Table 5.

Performance comparisons for each causal scenario F and F’ for lipophilic traditional standardization using our pooling protocols vs. naïve standardization after equal-volume pooling for 1000 simulated case–control studies of 500 cases and 500 controls each.

Beta	Pool size	Naïve standardization		Traditional standardization using our pooling protocols
		95% CI coverage	Bias (SE)	95% CI coverage	Mean 95% CI width	Power	Bias (SE)
			Scenario F
0	1a	0.94	−0.005 (0.003)	0.94	0.41	0.05	−0.005 (0.003)
0	2	0.94	−0.002 (0.003)	0.93	0.42	0.07	0.002 (0.004)
0	5	0.95	−0.001 (0.003)	0.95	0.46	0.06	−0.002 (0.004)
0	10	0.95	−0.001 (0.004)	0.96	0.52	0.06	−0.005 (0.004)
0.26	1a	0.94	0.003 (0.004)	0.94	0.45	0.96	0.003 (0.004)
0.26	2	0.93	−0.030 (0.004)	0.94	0.47	0.95	0.000 (0.004)
0.26	5	0.92	−0.040 (0.004)	0.96	0.55	0.91	0.023 (0.004)
0.26	10	0.92	−0.027 (0.006)	0.96	0.72	0.78	0.039 (0.006)
0.69	1a	0.95	−0.004 (0.004)	0.95	0.53	1.00	−0.004 (0.004)
0.69	2	0.91	−0.065 (0.005)	0.95	0.61	1.00	0.007 (0.005)
0.69	5	0.89	−0.069 (0.007)	0.95	0.88	1.00	0.045 (0.007)
0.69	10	0.94	0.092 (0.016)	0.98	1.85	1.00	0.228 (0.017)
			Scenario F’
0	1a	0.96	−0.002 (0.003)	0.96	0.33	0.04	−0.002 (0.003)
0	2	0.95	−0.004 (0.003)	0.95	0.33	0.05	−0.002 (0.003)
0	5	0.95	0.006 (0.002)	0.94	0.33	0.06	−0.003 (0.003)
0	10	0.96	0.001 (0.003)	0.96	0.33	0.05	−0.003 (0.003)
0.26	1a	0.96	0.003 (0.003)	0.96	0.35	1.00	0.003 (0.003)
0.26	2	0.93	−0.022 (0.003)	0.95	0.36	1.00	0.004 (0.003)
0.26	5	0.93	−0.031 (0.003)	0.94	0.38	1.00	0.004 (0.003)
0.26	10	0.92	−0.028 (0.003)	0.94	0.43	1.00	0.016 (0.004)
0.69	1a	0.95	−0.004 (0.004)	0.95	0.43	1.00	−0.004 (0.004)
0.69	2	0.91	−0.058 (0.004)	0.96	0.48	1.00	0.004 (0.004)
0.69	5	0.89	−0.074 (0.005)	0.95	0.63	1.00	0.028 (0.005)
0.69	10	0.90	−0.028 (0.008)	0.96	0.99	1.00	0.088 (0.009)