Sample size calculation due to heterogeneity.

<p>The increase in samples (γ) required as heterogeneity, defined by σ, increases for given values of a, b, c, d, when these values approach being equal. For example, if a = 1000, b = 2000, c = 1200 and d = 1800, and γ is estimated as 40% of cases not in the subgroup on which a given SNP acts, a relative increase in samples of 2.1 is needed to attain similar association statistics in the entire cohort as that of the underlying subgroup.</p

Error factor in ORs.

<p>OR error factor present with various minor allele frequencies. Each curve represents the range of OR error factors due to subgroups for a given MAF (minor allele frequency) observed in all cases. The Y-axis indicates the OR error factor corresponding to an increase in the subgroup MAF (as compared with all cases) given by the X-axis. For example, in the second curve corresponding to a MAF of 0.10 in cases, a subgroup with an increase of MAF of 0.20 (or 0.30 MAF) would have an OR in that subgroup approximately four times that reported for the overall group.</p

Pie model of sufficient causes for complex disease.

<p>Complex diseases may be multiple disorders with similar phenotypic manifestations, or a disorder with multiple genetic causes (subclasses). Each of the subclasses may be a result of combinations of similar, or unique, predisposing genes.</p

Allele frequency alterations due to the presence of a subgroup.

<p>The difference in allele frequencies for a SNP considered classically (top) and as a complex disorder with subgroups (below). In the example, a hypothetical subgroup denoted Subclass 1 contains allele counts <i>a₁</i> and <i>b₁</i>, while the rest of the cases contain allele counts <i>a₂</i> and <i>b₂</i>.</p

Expected allele counts in χ² statistic calculation.

<p>Expected allele counts in χ² statistic calculation.</p

A hypothetical example illustrating that in data with 1000 cases and 1000 controls, if a SNP had altered frequency only in a subgroup of 200 cases, the OR would be skewed.

<p>In the example, the allele frequency in the subclass (50%) masks the full effect of association, and moving the remaining cases to controls gives an OR of 2.08 for the SNP in the subclass. This corresponds to an OR error factor of 1.86, which can also be determined by inspecting the second lowermost curve in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0071614#pone-0071614-g003" target="_blank">Figure 3</a> (case MAF 0.35) with a MAF increase in the subgroup of 0.15.</p

2×2 contingency table of allele counts.

<p>2×2 contingency table of allele counts.</p

A hypothetical example demonstrating the effect of heterogeneity (cases without the minor allele affecting disease) in data with 1000 cases (MAF 30.0%) and 1000 controls (MAF 38.0%).

<p>The <i>p</i>-value, at the border of genome-wide significance, lowers as the percentage of heterogeneity (with MAF as given by cases) increases.</p

2×2 contingency table for samples increased by a factor of γ.

<p>2×2 contingency table for samples increased by a factor of γ.</p

Adjusted observed values when cases not present in a subgroup are removed.

<p>Adjusted observed values when cases not present in a subgroup are removed.</p