Rational Inferences about Departures from Hardy-Weinberg Equilibrium Jacqueline K. Wittke-Thompson, Anna Pluzhnikov, Nancy J. Cox  The American Journal of Human Genetics  Volume 76, Issue 6, Pages 967-986 (June 2005) DOI: 10.1086/430507 Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 1 Δp plotted versus the susceptibility-allele frequency for patients. A, B, and D, Data points are as follows: γ=1.1 (blackened diamonds), γ=1.3 (unblackened triangles), γ=1.5 (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). A, Dominant model. B, Recessive model. C, Additive model. Since γ<2 would not satisfy our definition of an additive model as γ=2β and β>1, the data points in C are as follows: γ=2.2 (β=1.1) (blackened diamonds), γ=2.6 (β=1.3) (unblackened triangles), γ=3 (β=1.5) (blackened triangles), γ=5 (blackened squares), γ=2 (unblackened diamonds). D, Multiplicative model. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 1 Δp plotted versus the susceptibility-allele frequency for patients. A, B, and D, Data points are as follows: γ=1.1 (blackened diamonds), γ=1.3 (unblackened triangles), γ=1.5 (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). A, Dominant model. B, Recessive model. C, Additive model. Since γ<2 would not satisfy our definition of an additive model as γ=2β and β>1, the data points in C are as follows: γ=2.2 (β=1.1) (blackened diamonds), γ=2.6 (β=1.3) (unblackened triangles), γ=3 (β=1.5) (blackened triangles), γ=5 (blackened squares), γ=2 (unblackened diamonds). D, Multiplicative model. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 2 Δc plotted versus the susceptibility-allele frequency for controls. A, B, and D, Data points are as follows: γ=1.1 (blackened diamonds), γ=1.3 (unblackened triangles), γ=1.5 (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). A, Dominant model, KP=0.1. B, Recessive model, KP=0.2. C, Additive model, KP=0.01. As in figure 1, because of our definition of an additive model (γ=2β and β>1), the data points in C are as follows: γ=4 (β=2) (unblackened diamonds), γ=2.2 (β=1.1) (blackened diamonds), γ=2.6 (β=1.3) (unblackened triangles), γ=3 (β=1.5) (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). D, Multiplicative model, KP=0.05. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 2 Δc plotted versus the susceptibility-allele frequency for controls. A, B, and D, Data points are as follows: γ=1.1 (blackened diamonds), γ=1.3 (unblackened triangles), γ=1.5 (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). A, Dominant model, KP=0.1. B, Recessive model, KP=0.2. C, Additive model, KP=0.01. As in figure 1, because of our definition of an additive model (γ=2β and β>1), the data points in C are as follows: γ=4 (β=2) (unblackened diamonds), γ=2.2 (β=1.1) (blackened diamonds), γ=2.6 (β=1.3) (unblackened triangles), γ=3 (β=1.5) (blackened triangles), γ=2 (unblackened diamonds), γ=5 (blackened squares), and γ=10 (unblackened circles). D, Multiplicative model, KP=0.05. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 3 A, Number of patients needed to detect DHW as the susceptibility-allele frequency changes at a significance level of 5% and 50% power. Data points are as follows: dominant model with γ=1.3 (unblackened triangles), dominant model with γ=10 (unblackened circles), recessive model with γ=1.5 (blackened triangles), recessive model with γ=2 (unblackened diamonds), additive model with γ=2.2 (blackened diamonds), and additive model with γ=5 (blackened squares). B, Number of controls needed to detect DHW as the susceptibility-allele frequency changes at a significance level of 5% and 50% power. Data points are as follows: dominant model with KP=0.2 and γ=10 (blackened circles), recessive model with KP=0.05 and γ=10 (blackened circles), recessive model with KP=0.2 and γ=5 (unblackened squares), additive model with KP=0.2 and γ=5 (blackened squares), multiplicative model with KP=0.1 and γ=10 (blackened squares with white cross), and multiplicative model with KP=0.2 and γ=5 (blackened squares with white star). C, Same data points as A but assessed at 80% power. D, Same data points as B but assessed at 80% power. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 3 A, Number of patients needed to detect DHW as the susceptibility-allele frequency changes at a significance level of 5% and 50% power. Data points are as follows: dominant model with γ=1.3 (unblackened triangles), dominant model with γ=10 (unblackened circles), recessive model with γ=1.5 (blackened triangles), recessive model with γ=2 (unblackened diamonds), additive model with γ=2.2 (blackened diamonds), and additive model with γ=5 (blackened squares). B, Number of controls needed to detect DHW as the susceptibility-allele frequency changes at a significance level of 5% and 50% power. Data points are as follows: dominant model with KP=0.2 and γ=10 (blackened circles), recessive model with KP=0.05 and γ=10 (blackened circles), recessive model with KP=0.2 and γ=5 (unblackened squares), additive model with KP=0.2 and γ=5 (blackened squares), multiplicative model with KP=0.1 and γ=10 (blackened squares with white cross), and multiplicative model with KP=0.2 and γ=5 (blackened squares with white star). C, Same data points as A but assessed at 80% power. D, Same data points as B but assessed at 80% power. The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 4 Sibling relative risk for dominant models with KP=0.2 and varied γ values: γ=10 (unblackened circles), γ=5 (blackened squares), γ=2 (unblackened diamonds), and γ=1.5 (blackened triangles). The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions

Figure 5 Simulations with the goodness-of-fit test. A, 1,000 simulations of a disease locus constructed under a general model (q=0.20, α=0.12, β=2.67, and γ=4.33), a dominant model (q=0.20, α=0.11, and β=γ=3.27), and a recessive model (q=0.20, α=β=0.18, and γ=3.78), in which the population prevalence is high (KP=0.20). Each simulation, in which DHW was observed in patients and/or controls, was assessed using the goodness-of-fit test and was compared with a simulated distribution of 1,000 χ2 values, with 1 df for a general model and 2 df for a dominant or recessive model. B, 1,000 simulations of a disease locus at a lower population prevalence (KP=0.005) than A constructed under a general model (q=0.10, α=0.003, β=4.17, and γ=10.67), a dominant model (q=0.10, α=0.0027, and β=γ=5.48), and a recessive model (q=0.10, α=β=0.0048, and γ=5.17). The American Journal of Human Genetics 2005 76, 967-986DOI: (10.1086/430507) Copyright © 2005 The American Society of Human Genetics Terms and Conditions