Journal of Probability and Statistics / 2012 / Article / Tab 1

Research Article

Genotype-Based Bayesian Analysis of Gene-Environment Interactions with Multiple Genetic Markers and Misclassification in Environmental Factors

Table 1

Biases and root mean squared errors (RMSEs) of risk parameters for the naive approach that ignores existence of misclassification and the proposed method in the case when pr ( 𝐷 = 1 ) is known and when it is estimated. The results are based on 500 samples of 1,500 cases and 1,500 controls. Genotype is simulated at the three marker loci with 𝑃 𝑀 𝑖 = 0 . 2 5 , 𝑖 = 1 , 2 , 3 , with linkage disequilibrium corresponding to Ξ” 𝑀 𝑖 𝑀 𝑗 = 0 . 0 3 . The environmental covariate ( 𝑋 ) is binary and measured with error with misclassification probabilities being 0 . 2 0 for exposed and 0 . 2 5 for nonexposed subjects. The data is simulated and analyzed under the genotype effect model.

ParameterTrue valueNaive analysisPseudo-MLEMCMC
BiasRMSEBiasRMSEBiasRMSE

ΞΊ0.4840.4810.231βˆ’0.0540.020βˆ’0.0320.013
Ξ² X0.693βˆ’0.3510.1320.0140.0390.0080.021
Ξ² A10.4060.2570.073βˆ’0.0110.016βˆ’0.0030.009
Ξ² A20.7890.1940.046βˆ’0.0030.015βˆ’0.0020.006
Ξ² A30.6930.2830.089βˆ’0.0050.016βˆ’0.0030.008
Ξ² AX10.916βˆ’0.4250.1930.0390.0460.0170.025
Ξ² AX20.693βˆ’0.3170.1130.0380.0410.0230.021
Ξ² AX31.099βˆ’0.5150.2820.0390.0580.0190.032
Ξ² D10.2620.2990.1330.0260.1520.0090.368
Ξ² D20.0950.2580.1050.0050.0990.0030.039
Ξ² D30.6930.2310.0920.0180.1280.0080.087
Ξ² DX11.099βˆ’0.4950.3260.0180.3010.0060.093
Ξ² DX20.916βˆ’0.4130.2350.0060.2080.0050.121
Ξ² DX31.099βˆ’0.4860.3130.0230.2860.0170.138
𝑃 𝑀 𝑖 0.250<0.001<0.001βˆ’0.001<0.001<0.001<0.001
pr ( 𝑋 = 1 ) 0.500    0.0030.001<0.001<0.001
pr ( 𝐷 = 1 ) 0.005    0.003<0.001<0.001<0.001

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