Impact of missing data on bias and precision when estimating change in patient-reported outcomes from a clinical registry

Ayilara, Olawale F.; Zhang, Lisa; Sajobi, Tolulope T.; Sawatzky, Richard; Bohm, Eric; Lix, Lisa M.

doi:10.1186/s12955-019-1181-2

Table 5 Simulation Performance Measures for Multiple Imputation (MI) without and with an Auxiliary Variable (MI-Aux)

From: Impact of missing data on bias and precision when estimating change in patient-reported outcomes from a clinical registry

Missing Mechanism	Model Parameter	Performance Measure	10% Missing				25% Missing				50% Missing
			MI	MI-Aux			MI	MI-Aux			MI	MI-Aux
				ρ = 0.2	ρ = 0.5	ρ = 0.8		ρ = 0.2	ρ = 0.5	ρ = 0.8		ρ = 0.2	ρ = 0.5	ρ = 0.8
MCAR	β ₀	Bias	4.48	3.75	3.70	3.29	2.31	3.05	3.25	0.74	3.89	4.81	5.05	4.36
		RMSE	1.78	1.78	1.77	1.74	1.88	1.89	1.85	1.77	2.19	2.18	2.11	1.94
		CI Width	8.11	8.09	8.03	7.92	8.58	8.53	8.39	8.09	9.50	9.42	9.10	8.46
	β _T	Bias	−2.16	−2.06	−0.54	2.18	−19.72	−21.47	−21.49	−12.81	−36.70	− 37.14	−31.22	−16.90
		RMSE	0.46	0.46	0.46	0.45	0.47	0.46	0.46	0.44	0.52	0.53	0.52	0.47
		CI Width	2.16	2.16	2.15	2.12	2.32	2.31	2.29	2.21	2.65	2.64	2.57	2.38
	β _TS	Bias	4.18	3.84	2.61	−1.39	29.38	32.62	33.04	21.74	61.45	62.28	52.82	29.08
		RMSE	0.56	0.56	0.56	0.56	0.57	0.57	0.57	0.56	0.60	0.60	0.60	0.58
		CI Width	2.82	2.82	2.81	2.77	3.00	3.00	2.96	2.88	3.34	3.31	3.25	3.05
MAR	β ₀	Bias	−1.29	−0.56	0.67	3.06	−11.52	−10.87	− 10.59	−8.20	−26.62	− 19.67	− 10.71	4.93
		RMSE	1.77	1.76	1.76	1.74	1.87	1.88	1.84	1.76	2.26	2.24	2.13	1.95
		CI Width	8.05	8.04	8.01	7.93	8.44	8.45	8.32	8.10	9.34	9.31	9.03	8.44
	β _T	Bias	9.13	6.53	4.63	3.17	−4.55	−11.15	−18.72	−18.78	−14.41	−14.83	− 10.96	−2.48
		RMSE	0.46	0.46	0.46	0.46	0.45	0.46	0.46	0.45	0.52	0.51	0.50	0.47
		CI Width	2.15	2.15	2.14	2.12	2.31	2.30	2.28	2.21	2.62	2.60	2.54	2.35
	β _TS	Bias	−8.19	−6.72	−6.81	−5.64	15.21	20.60	24.92	21.05	31.05	30.19	22.37	6.38
		RMSE	0.57	0.57	0.57	0.57	0.54	0.55	0.56	0.56	0.55	0.54	0.55	0.57
		CI Width	2.83	2.82	2.81	2.77	3.02	3.02	2.99	2.89	3.34	3.32	3.25	3.05
MNAR	β ₀	Bias	−42.75	−40.05	−31.76	−13.71	−86.54	−84.55	−73.35	− 42.67	−102.96	− 99.42	−89.10	−53.11
		RMSE	1.89	1.87	1.81	1.73	2.49	2.44	2.26	1.90	3.17	3.10	2.80	2.20
		CI Width	7.97	7.97	7.90	7.84	8.33	8.32	8.20	7.97	9.37	9.27	8.95	8.35
	β _T	Bias	7.95	6.41	3.46	1.73	−31.14	−34.74	−35.36	−25.04	− 101.73	− 99.73	−80.58	− 41.96
		RMSE	0.45	0.45	0.45	0.45	0.48	0.48	0.48	0.45	0.74	0.73	0.65	0.51
		CI Width	2.17	2.16	2.16	2.12	2.34	2.35	2.31	2.22	2.74	2.71	2.63	2.40
	β _TS	Bias	−16.91	−14.34	−8.65	−3.75	−5.30	1.39	11.72	16.71	16.66	18.66	15.27	8.17
		RMSE	0.55	0.55	0.55	0.56	0.53	0.54	0.55	0.55	0.54	0.54	0.55	0.57
		CI Width	2.82	2.82	2.80	2.77	3.01	3.02	2.98	2.88	3.41	3.39	3.30	3.07

CI Width Average width of the 95% confidence interval, Bias Standardized bias, RMSE Root mean squared error

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