. Author manuscript; available in PMC: 2024 Nov 20.

Published in final edited form as: Stat Med. 2023 Sep 3;42(26):4738–4762. doi: 10.1002/sim.9886

TABLE 2.

Posterior Summaries: Simulation Analyses Evaluating Handling of Completely Missing Within-Study Correlations

	Impute 0 (a)					Uniform(-1,1) Prior (b)					Conservative Prior (f)

Setup 1	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.28	0.55	0.88	0.87	−0.05	0.23	0.52	0.94	0.93	−0.05	−0.63	0.79	1.00	0.66	−0.01
u₀ = 0.4	0.48	0.63	0.74	0.74	−0.07	0.43	0.59	0.79	0.79	−0.06	−0.36	0.57	1.00	0.81	−0.01
u₀ = 0.6	0.67	0.76	0.55	0.55	−0.09	0.60	0.70	0.62	0.62	−0.08	−0.09	0.42	0.99	0.96	−0.03
u₀ = 0.8	0.83	0.88	0.32	0.32	−0.10	0.76	0.82	0.39	0.39	−0.10	0.17	0.44	0.88	0.88	−0.05

Setup 2	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.40	0.60	0.83	0.83	−0.06	0.34	0.56	0.86	0.86	−0.05	−0.69	0.92	1.00	0.68	0.00
u₀ = 0.4	0.60	0.75	0.67	0.67	−0.08	0.55	0.71	0.72	0.72	−0.07	−0.43	0.80	1.00	0.82	0.00
u₀ = 0.6	0.64	0.71	0.42	0.42	−0.10	0.59	0.68	0.52	0.52	−0.09	−0.06	0.58	0.97	0.93	−0.02
u₀ = 0.8	0.70	0.75	0.21	0.21	−0.11	0.67	0.72	0.30	0.30	−0.10	0.25	0.50	0.86	0.85	−0.04

Setup 3	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.01	0.19	0.95	0.93	0.00	0.02	0.19	0.96	0.94	0.00	0.00	0.19	0.96	0.93	0.00
u₀ = 0.4	0.01	0.19	0.97	0.94	0.00	0.01	0.18	0.97	0.94	0.00	0.00	0.19	0.97	0.93	0.00
u₀ = 0.6	0.02	0.19	0.97	0.94	0.00	0.01	0.19	0.97	0.94	0.00	0.00	0.19	0.98	0.94	0.00
u₀ = 0.8	0.04	0.20	0.93	0.91	0.00	0.03	0.20	0.94	0.91	0.00	0.01	0.19	0.97	0.94	0.00

Setup 4	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.03	0.26	0.97	0.95	−0.01	0.03	0.26	0.97	0.95	−0.01	−0.08	0.27	0.98	0.92	0.00
u₀ = 0.4	0.07	0.28	0.91	0.89	−0.02	0.07	0.28	0.91	0.89	−0.02	−0.05	0.27	0.98	0.94	−0.01
u₀ = 0.6	0.09	0.29	0.92	0.91	−0.02	0.09	0.29	0.92	0.91	−0.02	−0.01	0.27	0.97	0.91	−0.01
u₀ = 0.8	0.13	0.30	0.88	0.87	−0.02	0.13	0.29	0.88	0.87	−0.02	0.03	0.26	0.97	0.94	−0.01

Setup 5	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.23	0.48	0.87	0.85	−0.03	0.20	0.47	0.90	0.88	−0.02	−0.30	0.53	0.99	0.83	0.01
u₀ = 0.4	0.31	0.46	0.84	0.84	−0.03	0.28	0.44	0.86	0.86	−0.03	−0.14	0.37	0.99	0.94	0.01
u₀ = 0.6	0.38	0.50	0.72	0.72	−0.04	0.35	0.48	0.76	0.76	−0.04	0.03	0.38	0.94	0.93	−0.01
u₀ = 0.8	0.43	0.57	0.67	0.67	−0.06	0.41	0.55	0.68	0.68	−0.05	0.16	0.42	0.90	0.88	−0.03

Setup 6	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.46	0.68	0.83	0.83	−0.07	0.38	0.65	0.89	0.89	−0.05	−0.71	0.92	1.00	0.63	0.00
u₀ = 0.4	0.62	0.74	0.66	0.66		0.55	0.69	0.72	0.72		−0.47	0.81	1.00	0.83	−0.01
u₀ = 0.6	0.70	0.78	0.42	0.42	−0.10	0.66	0.77	0.50	0.50	−0.09	−0.08	0.64	0.98	0.93	−0.02
u₀ = 0.8	0.69	0.73	0.20	0.20	−0.12	0.66	0.73	0.25	0.25	−0.11	0.28	0.53	0.86	0.86	−0.05

Setup 7	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.29	0.50	0.91	0.90	−0.05	0.24	0.47	0.94	0.93	−0.04	−0.60	0.73	1.00	0.73	0.00
u₀ = 0.4	0.47	0.63	0.77	0.77	−0.07	0.42	0.59	0.79	0.79	−0.06	−0.34	0.56	0.99	0.84	−0.01
u₀ = 0.6	0.67	0.77	0.57	0.57	−0.09	0.62	0.73	0.60	0.60	−0.08	−0.05	0.41	0.99	0.97	−0.03
u₀ = 0.8	0.82	0.89	0.31	0.31	−0.10	0.76	0.82	0.37	0.37	−0.10	0.18	0.43	0.92	0.91	−0.05

Setup 8	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.28	0.54	0.89	0.88	−0.05	0.25	0.51	0.89	0.89	−0.05	−0.60	0.75	1.00	0.69	0.00
u₀ = 0.4	0.47	0.65	0.75	0.73	−0.07	0.41	0.61	0.79	0.77	−0.06	−0.38	0.59	1.00	0.85	−0.01
u₀ = 0.6	0.66	0.76	0.54	0.54	−0.09	0.59	0.70	0.61	0.61	−0.08	−0.08	0.43	0.98	0.94	−0.03
u₀ = 0.8	0.80	0.87	0.34	0.34	−0.10	0.73	0.81	0.39	0.39	−0.10	0.18	0.45	0.89	0.88	−0.05

Setup 9	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.31	0.54	0.90	0.90	−0.04	0.29	0.52	0.94	0.94	−0.03	−0.60	0.75	1.00	0.74	−0.05
u₀ = 0.4	0.50	0.69	0.77	0.77	−0.05	0.48	0.66	0.81	0.81	−0.04	−0.39	0.61	1.00	0.88	−0.04
u₀ = 0.6	0.76	0.88	0.57	0.57	−0.06	0.72	0.85	0.60	0.60	−0.06	−0.14	0.52	0.96	0.92	−0.04
u₀ = 0.8	1.01	1.11	0.32	0.32	−0.08	0.97	1.07	0.35	0.35	−0.08	0.17	0.51	0.90	0.89	−0.04

Setup 10	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.22	0.44	0.92	0.92	−0.03	0.16	0.42	0.94	0.94	−0.03	−0.57	0.72	1.00	0.65	0.03
u₀ = 0.4	0.37	0.50	0.81	0.81	−0.05	0.31	0.46	0.86	0.86	−0.04	−0.30	0.50	1.00	0.83	0.01
u₀ = 0.6	0.50	0.58	0.67	0.67	−0.06	0.43	0.52	0.74	0.74	−0.05	−0.05	0.35	0.98	0.95	−0.02
u₀ = 0.8	0.63	0.68	0.52	0.52	−0.06	0.56	0.62	0.57	0.57	−0.06	0.20	0.36	0.92	0.92	−0.04

Setup 11	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.23	0.71	0.97	0.97	−0.05	0.20	0.69	0.98	0.98	−0.04	−0.78	1.05	1.00	0.77	−0.02
u₀ = 0.4	0.42	0.71	0.91	0.90	−0.06	0.36	0.68	0.92	0.92	−0.06	−0.48	0.83	1.00	0.91	−0.02
u₀ = 0.6	0.67	0.85	0.81	0.81	−0.08	0.60	0.79	0.84	0.84	−0.08	−0.10	0.53	0.99	0.97	−0.04
u₀ = 0.8	0.80	0.91	0.72	0.72	−0.09	0.73	0.84	0.76	0.76	−0.09	0.09	0.56	0.95	0.95	−0.05

Setup 12	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias	β Bias	RMSE	CVG*	CVG	σ_e Bias

u₀ = 0.2	0.28	0.40	0.83	0.83	−0.05	0.24	0.36	0.89	0.88	−0.04	−0.54	0.61	1.00	0.52	0.01
u₀ = 0.4	0.47	0.55	0.55	0.55	−0.07	0.43	0.51	0.62	0.62	−0.06	−0.31	0.44	1.00	0.80	0.00
u₀ = 0.6	0.67	0.71	0.22	0.22	−0.10	0.61	0.66	0.34	0.34	−0.09	−0.03	0.27	1.00	0.97	−0.01
u₀ = 0.8	0.82	0.85	0.06	0.06	−0.11	0.75	0.79	0.09	0.09	−0.10	0.20	0.33	0.86	0.86	−0.04

u₀ is the true mean within-study correlation used for simulation. CVG* is the proportion of times the posterior 2.5^th percentile exceeded the true slope. Letters (e.g. (a)) displayed in the top row correspond to those used to define missing data handling strategies introduced in-text.