The use of complete-case and multiple imputation-based analyses in molecular epidemiology studies that assess interaction effects

Desai, Manisha; Esserman, Denise A; Gammon, Marilie D; Terry, Mary B

doi:10.1186/1742-5573-8-5

Epidemiologic Perspectives & Innovations

Table 6 Impact of Percentage Missing Under Conditions 1, 2, and 3.

From: The use of complete-case and multiple imputation-based analyses in molecular epidemiology studies that assess interaction effects

a. Condition 1^a
Scenario	Variable*	Method	Mean β	Mean SE	Mean Bias	MSE	RelMSE	Coverage
A1: 20% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.002	0.211	0.002	0.044	0.543	95.0 (93.6,96.4)
		CC	1.000	0.284	-0.000	0.081	1.000	95.8 (94.6,97.0)
		MI	1.062	0.230	0.062	0.052	0.644	95.9 (94.7,97.1)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.549	0.378	0.049	0.166	0.068	95.4 (94.1,96.7)
		CC	2.713	4.822	0.213	2.436	1.000	97.0 (95.9,98.1)
		MI	2.543	0.426	0.043	0.178	0.072	96.8 (95.7,97.9)
	Interaction (True effect = 1.5)	Full	1.547	0.434	0.047	0.204	0.082	95.7 (94.4,97.0)
		CC	1.713	4.894	0.213	2.503	1.000	96.7 (95.6,97.8)
		MI	1.482	0.483	-0.018	0.205	0.082	96.1 (94.9,97.3)
A2: 30% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.003	0.211	0.003	0.044	0.358	94.6 (93.2,96.0)
		CC	0.992	0.345	-0.008	0.122	1.000	95.0 (93.6,96.4)
		MI	1.095	0.245	0.095	0.065	0.531	94.9 (93.5,96.3)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.558	0.379	0.058	0.146	0.014	97.2 (96.2,98.2)
		CC	3.288	25.207	0.788	10.689	1.000	98.5 (97.7,99.3)
		MI	2.557	0.462	0.057	0.178	0.017	98.3 (97.5,99.1)
	Interaction (True effect = 1.5)	Full	1.555	0.435	0.055	0.195	0.018	96.1 (94.9,97.3)
		CC	2.295	25.290	0.795	10.904	0.018	96.1 (94.9,97.3)
		MI	1.462	0.515	-0.038	0.219	0.020	97.8 (96.9,98.7)
A3: 40% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.020	0.211	0.020	0.045	0.258	95.6 (94.3,96.8)
		CC	0.991	0.411	-0.009	0.175	1.000	95.5 (94.2,96.8)
		MI	1.137	0.263	0.137	0.083	0.474	94.1 (92.6,95.6)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.540	0.377	0.040	0.140	0.006	96.6 (95.5,97.7)
		CC	4.121	64.794	1.621	23.920	1.000	96.5 (95.4,97.6)
		MI	2.536	0.489	0.036	0.177	0.007	97.5 (96.5,98.5)
	Interaction (True effect = 1.5)	Full	1.520	0.433	0.020	0.191	0.008	96.0 (94.8,97.2)
		CC	3.131	64.890	1.631	24.283	1.000	97.0 (95.9,98.1)
		MI	1.399	0.538	-0.101	0.220	0.009	97.2 (96.2,98.2)
b. Condition 2^b
Scenario	Variable	Method	Mean β	Mean SE	Mean Bias	MSE	RelMSE	Coverage
A4: 20% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.007	0.108	0.007	0.012	0.590	95.5 (94.2,96.8)
		CC	1.010	0.147	0.010	0.021	1.000	95.9 (94.7,97.1)
		MI	1.059	0.115	0.059	0.017	0.820	92.5 (90.9,94.1)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.552	0.279	0.052	0.089	0.909	93.7 (92.2,95.2)
		CC	2.548	0.298	0.048	0.098	1.000	93.4 (91.9,94.9)
		MI	2.593	0.281	0.093	0.095	0.966	94.5 (93.1,95.9)
	Interaction (True effect = 1.5)	Full	1.544	0.300	0.044	0.102	0.872	93.6 (92.1,95.1)
		CC	1.538	0.332	0.038	0.117	1.000	94.0 (92.5,95.5)
		MI	1.534	0.304	0.034	0.101	0.863	94.0 (92.5,95.5)
A5: 30% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.003	0.108	0.003	0.012	0.437	94.5 (93.1,95.9)
		CC	1.008	0.168	0.008	0.027	1.000	94.6 (93.2,96.0)
		MI	1.079	0.118	0.079	0.020	0.741	92.4 (90.8,94.0)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.532	0.277	0.032	0.078	0.798	95.7 (94.4,97.0)
		CC	2.529	0.317	0.029	0.098	1.000	96.2 (95.0,97.4)
		MI	2.612	0.284	0.112	0.091	0.928	95.6 (94.3,96.9)
	Interaction (True effect = 1.5)	Full	1.529	0.297	0.029	0.091	0.731	95.4 (94.1,96.7)
		CC	1.521	0.359	0.021	0.125	1.000	94.8 (93.4,96.2)
		MI	1.533	0.308	0.033	0.093	0.743	95.4 (94.1,96.7)
A6: 40% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.005	0.108	0.005	0.011	0.330	95.8 (94.6,97.0)
		CC	1.007	0.197	0.007	0.035	1.000	95.9 (94.7,97.1)
		MI	1.109	0.123	0.109	0.026	0.749	87.5 (85.5,89.5)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.551	0.279	0.051	0.081	0.620	95.7 (94.4,97.0)
		CC	2.563	0.355	0.063	0.131	1.000	96.2 (95.0,97.4)
		MI	2.675	0.295	0.175	0.112	0.852	94.3 (92.9,95.7)
	Interaction (True effect = 1.5)	Full	1.547	0.300	0.047	0.094	0.563	95.1 (93.8,96.4)
		CC	1.557	0.406	0.057	0.168	1.000	95.3 (94.0,96.6)
		MI	1.565	0.319	0.065	0.098	0.588	96.9 (95.8,98.0)
c. Condition 3^c
Scenario	Variable	Method	Mean β	Mean SE	Mean Bias	MSE	RelMSE	Coverage
A7: 20% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.012	0.108	0.012	0.012	0.076	94.7 (93.3,96.1)
		CC	0.616	0.119	-0.384	0.162	1.000	11.9 (9.9,13.9)
		MI	0.999	0.109	-0.001	0.012	0.077	94.3 (92.9,95.7)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.549	0.279	0.049	0.080	0.667	96.1 (94.9,97.3)
		CC	2.320	0.289	-0.180	0.120	1.000	87.1 (85.0,89.2)
		MI	2.551	0.280	0.051	0.080	0.666	96.2 (95.0,97.4)
	Interaction (True effect = 1.5)	Full	1.537	0.300	0.037	0.091	0.635	96.1 (94.9,97.3)
		CC	1.704	0.313	0.204	0.143	1.000	92.6 (91.0,94.2)
		MI	1.552	0.301	0.052	0.092	0.642	95.7 (94.4,97.0)
A8: 30% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.006	0.108	0.006	0.012	0.027	95.0 (93.6,96.4)
		CC	0.331	0.127	-0.669	0.466	1.000	0.3 (0,0.6)
		MI	0.983	0.110	-0.017	0.013	0.028	95.0 (93.6,96.4)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.528	0.277	0.028	0.075	0.179	95.8 (94.6,97.0)
		CC	1.927	0.299	-0.573	0.419	1.000	48.6 (45.5,51.7)
		MI	2.492	0.277	-0.008	0.072	0.171	95.6 (94.3,96.9)
	Interaction (True effect = 1.5)	Full	1.522	0.297	0.022	0.084	0.743	96.0 (94.8,97.2)
		CC	1.596	0.325	0.096	0.113	1.000	95.7 (94.4,97.0)
		MI	1.509	0.298	0.009	0.081	0.713	96.1 (94.9,97.3)
A9: 40% missing
	X1 (X2 = 0) (True effect = 1.0)	Full	1.007	0.108	0.007	0.011	0.012	95.8 (94.6,97.0)
		CC	0.027	0.139	-0.973	0.966	1.000	0.0 (0.0,0.0)
		MI	0.968	0.110	-0.032	0.013	0.013	94.1 (92.6,95.6)
	X1 (X2 = 1) (True effect = 2.5)	Full	2.537	0.277	0.037	0.079	0.092	95.6 (94.3,96.9)
		CC	1.627	0.312	-0.873	0.864	1.000	23.1 (20.5,25.7)
		MI	2.461	0.276	-0.039	0.073	0.085	95.4 (94.1,96.7)
	Interaction (True effect = 1.5)	Full	1.531	0.298	0.031	0.089	0.683	96.1 (94.9,97.3)
		CC	1.600	0.342	0.100	0.130	1.000	95.2 (93.9,96.5)
		MI	1.493	0.297	-0.007	0.081	0.627	96.9 (95.8,98.0)

Results From Fitting Full, Complete-Case, and Multiple Imputation Models to 1000 Simulated Data Sets With a Sample Size of 1000 Where the Covariate of Interest and as a Result the Interaction Term Were Missing for Some Subjects and the Auxiliary Information Was Strong.
^aCondition 1: X1 is 7.4 times more likely to be missing if X1 = 1, where X1 is binary
^bCondition 2: Extreme values of X1 are more likely to be missing (probability of missing is a quadratic function of X1 or the log odds of missing X1 = γ₀+γ₁ X1 + γ₂ X1², where γ₁ = -1 and γ₂ = 2), where X1 is continuous
^cCondition 3: A 1-unit increase in X1 corresponds to a 7.4 times decrease in the probability of missing for controls, but a 7.4 times increase for cases, where X1 is continuous

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