Efficiency of two-phase methods with focus on a planned population-based case-control study on air pollution and stroke

Table 3 Simulation results based on 1,000 replications

		Scenario 1 Number of first-phase subjects: 400 cases 1,200 controls			Scenario 2 Number of first-phase subjects: 1,200 cases 1,200 controls			Scenario 3 Number of first- phase subjects: 400 cases 12,000 controls
	True OR††	OR*	SD*	Ef**	OR*	SD*	Ef**	OR*	SD*	Ef**
Individual-level information on all subjects †	1.50	1.49	0.18	100	1.50	0.12	100	1.50	0.16	100
	3.00	3.00	0.17	100	3.00	0.11	100	3.00	0.14	100
Method 1‡	1.50	1.48	0.25	53	1.50	0.24	25	1.50	0.25	43
	3.00	3.01	0.24	51	2.98	0.23	23	2.99	0.23	40
Method 2‡	1.50	1.60	0.32	29	1.56	0.24	25	1.59	0.29	28
	3.00	3.05	0.27	39	3.01	0.18	39	3.04	0.24	37
Method 3‡	1.50	1.49	0.24	58	1.50	0.22	29	1.50	0.24	46
	3.00	3.00	0.22	59	2.98	0.21	29	3.00	0.21	47
Method 4‡	1.50	1.49	0.19	81	1.50	0.20	37	1.51	0.19	68
	3.00	2.99	0.16	78	3.01	0.17	44	3.02	0.18	66

* Geometric mean of the OR estimates and the empiric standard deviation of the ln(OR) estimates.
** Efficiency of the ln(OR) estimates. eff₁ = (var(ln(OR₁)) + (ln(true OR₁))-ln(OR₁)))/(var(ln(OR_ref)) + (ln(true OR_ref))-ln(OR_ref))) where OR_ref is the estimate in the ideal scenario. Efficiencies calculated when varying the number of first-phase subjects. The number of second-phase cases and controls are held fixed at 300 cases and 300 controls.
† Ideal scenario.
‡ Methods 1–4 are further described in the Methods section and in Table 1.
†† A confounder with OR = 2 is introduced and a positive bias-effect of 20% for OR = 1.50 and 33% for OR = 3.00

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