Regression-based collapsed variant and conditional tests can greatly enhance association studies involving rare variants. Consider Figure 1C which plots the power to detect the effect of a variant on a quantitative trait for 1000 individuals as a function of the fraction of variation of the quantitative trait explained by that variant. If a set of rare variants each individually explain only a small fraction of the variation of the trait, they could be combined into a single predictor variable, perhaps by creating a dummy variable which equals 1 if an individual possesses any of the variants and 0 otherwise.33 This strategy should increase the fraction of variation explained by the variants as a whole and hence increase the power to detect their collective, rather than individual, effects. In addition, if one included other factors in a regression model - such as covariate effects, the effects of previously identified common variants, or other collapsed sets of rare variants - then the power to detect the association involving rare variants could increase substantially (Figure 1C). Not all analysis methods proposed for rare
