. Author manuscript; available in PMC: 2015 Sep 14.

Published in final edited form as: J Stat Comput Simul. 2014 Nov 25;85(17):3498–3511. doi: 10.1080/00949655.2014.983111

Table 3.

Performance of AUC estimation using MI methods as well as case deletion under MAR, MCAR and MNAR.

			% miss.		Case deletion			Joint imputation				Sequential imputation				Re-sampling (bootstrap)

MM	TV	CD(SE)	Y*	Y	CR	AW	RMSE	AUC (SE)	CR	AW	RMSE	AUC (SE)	CR	AW	RMSE	AUC (SE)	CR	AW	RMSE
Scenario 18:{n = 500 π_Y* = 0.25 σ_Y = 20}
MAR	0.76	0.71 (0.03)	0.42		0.19	0.06	0.05	0.75 (0.04)	0.93	0.15	0.03	0.75 (0.04)	0.78	0.17	0.06	0.75 (0.04)	0.97	0.17	0.030
MCAR	0.76	0.76 (0.03)	0.30	0.30	0.43	0.04	0.03	0.76 (0.04)	0.94	0.15	0.03	0.76 (0.04)	0.95	0.16	0.03	0.76 (0.04)	0.97	0.17	0.028
MNAR	0.76	0.72 (0.03)	0.22	0.30	0.27	0.06	0.05	0.75 (0.03)	0.88	0.13	0.04	0.69 (0.08)	0.96	0.41	0.09	0.75 (0.04)	0.97	0.17	0.030
Scenario 19:{n = 500 π_Y* = 0.50 σ_Y = 20}
MAR	0.76	0.71 (0.03)	0.35		0.20	0.06	0.05	0.77 (0.03)	0.87	0.11	0.03	0.75 (0.03)	0.75	0.14	0.05	0.76 (0.03)	0.95	0.14	0.03
MCAR	0.76	0.76 (0.03)	0.30	0.30	0.50	0.04	0.02	0.76 (0.03)	0.92	0.11	0.02	0.76 (0.03)	0.94	0.13	0.02	0.76 (0.03)	0.96	0.14	0.02
MNAR	0.76	0.72 (0.03)	0.16	0.30	0.21	0.06	0.05	0.75 (0.03)	0.87	0.11	0.03	0.69 (0.07)	0.91	0.34	0.09	0.75 (0.03)	0.94	0.14	0.03
Scenario 20:{n = 500 π_Y* = 0.5 σ_Y = 20}
MCAR	0.64	0.64 (0.04)	0.3	0.30	0.84	0.10	0.03	0.64 (0.03)	0.91	0.13	0.03	0.64 (0.04)	0.94	0.15	0.03	0.64 (0.04)	0.95	0.147	0.03
MAR	0.64	0.61 (0.03)	0.27		0.90	0.10	0.03	0.64 (0.03)	0.89	0.12	0.02	0.63 (0.04)	0.88	0.16	0.04	0.63 (0.04)	0.95	0.141	0.02
MNAR	0.64	0.60 (0.04)	0.31	0.30	0.76	0.12	0.06	0.61 (0.03)	0.71	0.13	0.06	0.62 (0.08)	0.99	0.36	0.05	0.62 (0.04)	0.91	0.196	0.05
Scenario 21:{n = 500 π_Y* = 0.25 σ_Y = 20}
MCAR	0.638	0.64 (0.04)	0.30	0.30	0.80	0.10	0.001	0.64 (0.04)	0.92	0.16	0.001	0.64 (0.05)	0.97	0.182	0.001	0.64 (0.05)	0.97	0.18	0.001
MAR	0.639	0.62 (0.03)	0.30	-	0.84	0.10	0.001	0.63 (0.04)	0.94	0.16	0.001	0.64 (0.05)	0.89	0.199	0.002	0.64 (0.04)	0.97	0.17	0.001
MNAR	0.637	0.59 (0.04)	0.36	0.30	0.76	0.13	0.003	0.59 (0.04)	0.64	0.16	0.005	0.64 (0.10)	0.99	0.434	0.002	0.62 (0.05)	0.94	0.23	0.003
Scenario 22:{n = 500 π_Y* = 0.25 σ_Y = 20}
MAR	0.85	0.80 (0.03)	0.54		0.03	0.03	0.07	0.85 (0.03)	0.94	0.11	0.03	0.85 (0.03)	0.68	0.14	0.06	0.85 (0.04)	0.97	0.16	0.03
MCAR	0.85	0.85 (0.02)	0.30	0.30	0.17	0.01	0.02	0.85 (0.03)	0.96	0.11	0.02	0.85 (0.03)	0.97	0.13	0.02	0.85 (0.03)	0.98	0.13	0.02
MNAR	0.85	0.81 (0.02)	0.24	0.30	0.06	0.02	0.05	0.85 (0.03)	0.93	0.11	0.02	0.73 (0.09)	0.88	0.47	0.14	0.85 (0.03)	0.97	0.13	0.02
Scenario 23:{n = 500 π_Y* = 0.50 σ_Y = 20}
MAR	0.85	0.80 (0.03)	0.43		0.02	0.03	0.07	0.85 (0.02)	0.88	0.08	0.02	0.83 (0.02)	0.67	0.12	0.06	0.85 (0.03)	0.95	0.13	0.02
MCAR	0.85	0.85 (0.02)	0.30	0.30	0.22	0.01	0.02	0.86 (0.02)	0.94	0.09	0.02	0.86 (0.02)	0.94	0.10	0.02	0.85 (0.03)	0.96	0.11	0.02
MNAR	0.85	0.81 (0.03)	0.17	0.30	0.06	0.02	0.05	0.85 (0.02)	0.88	0.08	0.02	0.75 (0.07)	0.83	0.35	0.11	0.85 (0.02)	0.93	0.10	0.02

Notes: MM (missingness mechanism), TV (true value), CD (case deletion), SE (standard error), CR (coverage rate), AW (average width of confidence intervals), RMSE (root-mean-square error). CR and AW are based on 95% nominal confidence rate. CD(SE) column contains AUC estimate and estimate of its standard error under case deletion.