Table 2

Simulation study results of the impact of two different methods of coding smoking on the accuracy of estimation for genetic main effect and gene-by-smoking interaction effects in the Alpha-1 Antitrypsin Genetic Modifiers Study*

Simulation parameters			Regression results^†
			Linear pack-years				Piecewise linear
			Main effects		G×S		Main effects		G×S
SNP main effect	G×S	MAF^‡	Bias^†	p Value^§	Bias^†	p Value^§	Bias^†	p Value^§	Bias^†	p Value^§
0	0	0.10	0.17	0.024	−0.02	<0.001	0.05	0.512	−0.004	0.523
0	0	0.25	0.04	0.464	−0.01	<0.001	0.03	0.597	−0.01	0.040
0	0	0.40	−0.07	0.265	0.01	0.002	−0.04	0.466	0.01	0.251
−1	0	0.10	−0.04	0.578	−0.01	0.029	−0.19	0.014	0.01	0.027
−1	0	0.25	0.04	0.464	−0.004	0.282	0.08	0.198	−0.01	0.061
−1	0	0.40	0.05	0.382	0.002	0.520	0.08	0.205	−0.003	0.588
−1	−0.07	0.10	−0.09	0.250	0.02	<0.001	−0.05	0.523	0.003	0.664
−1	−0.07	0.25	−0.18	0.002	0.03	<0.001	−0.02	0.770	0.001	0.839
−1	−0.07	0.40	−0.09	0.124	0.04	<0.001	0.11	0.054	0.003	0.503
−1	−0.33	0.10	−0.73	<0.001	0.16	<0.001	−0.11	0.157	0.03	<0.001
−1	−0.33	0.25	−0.78	<0.001	0.18	<0.001	0.03	0.665	0.03	<0.001
−1	−0.33	0.40	−0.83	<0.001	0.18	<0.001	−0.07	0.288	0.03	<0.001
−1	−0.45	0.10	−0.87	<0.001	0.24	<0.001	−0.03	0.651	0.08	<0.001
−1	−0.45	0.25	−1.24	<0.001	0.27	<0.001	−0.23	<0.001	0.08	<0.001
−1	−0.45	0.40	−1.17	<0.001	0.27	<0.001	−0.15	0.015	0.08	<0.001
−1	0.07	0.10	0.23	0.001	−0.04	<0.001	−0.04	0.601	0.01	0.305
−1	0.07	0.25	0.21	<0.001	−0.03	<0.001	0.004	0.943	0.004	0.457
−1	0.07	0.40	0.04	0.507	−0.02	<0.001	−0.05	0.429	<0.001	0.988
−1	0.33	0.10	0.91	<0.001	−0.17	<0.001	−0.06	0.470	0.002	0.775
−1	0.33	0.25	0.94	<0.001	−0.17	<0.001	0.02	0.726	<0.001	0.919
−1	0.33	0.40	0.81	<0.001	−0.15	<0.001	0.01	0.821	<0.001	0.993
−1	0.45	0.10	1.18	<0.001	−0.23	<0.001	−0.08	0.273	−0.004	0.459
−1	0.45	0.25	1.26	<0.001	−0.22	<0.001	0.12	0.043	−0.01	0.059
−1	0.45	0.40	1.16	<0.001	−0.22	<0.001	0.04	0.534	−0.002	0.756

↵* Simulations were performed for same direction and opposite direction main and interaction effects. Strength of interaction effect is based on the multivariate smoking main effect of −1 unit from FEV₁ percentage predicted per pack-year.
Model is FEV₁ (% predicted)=age + sex + pack-years + gene + G×S, where the pack-years variable and the gene-by-smoking interaction term are calculated using either the total number of pack-years smoked (linear pack-years adjustment) or a piecewise linear representation of pack-years.
↵† Mean bias of β coefficient for main effect and gene-by-smoking interaction term from 1000 regressions on 1000 simulated datasets (ie, mean of the observed β coefficients – the simulated value of the pertinent effect).
↵‡ Minor allele frequency of the simulated biallelic genetic variant.
↵§ p Value for test of null hypothesis that bias=0.
FEV₁, forced expiratory volume in 1 s; G×S, gene-by-smoking interaction term; MAF, minor allele frequency; SNP, single nucleotide polymorphism.