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Table 2 Differences between theoretic and estimated penetrance functions (models by Amato et al. [[14]])

From: Artificial neural networks modeling gene-environment interaction

    High risk scenario    Low risk scenario  
   Neural network Logistic regression Logistic regression (DV) Neural network Logistic regression Logistic regression (DV)
    n =1000 + 1000    n=1000 + 1000  
  Genetic model 40.79 31.31 48.15 48.22 40.85 83.62
g u E g u Environmental model 46.14 277.11 277.11 52.45 171.61 171.36
Additive model 45.13 256.52 260.10 47.99 163.19 189.92
  Interaction model 119.77 345.77 247.93 132.47 225.61 194.37
    n =500 + 500    n = 500 + 500  
  Genetic model 59.28 47.14 68.22 64.27 92.02 159.80
g u E g u Environmental model 60.57 277.51 277.15 90.76 174.37 174.16
Additive model 56.10 268.11 297.62 80.66 190.25 242.34
  Interaction model 138.91 344.50 268.75 153.56 233.16 210.98
    n = 200 + 200    n = 200 + 200  
  Genetic model 101.95 85.67 152.25 97.23 167.48 207.66
g u E g u Environmental model 96.32 278.40 278.93 163.16 177.14 175.27
Additive model 96.16 329.55 374.17 177.24 246.06 292.39
  Interaction model 168.90 349.88 316.01 207.81 256.22 291.88
  1. Sum of mean absolute differences between theoretic and estimated penetrance function for 100 case-control data sets in the low and high risk scenario for different sample sizes. Bold numbers mark the best model fit comparing neural networks and logistic regression models. DV = design variables.