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Table 6 Accuracy and execution time (in seconds) of Toxo and PyToxo for threshold, additive and multiplicative models with orders between 2 and 8 and different values of MAFs and heritability (\(h^2\))

From: PyToxo: a Python tool for calculating penetrance tables of high-order epistasis models

Model Order MAF h2 PyToxo error Toxo error Best PyToxo Time Toxo Time Speedup
Threshold 2 0.1 0.1 2.78\(\times 10^{-17}\) 2.45\(\times 10^{-8}\) PyToxo 0.20 0.55 2.70
Threshold 2 0.1 0.8 0 0 Same 0.18 0.23 1.22
Threshold 2 0.4 0.1 1.11\(\times 10^{-16}\) 0 Toxo 0.14 0.24 1.70
Threshold 2 0.4 0.8 1.11\(\times 10^{-16}\) 0 Toxo 0.14 0.22 1.57
Threshold 3 0.1 0.1 1.39\(\times 10^{-17}\) 1.70\(\times 10^{-7}\) PyToxo 0.39 0.31 0.79
Threshold 3 0.1 0.8 0 3.44\(\times 10^{-9}\) PyToxo 0.37 0.71 1.91
Threshold 3 0.4 0.1 0 0 Same 0.31 0.30 0.98
Threshold 3 0.4 0.8 1.11\(\times 10^{-16}\) 0 Toxo 0.32 0.29 0.92
Threshold 4 0.1 0.1 0 7.41\(\times 10^{-7}\) PyToxo 0.81 0.52 0.65
Threshold 4 0.1 0.8 0 1.60\(\times 10^{-8}\) PyToxo 0.80 0.92 1.15
Threshold 4 0.4 0.1 2.78\(\times 10^{-17}\) 0 Toxo 0.67 0.52 0.77
Threshold 4 0.4 0.8 0 0 Same 0.67 0.53 0.77
Threshold 5 0.1 0.1 0 1.41\(\times 10^{-6}\) PyToxo 1.95 1.99 1.02
Threshold 5 0.1 0.8 1.11\(\times 10^{-16}\) 5.71\(\times 10^{-8}\) PyToxo 2.04 2.34 1.15
Threshold 5 0.4 0.1 1.39\(\times 10^{-17}\) 0 Toxo 2.39 1.98 0.83
Threshold 5 0.4 0.8 1.11\(\times 10^{-16}\) 4.17\(\times 10^{-9}\) PyToxo 2.43 1.94 0.80
Threshold 6 0.1 0.1 1.39\(\times 10^{-17}\) 1.95\(\times 10^{-5}\) PyToxo 4.70 4.31 0.92
Threshold 6 0.1 0.8 2.22\(\times 10^{-16}\) 5.43\(\times 10^{-8}\) PyToxo 4.68 4.26 0.91
Threshold 6 0.4 0.1 1.39\(\times 10^{-17}\) 0 Toxo 6.64 4.29 0.65
Threshold 6 0.4 0.8 0 5.05\(\times 10^{-9}\) PyToxo 6.59 4.70 0.71
Threshold 7 0.1 0.1 1.39\(\times 10^{-17}\) 3.81\(\times 10^{-5}\) PyToxo 11.69 18.27 1.56
Threshold 7 0.1 0.8 1.11\(\times 10^{-16}\) 1.58\(\times 10^{-8}\) PyToxo 11.62 18.68 1.61
Threshold 7 0.4 0.1 4.16\(\times 10^{-17}\) 0 Toxo 18.50 18.33 0.99
Threshold 7 0.4 0.8 2.22\(\times 10^{-16}\) 0 Toxo 18.49 18.70 1.01
Threshold 8 0.1 0.1 2.78\(\times 10^{-17}\) \(2.42\times 10^{-4}\) PyToxo 28.72 39.03 1.35
Threshold 8 0.1 0.8 1.11\(\times 10^{-16}\) 1.29\(\times 10^{-6}\) PyToxo 28.70 39.23 1.37
Threshold 8 0.4 0.1 1.39\(\times 10^{-17}\) 3.51\(\times 10^{-8}\) PyToxo 52.58 38.91 0.74
Threshold 8 0.4 0.8 1.11\(\times 10^{-16}\) 0 Toxo 52.69 38.88 0.74
Additive 3 0.1 0.1 1.39\(\times 10^{-17}\) 1.05\(\times 10^{-6}\) PyToxo 2.13 3.04 1.43
Additive 3 0.1 0.8 2.22\(\times 10^{-16}\) 3.26\(\times 10^{-5}\) PyToxo 1.90 1.67 0.88
Additive 3 0.4 0.1 9.71\(\times 10^{-17}\) 0 Toxo 1.81 1.53 0.85
Additive 3 0.4 0.8 1.11\(\times 10^{-16}\) 1.62\(\times 10^{-7}\) PyToxo 1.76 1.62 0.92
Additive 4 0.1 0.1 2.78\(\times 10^{-17}\) 5.54\(\times 10^{-4}\) PyToxo 3.04 8.72 2.87
Additive 4 0.4 0.1 1.39\(\times 10^{-17}\) 0 Toxo 3.16 4.94 1.56
Additive 4 0.4 0.8 0 0 PyToxo 3.20 4.72 1.47
Additive 5 0.4 0.1 1.39\(\times 10^{-17}\) 2.66\(\times 10^{-8}\) PyToxo 6.14 8.80 1.43
Additive 6 0.4 0.1 1.39\(\times 10^{-17}\) 6.37\(\times 10^{-7}\) PyToxo 13.19 22.60 1.71
Additive 7 0.4 0.1 0 4.69\(\times 10^{-7}\) PyToxo 25.86 51.82 2.00
Multiplicative 2 0.1 0.1 0 4.16\(\times 10^{-6}\) PyToxo 0.67 2.84 4.25
Multiplicative 2 0.1 0.8 0 1.20\(\times 10^{-7}\) PyToxo 0.69 1.01 1.47
Multiplicative 2 0.4 0.1 0 0 Same 0.71 1.01 1.43
Multiplicative 2 0.4 0.8 0 4.88\(\times 10^{-9}\) PyToxo 0.64 1.00 1.56
Multiplicative 3 0.1 0.1 1.25\(\times 10^{-16}\) 7.51\(\times 10^{-4}\) PyToxo 1.62 5.88 3.62
Multiplicative 3 0.1 0.8 0 3.59\(\times 10^{-6}\) PyToxo 1.62 3.95 2.44
Multiplicative 3 0.4 0.1 4.16\(\times 10^{-17}\) 1.63\(\times 10^{-7}\) PyToxo 1.66 2.96 1.78
Multiplicative 3 0.4 0.8 1.11\(\times 10^{-16}\) 1.39\(\times 10^{-8}\) PyToxo 1.59 3.48 2.18
Multiplicative 4 0.1 0.1 8.33\(\times 10^{-17}\) 3.29\(\times 10^{-17}\) PyToxo 4.69 83.18 17.75
Multiplicative 4 0.1 0.8 3.33\(\times 10^{-16}\) 3.57\(\times 10^{-5}\) PyToxo 4.34 81.94 18.88
Multiplicative 4 0.4 0.1 1.39\(\times 10^{-17}\) 1.08\(\times 10^{-6}\) PyToxo 4.55 54.42 11.94
Multiplicative 4 0.4 0.8 1.11\(\times 10^{-16}\) 3.60\(\times 10^{-8}\) PyToxo 4.77 51.33 10.75