Chi-squared (1 df) Q-Q plot for Scenario 2 (Recessive effect at locus G).

<p>Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.</p

Chi-squared (1 df) Q-Q plot for Scenario 5d (Rare disease, Recessive effects at both loci).

<p>Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.</p

Description of simulation scenarios.

a<p>In each scenario (apart from 5c and 5d) the baseline regression coefficient was chosen to equal (0.02/0.98), corresponding to a baseline penetrance of 2%.</p>b<p>For Scenarios 6–9 we increased from 0 (no interaction) to a value at which the power to detect an effect (at significance level 0.01) was close to 100% for the best-performing statistics.</p

True and estimated haplotype frequencies and correlation measures used by different methods.

<p>Data was simulated under Scenario 7 (DominantDominant) with and . The table shows the mean of the relevant quantity (haplotype frequency or correlation measure) as estimated within cases or controls from 1000 simulation replicates. Wu: Estimated using EM algorithm as used by Wu et al. <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002625#pgen.1002625-Wu1" target="_blank">[1]</a> methods. FE: Estimated based on counts in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1002625#pgen-1002625-t002" target="_blank">Table 2</a>, as used by <i>fast-epistasis</i> methods. WZ: estimated using genotype-based correlation coefficient, as used by Wellek and Zigler inspired methods.</p

Chi-squared (1 df) Q-Q plot for Scenario 1 (Global Null).

<p>Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.</p

Power curves for Scenario 6 (Recessive Recessive).

<p> Power to achieve significance level . Top panels ((a) and (b)): Case/Control not in LD; Middle panels ((c) and (d)): Case/Control in LD; Bottom panels ((e) and (f)): Case-Only not in LD; Left hand panels ((a), (c) and (e)): No main effect; Right hand panels ((b), (d) and (f)): Locus G has main effect; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic; IWu: Ideal Wu statistic; C: Logistic regression using correct coding; IC: Logistic regression using incorrect ( = RecessiveDominant) coding; WZC: Wellek and Ziegler case-only statistic using correct coding; WZIC: Wellek and Ziegler case-only statistic using incorrect ( = RecessiveDominant) coding.</p

Multilocus genotype counts at two SNPs in a set of genotyped individuals.

<p>Multilocus genotype counts at two SNPs in a set of genotyped individuals.</p

Structure of log odds in disease models used for simulation study.

<p>Structure of log odds in disease models used for simulation study.</p

Summary of methods/software packages investigated.

<p>Summary of methods/software packages investigated.</p

Power and type 1 error of different methods.

<p>Powers (left hand plots) are defined as the proportion of replicates (out of 1000) in which both simulated disease loci are detected, with ‘detection’ corresponding to any SNP within 40 kb of the simulated disease locus reaching the specified <i>p</i>-value threshold. Type 1 errors (right hand plots) are defined as the proportion of null SNPs (out of 20,000 = 20 null SNPs times 1000 simulation replicates) that reach the specified <i>p</i>-value threshold. Horizontal dashed lines indicate the target <i>p</i>-value thresholds (i.e. the expected type 1 error rates).</p