.893	0.908	0.886	0.887	0.893	0.002
		60	0.952	0.394	0.955	0.944	0.937	0.961	0.947	0.017
		80	0.967	0.943	0.981	0.916	0.971	0.981	0.916	0.360
	Power	20	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.973
		40	0.998	0.985	1.000	1.000	1.000	1.000	1.000	0.826
		60	0.942	0.898	0.999	0.997	1.000	0.996	0.999	0.738
		80	0.256	0.094	0.358	0.527	0.394	0.364	0.519	0.331

^aAnalysis model A: complete case analysis (no multiple imputation [mi]); B: no outcome imputation, not included in mi model; C: no outcome imputation, outcome imputed in mi model; D: outcome imputed and included in mi model; E: outcome imputed and included in mi model but then observations where it was imputed are deleted; F as in C but also including a second correlated outcome in the mi model; G as in D but also including a second correlated outcome in the mi model; H as in D but the mi and analysis models do not include the covariate
^bMain models of interest, other models provided for comparison purposes
^cReported on log-odds scale and based on a true effect of log [2]

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