Sample^{b} | Estimated^{c} | |||||||
---|---|---|---|---|---|---|---|---|

Population
(μ^{a}_{1}, μ_{2}, σ) | N | Mean 1 | Mean 2 | SD | μ̂_{1} ± SE | μ̂_{2} ± SE | σ̂ ± SE | P-values^{d} |

(160, 160, 5.0)^{e} | 100 | 160.31 | 159.03 | 5.142 | 160.31 ± 0.72 | 159.03 ± 0.72 | 5.142 ± 0.319 | 0.223 |

200 | 159.00 | 159.94 | 5.148 | 159.00 ± 0.57 | 159.94 ± 0.47 | 5.148 ± 0.243 | 0.197 | |

400 | 159.87 | 159.78 | 4.860 | 159.87 ± 0.36 | 159.78 ± 0.33 | 4.860 ± 0.143 | 0.862 | |

1000 | 160.18 | 159.92 | 4.883 | 160.18 ± 0.23 | 159.92 ± 0.21 | 4.883 ± 0.114 | 0.404 | |

(161, 160, 5.0) | 100 | 161.17 | 159.75 | 5.271 | 161.17 ± 0.80 | 159.75 ± 0.71 | 5.271 ± 0.328 | 0.188 |

200 | 161.22 | 160.00 | 4.795 | 161.22 ± 0.46 | 160.00 ± 0.49 | 4.795 ± 0.191 | 0.0739 | |

400 | 160.89 | 160.01 | 4.788 | 160.89 ± 0.36 | 160.01 ± 0.32 | 4.788 ± 0.156 | 0.0661 | |

1000 | 161.38 | 160.16 | 5.091 | 161.38 ± 0.24 | 160.16 ± 0.22 | 5.091 ± 0.120 | 0.000159 | |

(163, 160, 5.0) | 100 | 163.27 | 160.23 | 4.925 | 163.27 ± 0.80 | 160.23 ± 0.63 | 4.926 ± 0.352 | 0.00312 |

200 | 162.90 | 159.38 | 5.020 | 162.90 ± 0.56 | 159.38 ± 0.47 | 5.020 ± 0.223 | 1.61 × 10^{−6} | |

400 | 162.74 | 159.70 | 4.858 | 162.74 ± 0.36 | 159.70 ± 0.33 | 4.859 ± 0.167 | 1.23 × 10^{−9} | |

1000 | 163.10 | 159.68 | 4.933 | 163.10 ± 0.23 | 159.68 ± 0.20 | 4.934 ± 0.107 | 3.86 × 10^{−26} | |

(165, 160, 5.0) | 100 | 163.80 | 160.07 | 5.159 | 163.80 ± 0.80 | 160.08 ± 0.69 | 5.159 ± 0.304 | 0.000598 |

200 | 164.99 | 160.17 | 4.953 | 164.99 ± 0.48 | 160.17 ± 0.51 | 4.953 ± 0.248 | 8.66 × 10^{−11} | |

400 | 165.16 | 160.67 | 4.894 | 165.16 ± 0.37 | 160.67 ± 0.33 | 4.895 ± 0.169 | 3.32 × 10^{−18} | |

1000 | 165.12 | 160.21 | 4.875 | 165.12 ± 0.23 | 160.21 ± 0.21 | 4.875 ± 0.113 | 1.30 × 10^{−50} |

↵

Values described in parentheses were given to the parameters μ^{a}_{1}, μ_{2}, and σ. Two haplotypes were selected from the population haplotype pool according to the haplotype frequencies (Θ) obtained from the four-locus data of the*SAA1*gene (see Table 1) and given to each subject. The quantitative phenotype was determined stochastically for each subject depending on whether the phenotype-associated haplotype (CCTC haplotype was assumed to be the phenotype-associated haplotype in this case) was present (μ_{1}was used) or absent (μ_{2}was used) using the two normal distributions*N*(μ_{1}, σ^{2}) and*N*(μ_{2}, σ^{2}).↵

For each sample, the means of the quantitative phenotypes for the subjects with the phenotype-associated haplotype (mean 1) and that for the subjects without the haplotype (mean 2) were determined. SDs of the quantitative phenotypes for all the subjects were calculated as follows: where^{b}*D*_{+}is a set of diplotype configurations with the phenotype-associated haplotype, while*d*is the diplotype configuration for the_{i}*i*th subject.*w*is the observed quantitative phenotype of the_{i}*i*th subject.↵

From the sample, phase information was removed. The genotype information and the phenotype information were used for the estimation of the parameters using QTLHAPLO. SEs of the estimated parameters were calculated as described in^{c}*Designs of simulations*.↵

At the same time, the sample statistic −2 log(^{d}*L*_{0max}/*L*_{max}) was calculated for each sample, and the*P*-value was determined by QTLHAPLO assuming that, under the null hypothesis, the sample statistic followed a χ^{2}distribution with 1 d.f.↵

This parameter set is equivalent to the null hypothesis.^{e}A sample of size

*N*was obtained by simulation using a set of given parameters, and the data obtained were analyzed, after removing the phase information, using QTLHAPLO for both the estimation of parameters and the test of the association between the presence of a haplotype and the quantitative phenotype.