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\subsubsection{Single-variant approach}  \bigskip  \begin{flushleft}  We evaluated Fisher's exact test, a classical tool of studying association between genotype and disease traits with the use of contingency tables. For each SNV, we tested the null hypothesis Each  of no the variant site in the case-control sample is tested for an  association between rows (disease), and columns (genotypes) of a with the disease outcome using  $2\times 3$ contingency table. Each table to compare genotype frequencies at each variant site. %Each  table contains the frequency of two homozygotes and the heterozygote in cases and controls.%We then computed the P-value from each association.  \end{flushleft}  \subsubsection{Pooled-variant methods}  \bigskip  The variable threshold (VT) approach of Price et al. \cite{Price_2010} is based on the regression of phenotypes onto the counts of variants meeting the MAF threshold. Variants with MAF below the some  threshold areassumed to be  more likely to be functional than variants with higher MAF. For each possible MAF threshold, a genotype score is computed based on a given collapsing theme. The chosen MAF threshold maximizes the association signal and permutation testing is used to adjust for multiple thresholds. \citeNP{Price_2010} found that the VT approach had high power to detect the association between rare variants and disease traits when effects are in one direction in their simulations. We used VTWOD function implemented in R package RVtests \cite{Xu_2012}.  Unlike the VT test, the C-alpha test of \cite{Neale_2011} is a variance components approach that assumes the effects of variants are random. The C-alpha procedure tests the variance of genetic effects under the assumption that variants observed in cases and controls are a mixture of deleterious, protective or neutral variants. We applied both the VT-test and C-alpha test across the simulated region by using sliding windows of 20 SNVs overlapping by 5 SNVs. \subsubsection{Joint-modeling methods}   \bigskip